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PROGRAM BOOK<br />

International workshop on<br />

Spin-Orbit and Interaction Effects<br />

in Nano-Electronics<br />

<strong>Aachen</strong>, 4-6 February, 2013<br />

Organizers:<br />

Sabine An<strong>der</strong>gassen, Fabian Hassler, Dirk Schuricht, Maarten Wegewijs<br />

1


Table of contents<br />

What comes with this <strong>book</strong>let . . . . . . . . . . . . . . . . . . . . . . . . . 3<br />

Organization and funding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4<br />

Getting to the institute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5<br />

<strong>Workshop</strong> lecture hall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7<br />

Internet access . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8<br />

Lunch information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9<br />

Conference dinner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10<br />

Talk program & abstracts . . . . . . . . . . . . . . . . . . . . . . . . . . . 11<br />

Talks Monday February 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 11<br />

Talks Tuesday February 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 29<br />

Talks Wednesday February 6 . . . . . . . . . . . . . . . . . . . . . . . . . 47<br />

Poster program & abstracts . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />

Posters Monday February 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 57<br />

Posters Tuesday February 5 . . . . . . . . . . . . . . . . . . . . . . . . . . 71<br />

List of participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85<br />

2


What comes with this <strong>book</strong>let<br />

With this <strong>book</strong>let you should have received<br />

• <strong>Aachen</strong> city plan - Stadtplan <strong>Aachen</strong><br />

• <strong>Aachen</strong> information <strong>book</strong>let - <strong>Aachen</strong> at a glance 2013<br />

which includes restaurant information<br />

If not, please ask at the reception of your hotel !<br />

Please check the workshop website for updates:<br />

http://www.physik.rwth-aachen.de/workshop2013/<br />

• Corrections<br />

• Electronic files of talks and posters<br />

3


Organization and funding<br />

The conference is organized by<br />

• Sabine An<strong>der</strong>gassen (Universität Wien)<br />

• Fabian Hassler (<strong>RWTH</strong> <strong>Aachen</strong> University)<br />

• Dirk Schuricht (<strong>RWTH</strong> <strong>Aachen</strong> University)<br />

• Maarten Wegewijs (Forschungszentrum Jülich)<br />

with administrative support by Julia Heuerz-Sengül, Gabriele Meeßen and<br />

technical support by Uwe Kahlert.<br />

The workshop is funded by<br />

• The European Science Foundation (ESF),through the Research Networking<br />

Programme Quantum Spin Coherence and Electronics<br />

http://www.esf.org/activities/research-networking-programmes/physical-and-engineering-sciences-pesc/currentresearch-networking-programmes/quantum-spin-coherence-andelectronics.html<br />

• DFG Research Unit 912 Coherence and Relaxation Properties of Electron<br />

Spins<br />

http://www.spintransport.de<br />

4


Getting to the institute<br />

(1) If you are staying at Hotel Marschiertor (down town)<br />

Monday:<br />

• Someone from the workshop will pick up a group at the hotel<br />

• To join the group you need to buy bus tickets yourself beforehand<br />

(to avoid ∼ 50 people annoying the bus driver at once):<br />

◦ A ticket machine is located at the central station at the bus<br />

stop and also at the Tabak & Zubehör Shop from T. H. Kleen<br />

on your left when you exit the central station on the side of the<br />

big square.<br />

◦ For the entire workshop you need 6 tickets<br />

2 x single trip (2.50 Euro) + 1x four trips (8.80 Euro) = 13.80 Euro<br />

• Travel time to the institute is about 30 minutes:<br />

The group will leave the hotel strictly at 8.00 to make it in time.<br />

Tuesday-Wednesday:<br />

• Take bus number 3 A or 3 B at central station (Hauptbahnhof )<br />

(Don’t worry that these busses depart in opposite directions.<br />

Also, depending on the departure time, you may need to change bus once)<br />

• Your destination is Campus Melaten<br />

• Exiting the bus, go up the stairs towards the ugly building with yellow<br />

on the roof (<strong>Physikzentrum</strong>) which has 26 written on it in big letters.<br />

• Enter the tower and go to lecture hall 28 D001 (Hörsaal Physik) on<br />

the 1st floor.<br />

5


(2) If you are staying at the <strong>RWTH</strong>-Guesthouse<br />

Travel time to the institute is about 15 minutes on foot.<br />

Monday: particant Fabian Heidrich-Meisner will bring a group to the institue.<br />

The group will leave the guesthouse strictly at 8.15 to make it in time.<br />

Tuesday-Wednesday:<br />

• Exiting the reception of the <strong>RWTH</strong>-Guesthouse, turn left on the<br />

Melatener Strasse and follow it all the way: you will cross an intersection<br />

with Halifaxtrasse and finally continue across a bridge over<br />

the highway (Pariser Ring).<br />

• Descent from the bridge and on go up the stairs to the ugly looking<br />

building with yellow on the roof (<strong>Physikzentrum</strong>). You will see it has<br />

28 written on it in big letters.<br />

• Enter the building and go to lecture hall 28 D001 (Hörsaal Physik) on<br />

the 1st floor.<br />

6


<strong>Workshop</strong> lecture hall<br />

• The workshop talks take place in the main lecture hall,<br />

28D 001 Hörsaal Physik, on the 1st floor<br />

Just follow the signs.<br />

• The poster sessions take place in front of the lecture hall.<br />

7


Internet access<br />

Power: all seats in the lecture hall are equipped with a power outlet.<br />

Wireless internet:<br />

• If you have an eduroam account:<br />

simply log on as usual<br />

• In all other cases, you can make use of a special workshop guest<br />

account.<br />

Simply fire up your browser, and try to go to an arbitrary website. You<br />

will be redirected to the login URL of the <strong>RWTH</strong> computing center<br />

(Rechenzentrum). Log on using:<br />

◦ Login name: see printed version<br />

◦ Password: see printed version<br />

For more advanced technical assistance, please contact:<br />

Uwe Kahlert<br />

Room: 26C 411 (4th floor)<br />

Tel: +49 241 80 27042<br />

uwe@physik.rwth-aachen.de<br />

8


Lunch information<br />

Lunch will be taken at the Mensa Vitae, just 5 minutes away on foot.<br />

Please follow the crowd as we go there at 12.30.<br />

• Vouchers are available each day at the workshop registration desk in<br />

front the lecture hall.<br />

• Coffee after lunch: please note that at the lecture hall there will be<br />

no coffee right after lunch. So if you need coffee, please get it at the<br />

Lavazza counter in the Mensa Vitae.<br />

Lab-tour: on Tuesday you have the possibility of taking a tour through some<br />

of the experimental labs in <strong>Aachen</strong>.<br />

• Please register for this at the workshop registration table in front of<br />

the lecture hall.<br />

• We will serve a few sandwiches for lunch (30 min) and start the tour<br />

with 4 locations immediately afterward:<br />

◦ 13:00 Sub-k scanning tunneling microscope (Morgenstern)<br />

◦ 13:15 Spin-qubits (Bluhm)<br />

◦ 13:30 Quantum-transport graphene nanostructures (Stampfer)<br />

◦ 13:45 Time-resolved optics for spintronics (Beschoten)<br />

◦ 14:00 <strong>Workshop</strong> continues<br />

9


Conference dinner<br />

The conference dinner will take place on<br />

Tuesday evening 19:30<br />

at the Ratskeller, located on the square in the old city center:<br />

To get there,<br />

Ratskeller <strong>Aachen</strong><br />

Markt 40<br />

52062 <strong>Aachen</strong><br />

Tel. 0241-35001<br />

http://www.ratskeller-aachen.de<br />

• Exit the institute using the main access tower 26 (at the side of the<br />

parking lots) and cross the street.<br />

• Take Bus 3B and get out at Ponttor, an old city gate.<br />

• Just walk down the Pontstrasse until you find yourself at the square<br />

After dinner: Many student pubs can be found in the Pontstrasse that you<br />

walked through above....<br />

10


Talks Monday February 4<br />

Talk program & abstracts<br />

Talks Monday February 4<br />

Monday (Feb. 4)<br />

8:45 Opening<br />

9:00 Herre van <strong>der</strong> Zant<br />

Transport through individual magnetic molecules<br />

9:45 San<strong>der</strong> Otte<br />

Atomically assembled quantum spin lattices<br />

10:30 Coffee break<br />

11:00 Ireneusz Weymann<br />

Interplay of the Kondo effect and spin-polarized transport<br />

in magnetic molecules, adatoms, and quantum dots<br />

11:45 Jens Paaske<br />

Fine structure in cotunneling spectroscopy<br />

12:30 Lunch<br />

14:00 Carsten Timm<br />

The master equation for nanoscopic transport:<br />

Spectral analysis, perturbation theory,<br />

and applications to molecular devices<br />

14:45 Jürgen König<br />

Superconducting proximity effect in quantum-dot systems<br />

15:30 Poster session<br />

17:00 Stefan Heinze<br />

Spontaneous atomic-scale magnetic skyrmion lattice<br />

in an ultra-thin film<br />

17:45 Achim Rosch<br />

Magnetic whirls in chiral magnets<br />

18:30<br />

11


Talks Monday February 4<br />

Transport through individual magnetic molecules<br />

Herre van <strong>der</strong> Zant, Kavli Institute of Nanoscience Delft, The Netherlands<br />

By merging the fields of molecular magnetism, molecular electronics and<br />

nanotechnology, we fabricate planar three-terminal nanodevices containing<br />

individual magnetic molecules or nanoparticles. Source and drain electrodes<br />

are made of Au or of (multi-layered) graphene. A third gate electrode allows<br />

the modification of charge transport independently from the source/drain<br />

electrodes. In this way, a spin transistor is built in which the electric current<br />

through the individual magnetic molecule or nanoparticle is sensitive to its<br />

spin properties. The molecular complexes of interest are single-molecule magnets<br />

(SMMs) and spin-crossover compounds. Coulomb blockade is generally<br />

observed but finer details such as Kondo correlations and excited states are<br />

observed at cryogenic temperatures [1]. In a Fe-4 SMM based transistor, we<br />

observe features that confirm the high-spin state and find Kondo behavior,<br />

spin blockade and a zero-field splitting that depends on the redox state; in<br />

the charged state the molecule turns out to be a better magnet. Using an<br />

in-situ sample rotator, direct observation of magnetic anisotropy has been<br />

demonstrated [3]. Recent progress includes transport through a single spincrossover<br />

molecule [4] and the fabrication of a molecular memory device based<br />

on a spin-crossover nanoparticle that operates near room temperature [5].<br />

Interestingly for molecular spintronics, the spin crossover in these devices<br />

can be induced by applying a voltage, showing that its magnetic state is<br />

controllable electrically.<br />

Work supported by FOM and through the EU FP7 program (ELFOS)<br />

[1] H.B. Heersche et al., Rev. Lett. 96 (2006) 206801; E.A. Osorio et al.,<br />

Nano Letters 10 (2010) 105; J.M. Thijssen and H.S.J. van <strong>der</strong> Zant, Phys.<br />

stat. sol. (b) 245 (2008) 1455-1470.<br />

[2] A. Zyazin et al. Nano Letters 10 (2010) 3307.<br />

[3] E. Burzurí, A.S. Zyazin, A. Cornia and H.S.J. van <strong>der</strong> Zant, Phys. Rev.<br />

Lett. 109 (2012) 147203.<br />

[4] V. Meded et al., Phys. Rev. B 83 (2011) 245115.<br />

[5] F. Prins et al. Adv. Mat. 23 (2011) 1545.<br />

12


Talks Monday February 4<br />

Notes<br />

13


Talks Monday February 4<br />

Atomically assembled quantum spin lattices<br />

San<strong>der</strong> Otte, Kavli Institute of Nanoscience Delft, The Netherlands<br />

The physical behavior of lattices consisting of coupled quantum spins is often<br />

hard to predict, even when only few spins are involved. Yet, insight into such<br />

basic lattices can be key towards un<strong>der</strong>standing the fascinating properties of<br />

complex magnetic materials on the macroscopic scale.<br />

In our lab we study small one- and two-dimensional lattices of magnetic<br />

atoms by building them from scratch, literally atom-by-atom, using low temperature<br />

scanning tunneling microscopy. Once built, the atomic structures<br />

can be probed locally using a combination of inelastic electron tunneling<br />

spectroscopy (IETS) and spin-polarized STM.<br />

14


Talks Monday February 4<br />

Notes<br />

15


Talks Monday February 4<br />

Interplay of the Kondo Effect and Spin-Polarized Transport in Magnetic<br />

Molecules, Adatoms, and Quantum Dots<br />

Ireneusz Weymann, Adam Mickiewicz University, Poznań<br />

Theoretical results on the interplay of the Kondo effect and spin-polarized<br />

tunneling in a class of systems exhibiting uniaxial magnetic anisotropy, such<br />

as magnetic molecules, magnetic adatoms, or quantum dots coupled to a<br />

localized magnetic moment will be presented. In particular, the dependence<br />

of the spectral functions and linear conductance on the system’s parameters<br />

will be thoroughly discussed. It will be shown that both the magnetic<br />

anisotropy as well as the exchange coupling between electrons tunneling<br />

through the conducting orbital and magnetic core play an important role<br />

in the formation of the Kondo resonance, leading generally to its suppression.<br />

Specific transport properties of such a system appear also as a nontrivial<br />

behavior of tunnel magneto-resistance. Moreover, the un<strong>der</strong>screened Kondo<br />

effect in spin S=1 magnetic quantum dots will be discussed.<br />

16


Talks Monday February 4<br />

Notes<br />

17


Talks Monday February 4<br />

Fine structure in cotunneling spectroscopy<br />

Jens Paaske, University of Copenhagen, Denmark<br />

Cotunneling through Coulomb blockaded nano-transistors provides an informative<br />

spectroscopy of the system bridging source and drain contacts. In this<br />

talk, I address the question to what extent this transport probe can also tell<br />

us more about the spin-orbit coupling in the dot, tube, wire or molecule un<strong>der</strong><br />

scrutiny. From inelastic cotunneling spectroscopy, one might directly observe<br />

avoided crossings between spin-orbit coupled states, but there are also a<br />

number of more subtle clues to be picked up. What happens to the Kondo<br />

resonances, reflecting the “flippable” degeneracies in the system, what are the<br />

effects on tunneling induced level renormalization, and to what extent have<br />

we already observed some of this spectroscopic fine structure experimentally?<br />

18


Talks Monday February 4<br />

Notes<br />

19


Talks Monday February 4<br />

The master equation for nanoscopic transport: Spectral analysis, perturbation<br />

theory, and applications to molecular devices<br />

Carsten Timm, Technische Universität Dresden, Germany<br />

The master equation is a powerful method for the description of nanostructures<br />

with strong interactions far from equilibrium. Using a master equation<br />

for a molecular device coupled to a vibrational mode as an example, I will<br />

analyze what information can be gained from the spectrum of eigenvalues<br />

of the transition-rate matrix. So far, research has mostly focused on the<br />

stationary state, which is the eigenstate to the (usually unique) vanishing<br />

eigenvalue of this matrix. I will show that its full spectrum and its slowly<br />

decaying eigenstates give useful information on the dynamics and are characteristic<br />

of various regimes, such as the Coulomb and the Franck-Condon<br />

blockade. In practice, the master equation is usually combined with perturbation<br />

theory in the hybridization between the nanostructure and the electronic<br />

leads. I will discuss recent theoretical progress regarding the exact time-convolutionless<br />

(time-local) master equation to all or<strong>der</strong>s in the hybridization.<br />

Finally, I will comment on applications of the master equation to molecular<br />

devices, including the direct comparison with break-junction experiments.<br />

20


Talks Monday February 4<br />

Notes<br />

21


Talks Monday February 4<br />

Superconducting Proximity Effect in Quantum-Dot Systems<br />

Jürgen König, University of Duisburg-Essen, Germany<br />

We theoretically analyze electronic transport through interacting quantum<br />

dots tunnel coupled to normal and superconducting leads. The proximity of<br />

superconducting leads induces superconducting correlations in the quantum<br />

dot which mediate Josephson and Andreev currents through the dot. Based<br />

on a real-time diagrammatic approach formalism, we address non-local<br />

Andreev effects in single- and double dot geometries and discuss the possibility<br />

to induce unconventional (e.g. odd-triplet) pairing amplitudes.<br />

22


Talks Monday February 4<br />

Notes<br />

23


Talks Monday February 4<br />

Spontaneous atomic-scale magnetic skyrmion lattice in an ultra-thin film<br />

Stefan Heinze, University of Kiel, Germany<br />

Skyrmions are topologically protected field configurations with particle-like<br />

properties that play an important role in various fields of science [1]. In<br />

the context of magnetism, they have been predicted to form stable phases<br />

and, recently, experimental evidence for their existence has been found for<br />

bulk materials in a certain range of temperature and magnetic field [2,3]. A<br />

very important ingredient for their occurrence is the Dzyaloshinskii-Moriya<br />

interaction (DMI) which was recently found to be strong also in ultrathin<br />

magnetic films on substrates with large spin-orbit coupling [4]. In these systems<br />

the DMI induces spin-spirals with a unique rotational sense propagating<br />

along one direction of the surface as observed for ultra-thin films [4-6] and<br />

atomic chains [7]. The latter case is a prototypical system in which the<br />

hybridization between the 3d-transition-metal chains (Fe) hybridize strongly<br />

with the heavy 5d-transition-metal substrate (Ir) which leads to a weak<br />

Heisenberg exchange interaction and a dominant DMI. Here, we go a step<br />

beyond and present an atomic-scale magnetic skyrmion lattice for a hexagonal<br />

Fe monolayer on the Ir(111) surface [8]. We develop a spin-model<br />

based on density functional theory that explains the interplay of Heisenberg<br />

exchange, DM interaction and the four-spin exchange as the microscopic<br />

origin of this intriguing magnetic state. Experiments using spin-polarized<br />

scanning tunneling microscopy confirm the skyrmion lattice which is incommensurate<br />

with the un<strong>der</strong>lying atomic lattice.<br />

This work is a collaboration with G. Bihlmayer, S. Blügel, K. von Bergmann,<br />

M. Menzel, A. Kubetzka, J. Brede, and R. Wiesendanger.<br />

[1] T. H. Skyrme, Proc. R. Soc. Lond. Ser. A 260, 127 (1961).<br />

[2] S. Mühlbauer et al., Science 323, 915 (2009).<br />

[3] X. Z. Yu et al., Nature 465, 901 (2010).<br />

[4] M. Bode et al., Nature 447, 190 (2007).<br />

[5] P. Ferriani et al., Phys. Rev. Lett. 101, 027201 (2008).<br />

[6] Y. Yoshida et al., Phys. Rev. Lett. 108, 087205 (2012).<br />

[7] M. Menzel et al., Phys. Rev. Lett. 108, 197204 (2012).<br />

[8] S. Heinze et al., Nature Phys. 7, 713 (2011).<br />

24


Talks Monday February 4<br />

Notes<br />

25


Talks Monday February 4<br />

Magnetic Whirls in Chiral Magnets<br />

Achim Rosch, University of Cologne, Germany<br />

In cubic magnets without inversion symmetry, lattices of magnetic whirls, socalled<br />

skyrmions are stabilized by spin-orbit interactions and thermal fluctuations.<br />

The coupling of these magnetic whirls to electrons can be described<br />

by emergent electric and magnetic field. This coupling is very efficient and<br />

allows to move the skyrmions by ultrasmall current densities. The emergent<br />

fields can be used to detect the presence and motion of the skyrmions. We also<br />

discuss how such skyrmion phases can be created and destroyed by changing<br />

the topology of the magnetic structure.<br />

26


Talks Monday February 4<br />

Notes<br />

27


Talks Tuesday February 5<br />

28


Talks Tuesday February 5<br />

Talks Tuesday February 5<br />

Tuesday (Feb. 5)<br />

9:00 Hartmut Buhmann<br />

Mercury telluride, a topological insulator<br />

9:45 Henrik Johannesson<br />

Electrical control of the Kondo effect in a helical edge liquid<br />

10:30 Coffee break<br />

11:00 Mircea Trif<br />

Resonantly tunable Majorana polariton in a microwave cavity<br />

11:45 Piet Brouwer<br />

Subgap states in Majorana wires<br />

12:30 Lunch + labtour (requires registration)<br />

14:00 Vlad Pribiag<br />

Spin-orbit-mediated control of electron<br />

and hole spins in InSb nanowire quantum dots<br />

14:45 Reinhold Egger<br />

Majorana single-charge transistor<br />

15:30 Poster session<br />

17:00 Silvano De Franceschi<br />

Tunnel spectroscopy of hybrid quantum dots<br />

17:45 Seigo Tarucha<br />

Generation and detection of quantum coherence<br />

and entanglement with quantum dots<br />

18:30<br />

19:30 Conference dinner<br />

29


Talks Tuesday February 5<br />

Mercury Telluride, A Topological Insulator<br />

Hartmut Buhmann, University Würzburg, Germany<br />

The increasing un<strong>der</strong>standing of topological phases in condensed matter<br />

physics, which was initiated by the quantum Hall effect, has inspired the<br />

search for further topological states, especially, in the absence of magnetic<br />

fields. As an example a new topological insulator state, the quantum spin<br />

Hall (QSH) effect, was proposed for two-dimensional electron system with<br />

strong spin-orbit coupling [1,2] This new state is characterized by an insulating<br />

bulk and two counter-propagating helical edge states, which give rise<br />

for quantized conductance and propagating spin currents without dissipation.<br />

After the successful experimental demonstration of the QSH effect [3],<br />

the concept of topological insulators was extended to three-dimensional systems<br />

[4] where two-dimensional Dirac-like surface states dominate electronic<br />

and optical excitations resulting in new exotic properties.<br />

In this presentation, the material system of mercury-telluride (HgTe) is<br />

introduced. The realization of transport experiments in a two-dimensional<br />

topological insulator (TI) state is shown [5,6,7] which demonstrates the<br />

potential of the QSH effect for spin injection and detection in spintronics<br />

applications. Recently, the three-dimensional TI state has been realized in<br />

strained HgTe bulk layers [8]. The magneto-transport data show characteristic<br />

Hall-sequences of two independent 2D Dirac surfaces.<br />

1) C.L. Kane and E.J. Mele, Phys. Rev. Lett 95, 226801 (2005).<br />

2) B.A. Bernevig and S.C. Zhang, Phys. Rev. Lett. 96, 106802 (2006).<br />

3) M. König et al., Science 318, 766 (2007).<br />

4) L. Fu and C.L. Kane, Phys. Rev. B 76, 045302 (2007).<br />

5) M. König et al. Journ. Phys. Soc. Japn. 77, 031007 (2008).<br />

6) A. Roth et al., Science 325, 294 (2009).<br />

7) C. Brüne et al., Nature Physics 8, 485 (2012).<br />

8) C. Brüne et al., Phys. Rev. Lett. 106, 126803 (2011).<br />

30


Talks Tuesday February 5<br />

Notes<br />

31


Talks Tuesday February 5<br />

Electrical control of the Kondo effect in a helical edge liquid<br />

Henrik Johannesson, University of Gothenburg, Sweden<br />

Magnetic impurities affect the transport properties of the helical edge states<br />

of quantum spin Hall insulators by causing single-electron backscattering.<br />

We study such a system in the presence of a Rashba spin-orbit interaction<br />

induced by an external electric field, showing that this can be used to control<br />

the Kondo temperature, as well as the correction to the conductance due to<br />

the impurity. Surprisingly, for a strongly anisotropic electron-impurity spin<br />

exchange, Kondo screening may get obstructed by the presence of a noncollinear<br />

spin interaction mediated by the Rashba coupling. This challenges<br />

the expectation that the Kondo effect is stable against time-reversal invariant<br />

perturbations.<br />

32


Talks Tuesday February 5<br />

Notes<br />

33


Talks Tuesday February 5<br />

Resonantly Tunable Majorana Polariton in a Microwave Cavity<br />

Mircea Trif, UCLA, USA<br />

We study the spectrum of a one-dimensional Kitaev chain placed in a<br />

microwave cavity. In the o-resonant regime, the frequency shift of the cavity<br />

can be used to identify the topological phase transition of the coupled system.<br />

In the resonant regime, the topology of the system is sensitive to the presence<br />

of photons in the microwave cavity and, moreover, for a large number<br />

of photons (classical limit), the physics becomes similar to that of periodically-driven<br />

systems (Floquet insulators). We also analyze numerically a<br />

finite chain and show the existence of a degenerate subspace in the presence<br />

of the cavity that can be interpreted as a Majorana polariton.<br />

34


Talks Tuesday February 5<br />

Notes<br />

35


Talks Tuesday February 5<br />

Subgap states in Majorana wires<br />

Piet Brouwer, Freie Universität Berlin, Germany<br />

A one-dimensional spin-orbit coupled nanowire with proximity-induced<br />

pairing from a nearby s-wave superconductor may be in a topological nontrivial<br />

state, in which it has a zero energy Majorana bound state at each end.<br />

In this talk, I will discuss how non-idealities in this proposal, such as disor<strong>der</strong><br />

or deviations from a strict one-dimensional limit, affect the topological phase.<br />

36


Talks Tuesday February 5<br />

Notes<br />

37


Talks Tuesday February 5<br />

Spin-orbit-mediated control of electron and hole spins in InSb nanowire<br />

quantum dots<br />

Vlad Pribiag, Kavli Institute of Nanoscience Delft, The Netherlands<br />

The spin-orbit interaction allows fast control of individual spins in quantum dots<br />

using electric fields. Narrow-gap III-V semiconductor nanowires (InAs and InSb)<br />

exhibit strong spin-orbit coupling, which makes them a promising platform for spinbased<br />

qubits [1,2]. In this talk I will focus on InSb nanowires, which are of high<br />

interest both for qubits and for observing Majorana fermions.<br />

Using electric-dipole spin resonance (EDSR) we demonstrate coherent and universal<br />

control over the spin-orbit eigenstates of individual electrons, with Rabi<br />

frequencies in excess of 100 MHz and estimated fidelities of ∼ 81%. The large<br />

Zeeman energy difference between adjacent dots enables selective addressing of each<br />

qubit. Furthermore, we use EDSR in the strong interdot coupling regime to probe<br />

the strength and anisotropy of the spin-orbit coupling. The data in agreement with<br />

Rashba spin-orbit coupling, with α∼ 0.23 eVÅ. Although the Rabi oscillations for<br />

InSb nanowire qubits are consi<strong>der</strong>ably faster than for GaAs qubits, the coherence<br />

times are relatively short (Techo ∼ 35 ns) and show no significant dependence on<br />

driving frequency within the accessible range of 8-32 GHz. This is consistent with<br />

dephasing due to a fast spin bath that likely originates from the large nuclear spins<br />

of InSb (5/2 and 7/2 for 121Sb and 123Sb respectively, and 9/2 for In).<br />

A promising approach to enhancing qubit coherence is to use hole spins as qubits<br />

instead of electron spins because hole spins exhibit weaker hyperfine coupling [3].<br />

Taking advantage of the small bandgap of InSb, we can readily gate-tune our<br />

nanowire devices between few-electron and few-hole quantum dots [4]. Comparison<br />

between the two regimes suggests that the holes are primarily of light character and<br />

that the hyperfine interaction is about an or<strong>der</strong> of magnitude weaker for holes than<br />

for electrons. We demonstrate rotation of hole spin states via EDSR and use this<br />

to extract the hole g-factor, which is about an or<strong>der</strong> of magnitude smaller than for<br />

electrons. We compare the anisotropies of the g-factor and spin blockade leakage<br />

current for holes and electrons. The ability to control and read out hole spin states<br />

paves the way for coherent, all-electrical hole-spin qubits.<br />

[1] C. Flindt, A. S. Sørensen, K. Flensberg, Phys. Rev. Lett. 97 240501 (2006).<br />

[2] S. Nadj-Perge, S. M. Frolov, E. P. A. M. Bakkers, and L. P. Kouwenhoven,<br />

Nature 468, 1084 (2010).<br />

[3] D. Brunner, B. D. Gerardot, P. A. Dalgarno, G. Wüst, K. Karrai, N. G. Stoltz,<br />

P. M. Petroff, R. J. Warburton, Science 325, 70 (2009).<br />

[4] V. S. Pribiag, S. Nadj-Perge, S. M. Frolov, J. van den Berg, I. van Weperen,<br />

S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Submitted.<br />

38


Talks Tuesday February 5<br />

Notes<br />

39


Talks Tuesday February 5<br />

Majorana single-charge transistor<br />

Reinhold Egger, Heinrich-Heine-Universität Düsseldorf, Germany<br />

I discuss quantum transport properties through a topological insulator<br />

nanowire with proximity-induced pairing correlations, where Majorana<br />

fermions are present at the ends as a consequence of strong spin-orbit interactions.<br />

When contacted by normal leads, and taking into account the charging<br />

energy, this Majorana single-charge transistor allows to study Majorana<br />

physics in a well-defined and relatively simple interacting model.<br />

40


Talks Tuesday February 5<br />

Notes<br />

41


Talks Tuesday February 5<br />

Tunnel spectroscopy of hybrid quantum dots<br />

Silvano De Franceschi, CEA, Grenoble, France<br />

Creating direct electrical connections between metal electrodes and lowdimensional<br />

semiconductor nanostructures has recently become possible<br />

thanks to the development of new nanomaterials and nanofabrication<br />

methods. Hybrid devices can thus be made in which macroscopic properties,<br />

such as superconductivity or ferromagnetism, are combined with microscopic<br />

properties, such as the charge or the spin state of individual electrons. Such<br />

hybrid devices open a wide range of opportunities for the study of new<br />

quantum phenomena and, in the long term, they may lead to the development<br />

of useful electronic devices with quantum functionalities.<br />

In this talk I will focus on hybrid devices made of zero-dimensional, quantumdot<br />

structures coupled to either normal or superconducting electrodes. I will<br />

present recent results obtained with hybrid devices made from self-assembled<br />

SiGe nanocrystals and InAs-based nanowires. Special attention will be<br />

devoted to the magnetic properties of the confined states in both normal and<br />

superconducting regime.<br />

42


Talks Tuesday February 5<br />

Notes<br />

43


Talks Tuesday February 5<br />

Generation and Detection of Quantum Coherence and Entanglement with<br />

Quantum Dots<br />

Seigo Tarucha, University of Tokyo, Japan<br />

Generation and detection of quantum coherence and entanglement is the core<br />

of quantum information processing. In this talk I will discuss new approaches<br />

to manipulate these concepts for electrons in semiconductor nanostructures.<br />

We have recently developed a two-path interferometer consisting of an<br />

Aharonov-Bohm ring connected to two tunnel-coupled quantum wires [1].<br />

Conventional AB rings are connected to two terminals and therefore suffer<br />

from phase rigidity which fixes the phase of AB oscillations at either 0 or<br />

π at zero-magnetic field. On the other hand, our interferometer operating<br />

in the non-adiabatic transport through the tunnel coupled wire does not<br />

suffer from the phase rigidity. We electrically control the dynamical phase<br />

through the AB ring and apply this technique to achieve full electrical control<br />

of a flying charge qubit defined by the presence of electron in either<br />

part of the two paths. We also use a similar interferometer but having a<br />

quantum dot in one of the two AB ring arms to detect the transport phase<br />

through the dot. We observe a well-defined π/2 phase through the dot when<br />

the dot is in the Kondo regime.<br />

The concept of non-local entanglement is well established for correlated<br />

photon pairs, but not yet for electrons in solid state systems. We have<br />

studied non-local entanglement using double dot Josephson junctions. The<br />

splitting of Cooper pairs into both dots may contribute to generate supercurrent,<br />

because Cooper pair tunneling through the same dot is strongly<br />

suppressed by the electron-electron interaction [2]. We observe the supercurrent<br />

depending on the double dot charge state and discuss the contribution<br />

from the split Cooper pair tunneling to the supercurrent.<br />

[1] M. Yamamoto et al. Nature Nanotechnology, 7, 247 (2012).<br />

[2] Y. Kanai et al. Appl. Phys. Lett. 100, 202109 (2012).<br />

44


Talks Tuesday February 5<br />

Notes<br />

45


Talks Tuesday February 5<br />

46


Talks Wednesday February 6<br />

Talks Wednesday February 6<br />

Wednesday (Feb. 6)<br />

9:00 Christian Schönenberger<br />

Interference and interaction in ultraclean<br />

suspended monolayer and bilayer graphene<br />

9:45 Bernd Braunecker<br />

Spin-orbit interaction in carbon nanotubes<br />

and its utility for proving entanglement of electrons<br />

10:30 Coffee break<br />

11:00 Kasper Grove-Rasmussen<br />

Level structure and tunnel coupling of carbon nanotube quantum dots<br />

11:45 Charlie Marcus<br />

(to be announced)<br />

12:30 Lunch<br />

Talks of the Research Unit<br />

Coherence and Relaxation Properties of Electron Spins<br />

All participants of the workshop are invited.<br />

14:00 Y. Mokrousov<br />

Engineering Chern insulators with spin and orbital degrees of freedom<br />

14:25 R. Steinigeweg<br />

Real-time dynamics of spin-currents in quantum magnets:<br />

Coherence and momentum dependence<br />

14:50 V. Kataev<br />

ESR spectroscopy on spin-orbital Mott insulators<br />

15:15 S. Müller<br />

Magnetic field effects on the finite-frequency noise<br />

and ac conductance of a Kondo quantum dot out of equilibrium<br />

15:40 B. Büchner<br />

Quasi-ballistic transport of Dirac fermions in Bi2Se3 nanowires<br />

16:05 Coffee break<br />

16:30 I. Stepanov<br />

Spintronics without ferromagnets<br />

16:55 C. Honerkamp<br />

Interacting ground states of few-layer graphene<br />

17:10 B. Beschoten<br />

Spin transport in graphene<br />

17:35 C. Volk<br />

Probing relaxation times in graphene quantum dots<br />

18:05 P. Struck<br />

Nanomechanical read-out of a single spin<br />

18:20 End of the workshop<br />

47


Talks Wednesday February 6<br />

Interference and interaction in ultraclean suspended monolayer and bilayer<br />

graphene<br />

Christian Schönenberger, University of Basel, Switzerland<br />

We first show that graphene (monolayer and bilayer) with exceptional high<br />

mobilities approaching 100 m 2 /Vs can be obtained when suspended and insitu<br />

current annealed. Using such materials, we then first summarize recent<br />

results obtained with bilayer graphene where a pronounced gap emerges at<br />

the charge-neutrality point. This gap forms in zero electric and magnetic field<br />

and is thought to be accompanied by a transition into a broken symmetry<br />

state. The precise nature of this ground state is currently debated. We show<br />

that our results are consistent with both the layer anti-ferromagnetic state<br />

(LAF) and the quantum-spin Hall state (QSH). While we cannot distinguish<br />

these two states, we can exclude the quantum anomalous Halls state based<br />

on electrical measurements in parallel magnetic field.<br />

We further will demonstrate electrical transport experiments in monolayer<br />

graphene with top gates arranged in the form of strips. The gates allow to<br />

define n-p regions yielding a peculiar interference pattern in high mobility<br />

samples caused by Klein tunneling.<br />

Coauthors:<br />

Frank Freitag, Peter Rickhaus, Romain Maurand, Jelena Trbovic, Markus<br />

Weiss and Christian Schönenberger<br />

48


Talks Wednesday February 6<br />

Notes<br />

49


Talks Wednesday February 6<br />

Spin-orbit interaction in carbon nanotubes and its utility for proving entanglement<br />

of electrons<br />

Bernd Braunecker, Universidad Autónoma de Madrid, Spain<br />

I will discuss spin-orbit interaction in carbon nanotubes and show that it<br />

has distinct features that allow to obtain information on the entanglement of<br />

injected pairs of electrons. I will briefly review the form of spin-orbit interaction<br />

in single-wall nanotubes, and demonstrate that it leads to a perfect<br />

spin filter with spin orientations that are tunable by external fields. Based on<br />

this, I will focus on a Cooper pair splitter setup and show that the tunable<br />

spin-filtering allows to implement entanglement detectors, such as probing a<br />

Bell inequality. These detectors can rely on conductance measurements alone<br />

and do not require the precise knowledge of the spin orientations of the spin<br />

filter. Yet if in addition the spin orientations are known, the same setup can<br />

be used for full quantum state tomography.<br />

50


Talks Wednesday February 6<br />

Notes<br />

51


Talks Wednesday February 6<br />

Level structure and tunnel coupling of carbon nanotube quantum dots<br />

Kasper Grove-Rasmussen, University of Copenhagen, Denmark<br />

We present our current un<strong>der</strong>standing of the quantum states in a carbon<br />

nanotube quantum dot deduced from low temperature transport measurements<br />

in parallel and perpendicular magnetic fields. The observed energy<br />

spectrum is shown to be or<strong>der</strong>ed in shells of two doublets consistent with a<br />

single-particle four-state model including spin-orbit interaction, intra-shell<br />

valley mixing and an orbital g-factor. To fully capture the behavior in the<br />

multi-shell case, additional inter-shell valley mixing parameters are needed,<br />

describing valley mixing between states belonging to different shells [1, 2].<br />

Furthermore, for certain shells, the two doublets are observed to be differently<br />

coupled to the leads, resulting in gate-dependent level renormalization.<br />

By comparison to the one-shell model this is shown to be a consequence<br />

of intra-shell valley mixing in the nanotube. Moreover, a parallel magnetic<br />

field is shown to reduce this mixing and thus suppress the effects of tunnelrenormalization<br />

[3].<br />

[1] T. Sand Jespersen, K. Grove-Rasmussen, J. Paaske, K. Muraki, T. Fujisawa,<br />

J. Nygård, and K. Flensberg, Nat. Phys. 7, 348 (2011).<br />

[2] T. S. Jespersen, K. Grove-Rasmussen, K. Flensberg, J. Paaske, K.<br />

Muraki, T. Fujisawa, and J. Nygård, Phys. Rev. Lett. 107, 186802 (2011)<br />

[3] K. Grove-Rasmussen, S. Grap, J. Paaske, K. Flensberg, S. An<strong>der</strong>gassen,<br />

V. Meden, H. I. Jørgensen, K. Muraki, and T. Fujisawa, Phys. Rev. Lett.<br />

108, 176802 (2012).<br />

52


Talks Wednesday February 6<br />

Notes<br />

53


Talks Wednesday February 6<br />

(to be announced)<br />

Charles Marcus, University of Copenhagen, Denmark<br />

(to be announced)<br />

54


Talks Wednesday February 6<br />

Notes<br />

55


Posters Monday February 4<br />

Poster program & abstracts<br />

Posters Monday February 4<br />

Time: 15:30 - 17:00<br />

Poster numbers: 1-20<br />

Topics:<br />

Atomic and molecular scale devices<br />

Semiconductor quantum dots and wires<br />

57


Posters Monday February 4<br />

Poster 1:<br />

Dynamical spin and charge excitations with spin–orbit coupling in 3d adatoms<br />

on Cu(111) and Pt(111)<br />

Manuel dos Santos Dias<br />

The presence of spin–orbit coupling has a fundamental impact on the<br />

magnetic excitation spectrum: there is a finite gap at zero frequency and<br />

spin and charge excitations become coupled. The excitation spectrum is<br />

<strong>der</strong>ived from the dynamical magnetic susceptibility of the electronic system,<br />

for which we developed a formalism based on Time–Dependent Density<br />

Functional Theory, as implemented in the Korringa–Kohn–Rostoker Green<br />

function method [1,2]. As an application, we present first–principles calculations<br />

of the charge, longitudinal and transverse magnetic excitations of<br />

3d adatoms deposited on the Cu(111) and Pt(111) surfaces. Focus is on<br />

the expected spin–charge coupling induced by the the spin–orbit interaction,<br />

and on the dynamical anisotropic effects that generalize the familiar<br />

magnetic anisotropy.<br />

Work supported by the HGF-YIG Programme FunSiLab – Functional<br />

Nanoscale Structure Probe and Simulation Laboratory (VH-NG-717).<br />

[1] S. Lounis, A. T. Costa, R. B. Muniz and D. L. Mills, Phys. Rev. Lett.<br />

105, 187205 (2010)<br />

[2] S. Lounis, A. T. Costa, R. B. Muniz and D. L. Mills, Phys. Rev. B 83,<br />

035109 (2011)<br />

58


Posters Monday February 4<br />

Poster 2:<br />

Spintronic molecular magnetism: zero field splitting without spin-orbit coupling<br />

Michael Hell<br />

Single-molecule magnets (SMMs) and magnetic adatoms have been studied<br />

intensely mainly because of their large spin anisotropy. In these systems,<br />

a spin-anisotropy barrier arises from internal quantum fluctuations due to<br />

strong spin-orbit interaction. However, such a spin-anisotropy barrier can<br />

also be externally induced into an intrinsically spin-isotropic system by coupling<br />

it to an spin-anisotropic environment.<br />

We illustrate this new idea for an interacting quantum dot (QD) with a high<br />

spin S>1/2, tunnel-coupled to spin-polarized electrodes. Besides dissipative<br />

effects, multi-spin currents generate an additional coherent time evolution<br />

of the QD, which is described by an effective Hamiltonian. The latter contains<br />

the dipolar exchange field [1-3], well known from spintronics, and an<br />

additional, new exchange field coupling to the spin-quadrupole moment of<br />

the QD. This spintronic spin-anisotropy barrier can be comparable in size to<br />

that of SMMs, but grants the additional flexibility of electric and magnetic<br />

tunability.<br />

We compare these analytic results, obtained by a perturbative treatment<br />

of the tunnel-couplings, to predictions by DM-NRG calculations accessing<br />

the strong coupling regime. We show that transport characteristics can be<br />

used to directly read out the quadrupolar field, utilizing its competition<br />

with Kondo spin-exchange processes with the ferromagnets. Furthermore,<br />

the quadrupolar exchange field can dominate over the dipolar exchange field,<br />

thereby strongly enhancing the low-temperature spin-filtering as compared<br />

to spin-1/2 QD spin-valves.<br />

References:<br />

[1] J. Martinek et al., Phys. Rev. Lett. 91, 127203 (2003); Phys. Rev. B 72,<br />

121302 (2005).<br />

[2] J. Hauptmann et al., Nature Phys. 4, 373 (2008).<br />

[3] M. Gaass et al., Phys. Rev Lett. 107, 176808 (2011).<br />

[4] M. Baumgärtel et al., Phys. Rev. Lett. 107, 087202 (2011)<br />

Coauthors<br />

M. Misiorny and M. R. Wegewijs<br />

59


Posters Monday February 4<br />

Poster 3:<br />

Influence of magnetic anisotropy on the un<strong>der</strong>screened Kondo effect in the<br />

presence of ferromagnetism<br />

Maciej Misiorny<br />

The prominent role of magnetic anisotropy (MA) in formation of the Kondo<br />

effect has recently been demonstrated experimentally [1,2]. In particular, it<br />

turned out that in systems of spin S>1/2, such as magnetic adatoms (i.e.<br />

Fe, Co or Mn) or magnetic molecules, the Kondo effect can be tuned by<br />

modifying the system’s MA. Furthermore, theoretical studies also indicate<br />

that MA can be a key factor determining spin-polarized transport through<br />

a magnetic nanosystem [3]. Motivated by the recent experiment [2], in this<br />

communication we address how the MA affects the un<strong>der</strong>screened Kondo<br />

effect (i.e. partial compensation of the molecular spin by conduction electrons)<br />

in the case of an artificial molecule of spin S=1 coupled to a reservoir<br />

of spin-polarized conduction electrons [4]. The crucial ingredient of the model<br />

is the presence of uniaxial MA. The problem is analyzed by means of Wilson’s<br />

numerical renormalization group (NRG) method, which allows for calculating<br />

the spectral function of the molecule. We show that the interplay of MA and<br />

ferromagnetism has a fundamental significance for occurring of the Kondo<br />

effect. Most importantly, despite the presence of the effective exchange field<br />

[5] the Kondo effect can be restored by adjusting the magnitude of MA.<br />

1. A.F. Otte et al., Nature Phys. 4, 847 (2008).<br />

2. J.J. Parks et al., Science 328, 1370 (2010).<br />

3. M. Misiorny, I. Weymann and J. Barnas, Phys. Rev. Lett. 106, 126602<br />

(2011); Phys. Rev. B 84, 035445 (2011).<br />

4. I. Weymann and L. Borda, Phys. Rev. B 81, 115445 (2010).<br />

5. J. Martinek et al., Phys. Rev. Lett. 91, 127203 (2003); Phys. Rev. B 72,<br />

121302 (2005).<br />

Coauthors<br />

I. Weymann and J. Barnaś<br />

60


Posters Monday February 4<br />

Poster 4:<br />

Kondo effect and magnetic frustration in a system of magnetic trimer on a<br />

metal surface<br />

Hoa Nghiem<br />

We use quantum Monte Carlo simulation to clarify the competition between<br />

Kondo screening and magnetic frustration in a system of three magnetic<br />

adatoms on a metal surface [1]. We observe the feature of spectral density<br />

depending on the geometric configuration of three magnetic adatoms on the<br />

surface [2, 3]. In the isosceles configuration, the spectral density exhibits a<br />

significant peak near the Fermi level, which we attribute to the Yosida-Kondo<br />

resonance. In the equilateral configuration, no peak is observed near the<br />

Fermi level. This observation suggests the two separate regimes; the Yosida-<br />

Kondo dominant regime with the singlet ground state, and the magnetic<br />

frustration dominant regime with the degenerate ground state, - changing<br />

from one regime to another is realized as we gradually switch the geometric<br />

configuration from the isosceles triangle to equilateral one. By calculating<br />

the spectral density and the magnetic susceptibility in a wide range of temperatures,<br />

we prove the existence of the two separate regimes and suggest<br />

the critical crossover between them.<br />

[1] N. T. M. Hoa, W. A. Dino, and H. Kasai: J. Phys. Soc. Jpn. 81 (2012)<br />

023706.<br />

[2] T. Jamneala, V. Madhavan, and M. F. Crommie: Phys. Rev. Lett 87<br />

(2001) 256804.<br />

[3] N. T. M. Hoa, W. A. Dino, and H. Kasai: J. Phys. Soc. Jpn. 79 (2010)<br />

113706.<br />

Poster 5:<br />

Spin dynamics in nanoparticles near Stoner instability<br />

Philipp Stegmann<br />

We analyse the spin dynamics of a nanoparticle close to the Stoner instability.<br />

The nanoparticle is weakly tunnel coupled to two ferromagnetic leads. By<br />

mapping to an effective Fokker-Planck description we identify two different<br />

types of dynamic behaviour (diffusion vs. drift), which are revealed by characteristic<br />

relaxation times and a Fano factor that oscillates as a function of an<br />

applied bias voltage. Finally, we propose biasing schemes to generate states<br />

with magnetic quadrupole moments that dominate over a negligible dipole<br />

moment.<br />

61


Posters Monday February 4<br />

Poster 6:<br />

Nonequilibrium transport through quantum dots with Dzyaloshinskii-Moriya<br />

interactions<br />

Mikhail Pletyukhov<br />

We study nonequilibrium transport through a single-orbital An<strong>der</strong>son<br />

model in a magnetic field with spin-dependent hopping amplitudes. In<br />

the cotunneling regime it is described by an effective spin-1/2 dot with a<br />

Dzyaloshinsky-Moriya-Kondo (DMK) interaction between the spin on the<br />

dot and the electron spins in the leads. Using a real-time renormalization<br />

group technique we show that at low temperatures (i) the DMK interaction<br />

is strongly renormalized, (ii) the renormalized magnetic field acquires a linear<br />

voltage dependence, and (iii) the differential conductance exhibits a voltage<br />

asymmetry which is strongly enhanced by logarithmic corrections. We propose<br />

transport measurements in which these signatures can be observed.<br />

62


Posters Monday February 4<br />

Poster 7:<br />

Spin-Orbit interactions and the Kondo effect<br />

Nancy Sandler<br />

Recent studies [1] have pointed out that the thermodynamics of the Kondo<br />

effect are essentially unaltered by the presence of Rashba spin-orbit interactions<br />

in a host two-dimensional electron gas. However, it has also been<br />

proposed [2]that the presence of bulk Rashba interactions induces a coupling<br />

between a magnetic impurity and conduction electrons with nonzero orbital<br />

angular momentum about the impurity site. This coupling appears as a<br />

combination of the standard Kondo exchange and the Dzyaloshinskii-Moriya<br />

interaction that, in the appropriate regime, produces an exponential enhancement<br />

of the Kondo temperature. In this work we review previous works and<br />

present recent results obtained by using the numerical renormalization group.<br />

In agreement with previous studies, we find only minor changes in the Kondo<br />

temperature scale when the Rashba coupling is increased at fixed Fermi<br />

energy. However, for fixed band filling, increasing the spin-orbit coupling can<br />

move the Fermi energy near to a Van Hove singularity in the effective density<br />

of states, leading to an exponential enhancement of the Kondo scale. Static<br />

spin correlations confirm that the impurity couples to conduction channels<br />

of nonzero orbital angular momentum. We also explore the effects of a magnetic<br />

field applied in the plane of the host system and extend our results to<br />

graphene systems.<br />

[1] J. Malecki, J. Stat. Phys. 129, 741 (2007); R. Zitko and J. Bonca, Phys.<br />

Rev. B 84, 193411 (2011).<br />

[2] M. Zarea, S. Ulloa and N. Sandler, Phys. Rev. Lett. 108, 046601 (2012).<br />

63


Posters Monday February 4<br />

Poster 8:<br />

Influence of Noise on the Exchange-Only Qubit<br />

Sebastian Mehl<br />

Spin qubits have attracted interest as one realization scheme to achieve<br />

quantum computation in a solid state system. Encoding qubits into more<br />

than one quantum dot has turned out to be experimentally very favorable.<br />

When encoding a qubit into three quantum dots one can show that electrostatic<br />

bias offers full control of the qubit. It generates tunable exchange<br />

interactions between neighboring quantum dots. We present the influence<br />

of noise on the exchange-only qubit and discuss coherence properties. We<br />

especially point out how the definition of the qubit in the embedding Hilbert<br />

space can lead to different coherence properties.<br />

Poster 9:<br />

Effect of many-body correlations on mesoscopic charge relaxation<br />

Jonckheere Thibaut<br />

We investigate nonperturbatively the charge relaxation resistance and<br />

quantum capacitance in a coherent RC circuit in the strong-coupling regime.<br />

We find that the many-body correlations break the universality in the charge<br />

relaxation resistance: (i) The charge relaxation resistance has peaks at finite<br />

frequencies Γ/ , where Γ is an effective level broadening, and (ii) the zerofrequency<br />

resistance deviates from the universal value when the Zeeman splitting<br />

is comparable to Γ. This behavior becomes even more prominent in<br />

the Kondo regime. The observed features are ascribed to the generation<br />

of particle-hole excitations in the contacts accomplished by spin-flip processes<br />

in the dot.<br />

64


Posters Monday February 4<br />

Poster 10:<br />

Interplay of Coulomb interaction and spin-orbit effects in multi-level quantum<br />

dots<br />

Stephan Grap<br />

We study electron transport through a multi-level quantum dot with Rashba<br />

spin-orbit interaction in the presence of local Coulomb repulsion. Motivated<br />

by recent experiments, we compute the level splitting induced by the spinorbit<br />

interaction at finite Zeeman fields B, which provides a measure of<br />

the renormalized spin-orbit energy. This level splitting is responsible for<br />

the suppression of the Kondo ridges at finite B characteristic for the multilevel<br />

structure. In addition, the dependence of renormalized g-factors on<br />

the relative orientation of the applied B field and the spin-orbit direction<br />

following two different protocols used in experiments is investigated.<br />

Poster 11:<br />

Transport properties of a multichannel Kondo dot in a magnetic field<br />

Christoph Hörig<br />

We study the nonequilibrium transport through a multichannel Kondo<br />

quantum dot in the presence of a magnetic field. We use the exact solution<br />

of the two-loop renormalization group equation to <strong>der</strong>ive analytical results<br />

for the g-factor, the spin relaxation rates, the magnetization, and the differential<br />

conductance. We show that the finite magnetization leads to a coupling<br />

between the conduction channels which manifests itself in additional features<br />

in the differential conductance.<br />

65


Posters Monday February 4<br />

Poster 12:<br />

An alternative functional renormalization group approach to the single impurity<br />

An<strong>der</strong>son model<br />

Michael Kinza<br />

We present an alternative functional renormalization group (fRG) approach<br />

to the single-impurity An<strong>der</strong>son model at finite temperatures. Starting<br />

with the exact self-energy and interaction vertex of a small system (’core’)<br />

containing a correlated site, we switch on the hybridization with a noninteracting<br />

bath in the fRG-flow and calculate spectra of the correlated site.<br />

Different truncations of the RG-flow-equations and choices of the core are<br />

compared and discussed. Furthermore we calculate the linear conductance<br />

and the magnetic susceptibility as functions of temperature and interaction<br />

strength. The signatures of Kondo physics arising in the flow are compared<br />

with numerical renormalization group results.<br />

Poster 13:<br />

Conductance scaling in Kondo correlated quantum dots: role of level asymmetry<br />

Lukas Merker<br />

The low temperature electrical conductance through correlated quantum dots<br />

provides a sensitive probe of the physics (e.g., of Fermi-liquid vs non-Fermiliquid<br />

behavior) of such systems. Here, we investigate the role of level asymmetry<br />

(gate voltage) and local Coulomb repulsion (charging energy) on the<br />

low temperature and low field scaling properties of the linear conductance of a<br />

quantum dot described by the single level An<strong>der</strong>son impurity model. We use<br />

the numerical renormalization group and renormalized perturbation theory<br />

to quantify the regime of gate voltages and charging energies where universal<br />

Kondo scaling may be observed and also quantify the deviations from this<br />

universal behavior with increasing gate voltage away from the Kondo regime<br />

and with decreasing charging energy. Our results could be a useful guide for<br />

detailed experiments on conductance scaling in semiconductor and molecular<br />

quantum dots exhibiting the Kondo effect.<br />

Coauthors<br />

T. A. Costi, E. Munoz, S. Kirchner<br />

66


Posters Monday February 4<br />

Poster 14:<br />

Fermionic superoperators in application to non-linear transport: real-time<br />

renormalization group, time-evolution and exact relations for An<strong>der</strong>son<br />

quantum dots.<br />

Roman Saptsov<br />

We introduced a new formalism of fermionic superoperators in Liouville-<br />

Fock space to enable a real-time renormalization group analysis of the nonequilibrium<br />

An<strong>der</strong>son model in the stationary state. The RT-RG equations<br />

were solved numerically including both 1- and 2- loop or<strong>der</strong>s in the limit of<br />

zero temperature and non-linear transport voltages where most standard theoretical<br />

methods break down. We predict non-perturbative tunneling effects<br />

in the transport stability diagram which can be measured experimentally.<br />

Moreover, we found the exact functional form of the renormalized spectra of<br />

the dot at any loop or<strong>der</strong>. In the strong-interacting limit the method breaks<br />

down as expected only at very small voltages on the or<strong>der</strong> of the Kondo<br />

temperature, which we illustrate by comparison with the Friedel sum rule.<br />

For the time dependent non-interacting case with help of fermionic superoperators<br />

we show that the perturbation expansion in tunnel coupling automatically<br />

truncates at the second loop and discuss solutions in the Wide Band<br />

Limit and beyond of it. We also discuss extension of our time-dependent<br />

results to the weakly interacting case.<br />

67


Posters Monday February 4<br />

Poster 15:<br />

Mechanism for Giant Thermopower in Negative-U Molecular Quantum Dots<br />

Theo Costi<br />

We investigate with the aid of numerical renormalization group techniques<br />

the thermoelectric properties of a molecular quantum dot described by the<br />

negative-U An<strong>der</strong>son model. We show that the charge Kondo effect provides<br />

a mechanism for enhanced thermoelectric power via a correlation-induced<br />

asymmetry in the spectral function close to the Fermi level. We show that<br />

this effect results in a dramatic enhancement of the Kondo-induced peak in<br />

the thermopower of negative-U systems with Seebeck coefficients exceeding<br />

50 µV/K over a wide range of gate voltages [1,2].<br />

[1] S. An<strong>der</strong>gassen, T. A. Costi and V. Zlatic, Phys. Rev. B 84, 241107 (R)<br />

(2011)<br />

[2] T. A. Costi and V. Zlatic, Phys. Rev. Lett. {bf 108}, 36402 (2012); in<br />

"New Materials for Thermoelectric Applications: Theory and Experiment",<br />

ed. V. Zlatic and A. C. Hewson, ISBN 978-94-007-4983-2 (Springer, Berlin,<br />

2012)<br />

Coauthors: S. An<strong>der</strong>gassen and V. Zlatic<br />

Poster 16:<br />

Boltzmann-type approach to thermal drag in spin-1/2-lad<strong>der</strong> systems coupled<br />

to phonons<br />

Christian Bartsch<br />

We quantitatively investigate the spin-phonon drag contributions to the<br />

thermal conductivity of a two-leg-spin-1/2-lad<strong>der</strong> coupled to lattice vibrations<br />

in a magnetoelastic way. By applying suitable transformations the<br />

system is mapped onto a weakly interacting quantum gas model of bosonic<br />

spin excitations (magnons) and phonons. We adequately construct a collision<br />

term of a linear(ized) Boltzmann equation from the un<strong>der</strong>lying quantum<br />

dynamics by means of a pertinent projection operator technique. From the<br />

Boltzmann equation we obtain concrete numerical values for the drag conductivity<br />

and relate it to the individual thermal conductivities of magnons and<br />

phonons for parameter ranges which are typical for certain material classes.<br />

68


Posters Monday February 4<br />

Poster 17:<br />

Rashba spin-orbit interaction in a quantum wire superlattice<br />

Sigurdur I. Erlingsson<br />

We study the effects of a longitudinal periodic potential on a parabolic<br />

quantum wire, and long quantum point contacts, defined in a two-dimensional<br />

electron gas with Rashba spin-orbit interaction. For an infinite wire<br />

superlattice we find that the energy gaps are shifted away from the usual<br />

Bragg planes due to the Rashba spin-orbit interaction. We have also calculated<br />

the charge conductance through a periodic potential of a finite length<br />

via the nonequilibrium Green’s function method combined with the Landauer<br />

formalism. We find dips in the conductance that correspond well to<br />

the energy gaps of the infinite wire superlattice. From the infinite wire energy<br />

dispersion, we <strong>der</strong>ive an equation relating the location of the conductance<br />

dips as a function of the Fermi energy to the Rashba spin-orbit coupling<br />

strength. We propose that the strength of the Rashba spin-orbit interaction<br />

can be extracted via a charge conductance measurement.<br />

Poster 18:<br />

Electronic states in a cylindrical nanowire in magnetic and electric fields<br />

Andrei Manolescu<br />

Single particle states of electrons situated on a closed cylindrical surface of<br />

radius 30-100 nm are calculated. The length of the cylin<strong>der</strong> may be either<br />

infinite or finite. In the presence of a magnetic field uniform in space, but perpendicular<br />

to the longitudinal axis of the cylin<strong>der</strong>, the orbital effects depend<br />

on the radial component of the magnetic field. For a sufficiently strong field,<br />

when the magnetic length becomes comparable to the radius of the cylin<strong>der</strong>,<br />

the orbital motion corresponds to closed cyclotron orbits in the regions with<br />

strong radial field, but to open quasi one-dimensional snaking orbits in the<br />

regions where the radial field vanishes and changes sign. The energy of the<br />

cyclotron states increases with the magnetic field relatively to the energy of<br />

the snaking states such that at high magnetic fields the electrons concentrate<br />

around the snaking orbits. The spin of the electron is included via Zeeman<br />

and Rashba spin-orbit effects. A uniform electric field perpendicular to the<br />

cylin<strong>der</strong> is also consi<strong>der</strong>ed, as being produced by a metallic electrode placed<br />

near the cylin<strong>der</strong>. In this case the spin-orbit coupling becomes anisotropic.<br />

Attempts to include Coulomb effects in the Hartree-Fock approximation are<br />

discussed.<br />

69


Posters Monday February 4<br />

Poster 19:<br />

Quantized conductance in InSb nanowires and electrical characterization of<br />

branched InSb nanowires<br />

Ilse van Weperen<br />

Indium antimonide (InSb) nanowires have shown potential for creation of<br />

topological superconducting and helical liquid states. We report on transport<br />

measurements of single high-mobility indium antimonide nanowires and<br />

branched InSb nanowires.<br />

A novel growth mechanism allows two InSb nanowires to merge into a nano-<br />

T or nanocross. Transport measurements of branched nanowires show characteristics<br />

similar to that of single nanowires. Magnetoresistance measurements<br />

of nanocrosses allow extraction of nanowire electron density.<br />

A mean free path of ∼ 300 nm in InSb nanowires enables observation of<br />

one-dimensional conductance channels at high (B > 2 T) magnetic fields.<br />

Conductance quantization is studied as a function of magnetic field and bias<br />

voltage, enabling extraction of an effective g-factor of ∼ 65 and a subband<br />

spacing of ∼ 15 meV.<br />

Poster 20:<br />

Phase-Coherent Transport and Spin-Orbit Coupling in InAs Nanowires<br />

Sebastian Heedt<br />

We report on phase-coherent transport measurements on differently doped<br />

InAs nanowires grown by selective area metalorganic vapor phase epitaxy.<br />

The nanowires are contacted individually and the low-temperature electronic<br />

transport properties are investigated for temperatures down to 30 mK and<br />

magnetic fields up to 10 T. To this end, top-gates with high-k dielectrics are<br />

prepared. At small current-bias the transport is phase-coherent and gives<br />

us the opportunity to determine the phase-coherence length and the spin<br />

relaxation length. The band profile and the carrier concentration of the<br />

nanowires can be manipulated by the application of a gate voltage. An analytical<br />

model for the low-field quantum conductivity correction is utilized<br />

to quantify Rashba and Dresselhaus spin-orbit coupling effects. Nanowires<br />

with different doping concentrations are investigated to gain information<br />

on how the doping of the highly spin-orbit coupled InAs nanowires impacts<br />

the spin-lifetime.<br />

70


Posters Tuesday February 5<br />

Posters Tuesday February 5<br />

Time: 15:30 - 17:00<br />

Poster numbers: 21-43<br />

Topics:<br />

Spin-orbit hybrid systems<br />

Carbon nanotubes and graphene<br />

71


Posters Tuesday February 5<br />

Poster 21:<br />

Optical Josephson radiation from a Majorana Josephson junction<br />

Christoph Ohm<br />

We consi<strong>der</strong> a voltage-biased Josephson junction between two nanowires<br />

hosting Majorana fermions which occur as topological protected zero-energy<br />

excitations at the junction. We show that two Majorana fermions localized<br />

at the junction, though being neutral excitations, interact with the electromagnetic<br />

field and generate coherent radiation similar to the conventional<br />

Josephson radiation in a voltage biased Josephson junction. Within a semiclassical<br />

analysis of the light field, we find that the optical phase gets locked<br />

to the superconducting phase difference and that the radiation is emitted<br />

at half of the Josephson frequency. In or<strong>der</strong> to confirm the coherence of<br />

the radiation, we study correlations of the light emitted by two spatiallyseparated<br />

junctions in a SQUID geometry taking into account decoherence<br />

by spontaneous phase-switchings due to quasi-particle poisoning as well as<br />

by thermal effects.<br />

Poster 22:<br />

Spin-flip excitations induced by time-dependent electric fields in surfaces with<br />

strong spin-orbit interaction<br />

Julen Ibanez<br />

Heavy element surfaces have become an ideal testing ground for investigating<br />

the nature and effects of the relativistic spin-orbit interaction in low<br />

dimensional systems. In this work, we study spin-flip transitions between the<br />

metallic surface states of the Pb/Ge(111) and the Rashba prototype Au(111)<br />

surfaces. We calculate the spin-flip matrix elements following an approach<br />

based on the interpolation of maximally localized Wannier functions. The<br />

obtained results show that spin-flip absorptions are one or<strong>der</strong> of magnitude<br />

larger in Pb/Ge(111) than in Au(111), reaching a remarkable maximum of<br />

6% absorption of the total irradiated light.<br />

We find that the enhanced spin-flip contribution in Pb/Ge(111) is closely<br />

connected to the behavior of the momentum dependent spin-polarization<br />

associated to the surface states.<br />

72


Posters Tuesday February 5<br />

Poster 23:<br />

Quantum Dots and Majorana Fermions<br />

Martin Leijnse<br />

Majorana fermions, particles which are their own anti-particles, may or may<br />

not exist as elementary particles in nature. However, it was shown theoretically<br />

a few years ago that they can appear as quasiparticle excitations in<br />

certain condensed matter systems combining superconductivity, magnetism,<br />

and strong spin-orbit coupling. This has quickly become one of the hottest<br />

topics in mesoscopic physics research, partly because of the possibility to use<br />

Majorana fermions for quantum information processing.<br />

I will present work suggesting a new and perhaps easier way to generate<br />

Majorana-like bound states in a double quantum dot system, where the dots<br />

are tunnel coupled to each other via a superconductor. I will also show that<br />

quantum dots can be used to do more accurate spectroscopy of Majorana<br />

systems, and even to manipulate quantum information stored in Majoranabased<br />

qubits.<br />

Poster 24:<br />

Disor<strong>der</strong>-induced topological phase transitions in a quasi-1D spinless p-wave<br />

superconductor<br />

Maria-Theresa Rie<strong>der</strong><br />

Topological phases and the surface states associated with them are known<br />

to be robust against weak disor<strong>der</strong> and to break down at a critical disor<strong>der</strong><br />

strength. In this letter we show how disor<strong>der</strong> induces a series of topological<br />

phase transitions in a spinless multichannel p-wave superconducting<br />

wire. We find that the wire alternates between topologically trivial and nontrivial<br />

phases as the induced superconductivity is increased in a perturbative<br />

approach to the transverse coupling.<br />

73


Posters Tuesday February 5<br />

Poster 25:<br />

Majorana modes and complex band structure of quantum wires<br />

Llorens Serra<br />

We describe Majorana edge states of a semi-infinite wire using the complex<br />

band structure approach. In this method the edge state at a given energy is<br />

built as a superposition of evanescent waves. It is shown that the superposition<br />

can not always satisfy the required boundary condition, thus restricting<br />

the existence of edge modes. We discuss purely 1D and 2D systems, focussing<br />

in the latter case on the effect of the Rashba mixing term. We also review<br />

recent results on the calculation of Majorana modes in finite systems and of<br />

the linear transport within a coupled-channels model.<br />

References:<br />

[1] Majorana modes and complex band structure of quantum wires, L. Serra,<br />

arXiv:1210.4817<br />

[2] Transport through Majorana nanowires attached to normal leads, J.S.<br />

Lim, R. Lopez and L. Serra, New J. Phys. 14, 083020 (2012).<br />

[3] Magnetic field instability of Majorana modes in multiband semiconductor<br />

wires, J.S. Lim, L. Serra, R. Lopez and R. Aguado, Phys. Rev. B 86,<br />

121103(R) (2012).<br />

74


Posters Tuesday February 5<br />

Poster 26:<br />

Interaction induced charge and spin pumping in non-linear transport through<br />

a quantum dot<br />

Hernan Calvo<br />

We investigate charge and spin transport through an adiabatically driven,<br />

strongly interacting quantum dot weakly coupled to two metallic contacts<br />

with finite bias voltage. Within a kinetic/master equation approach we identify<br />

coefficients of response to the time-dependent external driving and relate<br />

these to the concepts of charge and spin emissivities in the time-dependent<br />

scattering matrix approach. Expressed in terms of auxiliary vector fields the<br />

response coefficients allow for a straightforward analysis of recently predicted<br />

interaction-induced pumping un<strong>der</strong> periodic modulation of the gate and bias<br />

voltage [1]. We perform a detailed study of this effect and the related adiabatic<br />

Coulomb blockade spectroscopy, and, in particular, extend it to spin<br />

pumping. Analytic formulas for the pumped charge and spin in the regimes<br />

of small and large driving amplitude are provided for arbitrary bias. In the<br />

absence of a magnetic field, we obtain a striking, simple relation between<br />

the pumped charge at zero bias and at bias equal to the Coulomb charging<br />

energy. At finite magnetic field, interaction-induced pure spin pumping is<br />

shown to be possible at this finite bias value, and additional features appear<br />

in the pumped charge. For large-amplitude adiabatic driving, the magnitude<br />

of both the pumped charge and spin at the various resonances saturate at<br />

values which are independent of the specific shape of the pumping cycle.<br />

Each of these values provide an independent, quantitative measurement of<br />

the junction asymmetry.<br />

75


Posters Tuesday February 5<br />

Poster 27:<br />

Adiabatic pumping through an interacting quantum dot with spin-orbit coupling<br />

Stephan Rojek<br />

We study adiabatic pumping through a two-level quantum dot coupled to two<br />

normal metallic leads in the presence of spin-orbit coupling.[1] The variation<br />

of the two energy levels of the dot periodically in time leads to finite charge<br />

and spin currents.<br />

We calculate the pumped charge and spin using a diagrammatic real-time<br />

approach.[2] Going beyond the limit of noninteracting electrons on the<br />

quantum dot,[3] we study the situation of strong Coulomb interaction. In<br />

both limits of noninteracting and strongly interacting electrons, spin-orbit<br />

coupling provides the possibility for pure spin current. We introduce an<br />

isospin to describe the level degree of freedom. This isospin feels an exchange<br />

field similar to the exchange field in a quantum-dot spin valve. The exchange<br />

field originates form the Coulomb interaction and its strength is sensitive<br />

to the symmetry in the tunneling matrix elements. New features concerning<br />

the pure spin pumping as well as the absolute pumped charge of the two-level<br />

quantum dot with spin-orbit coupling arises from the Coulomb interaction.<br />

[1] S. Rojek, J. König, and A. Shnirman, arXiv: 1209.4770v1 (2012)<br />

[2] J. Splettstoesser, M. Governale, J. König, and R. Fazio, Phys. Rev. B<br />

74, 085305 (2006).<br />

[3] V. Brosco, M. Jerger, P. San-José, G. Zaránd, A. Shnirman, and G.<br />

Schön, Phys. Rev. B 82, 041309(R) (2010).<br />

Coauthors<br />

Jürgen König and Alexan<strong>der</strong> Shnirman<br />

76


Posters Tuesday February 5<br />

Poster 28:<br />

Explicit staggered grid finite difference scheme for (2+1)D Dirac fermions<br />

René Hammer<br />

We study the dynamics of Dirac fermion wave packets on magnetically structured<br />

surfaces of topological insulators and propose a gate-controlled Dirac<br />

fermion interferometer based on a solitonic domain wall structure which functions<br />

as a transistor. A preliminary summary of related work can be found<br />

online (arXiv:1205.6941). Work supported by FWF Project P21289-N16<br />

We discuss and compare several algorithms for a numerical solution of the<br />

time-dependent Dirac equation in 2 spatial dimensions which allow the use of<br />

a finite simulation region for open boundary situations. The newly proposed<br />

explicit finite difference schemes use space and time staggering of the grid,<br />

showing a computational complexity growing only linearly with the number<br />

of space-time grid-points. One of them preserves the linear dispersion relation<br />

of the Weyl equation for wave vectors aligned with the grid and yields only<br />

one additional Dirac cone. The second scheme leads to a purely monotonic<br />

free-particle dispersion avoiding an additional cone altogether. We discuss the<br />

energy dispersion relation, the proof of stability, a definition of the norm on<br />

the staggered grid, and the important issue of absorbing boundary conditions.<br />

These schemes are useful for numerical studies of Dirac fermions on topological<br />

insulators, where the surface state energy spectrum can be m! anipulat ed<br />

by perturbations which break time-reversal symmetry introducing an energy<br />

gap. Work supported by FWF Project P21289-N16<br />

René Hammer, Christian Ertler, and Walter Pötz<br />

Poster 29:<br />

Microwave-controlled manipulation of Majorana bound states<br />

Thomas Schmidt<br />

Majorana bound states have been proposed as building blocks for qubits on<br />

which certain operations can be performed in a topologically protected way<br />

using braiding. However, the set of these protected operations is not sufficient<br />

to realize universal quantum computing. We show that the electric field in<br />

a microwave cavity can induce Rabi oscillations between adjacent Majorana<br />

bound states. These oscillations can be used to implement an additional<br />

single-qubit gate. Supplemented with one braiding operation, this gate allows<br />

to perform arbitrary single-qubit operations.<br />

77


Posters Tuesday February 5<br />

Poster 30:<br />

Topological edge states in a HgTe quantum well in proximity to an s-wave<br />

superconductor<br />

Luzie Weithofer<br />

Topological insulators represent a new class of condensed matter systems<br />

which are characterized by topologically protected edge states. Two-dimensional<br />

topological insulators have been experimentally realized in HgTe<br />

quantum wells [1]. In a HgTe quantum well in the topologically non-trivial<br />

phase, two edge states of different spin propagate in opposite directions at<br />

the same boundary.<br />

Here, we consi<strong>der</strong> the proximity-induced superconductivity in the bulk of<br />

a HgTe quantum well in terms of a four-band model [2]. In addition, we<br />

include various symmetry-breaking terms and discuss their consequences on<br />

the topological properties of the system, focusing on the existence of edge<br />

states.<br />

[1] M. König et al., Science 318, 766 (2007) [2] B. Bernevig et al., Science<br />

314, 1757 (2006)<br />

Poster 31:<br />

z→−z Symmetry of Spin-Orbit Coupling and Weak Localization in Graphene<br />

Vladimir Falko<br />

We show that the influence of spin-orbit (SO) coupling on the weak-localization<br />

effect for electrons in graphene depends on the lack or presence of<br />

z→−z symmetry in the system. While, for z→−z asymmetric SO coupling,<br />

disor<strong>der</strong>ed graphene should display a weak antilocalization behavior at lowest<br />

temperature, z→−z symmetric coupling leads to an effective saturation of<br />

decoherence time which can be partially lifted by an in-plane magnetic field,<br />

thus tending to restore the weak-localization effect.<br />

78


Posters Tuesday February 5<br />

Poster 32:<br />

Intrinsic and substrate induced spin-orbit interaction in chirally stacked trilayer<br />

graphene<br />

Andor Kormanyos<br />

We present a combined group-theoretical and tight-binding approach to<br />

calculate the intrinsic spin-orbit coupling (SOC) in ABC stacked trilayer<br />

graphene. As a special case of our calculations we also consi<strong>der</strong> the intrinsic<br />

SOC in bilayer graphene. The comparison between our tight-binding bilayer<br />

results and the density functional computations of Konschuh et. al. allows<br />

us to estimate the values of the trilayer SOC parameters as well. We also<br />

discuss the situation when a substrate or adatoms induce strong SOC in<br />

only one of the layers of bilayer or ABC trilayer graphene. Both for the<br />

case of intrinsic and externally induced SOC we <strong>der</strong>ive effective Hamiltonians<br />

which describe the low-energy spin-orbit physics. We find that at the K point<br />

of the Brillouin zone the effect of Bychkov-Rashba type SOC is suppressed<br />

in bilayer and ABC trilayer graphene compared to monolayer graphene.<br />

Poster 33:<br />

Spin-orbit induced strong coupling of a single spin to a nanomechanical resonator<br />

Andras Palyi<br />

We theoretically investigate the spin-orbit-induced coupling of an electron<br />

spin to a bending vibrational mode in suspended carbon nanotube quantum<br />

dots. Our estimates indicate that, with current capabilities, a quantum dot<br />

with an odd number of electrons can serve as a realization of the Jaynes-<br />

Cummings model of quantum electrodynamics in the strong-coupling regime.<br />

A bending mode of the suspended tube plays the role of the optical mode and<br />

we identify two distinct two-level subspaces, at small and large magnetic field,<br />

which can be used as qubits in this setup. The strong intrinsic spin-mechanical<br />

coupling allows for detection, as well as manipulation of the spin qubit,<br />

and may yield enhanced performance of nanotubes in sensing applications.<br />

Reference:<br />

A. Palyi, P. R. Struck, M. Rudner, K. Flensberg and G. Burkard, Phys.<br />

Rev. Lett. 108, 206811 (2012)<br />

79


Posters Tuesday February 5<br />

Poster 34:<br />

Spin-orbit effects in electronic transport in DNA-CNT hybrids<br />

Sergio Ulloa<br />

We report on theoretical studies of electronic transport in the archetypical<br />

molecular hybrid formed by DNA wrapped around single-walled carbon<br />

nanotubes (CNTs). Using a Green’s function formalism in a π-orbital tightbinding<br />

representation, we investigate the role that spin-orbit interactions<br />

play on the CNT in the case of the helicoidal electric field induced by the<br />

polar nature of the adsorbed DNA molecule. We find that spin polarization<br />

of the current can take place in the absence of magnetic fields, depending<br />

strongly on the direction of the wrapping and length of the helicoidal field.<br />

These findings open new routes for using CNTs in spintronic devices.<br />

Poster 35:<br />

Covalent functionalization of carbon nanotubes with tetramanganese complexes<br />

Robert Frielinghaus<br />

We present first results on the covalent chemical functionalization of carbon<br />

nanotubes (CNTs) with polynuclear Mn 4 coordination complexes. Raman<br />

spectra give direct and indirect evidence of a successful reaction. It can only<br />

be achieved for tubes which contain defects with carboxylic groups. Changes<br />

in the magnetization behavior of the Mn 4 complexes due to the bonding<br />

to the CNTs are analyzed using data obtained in temperature-dependent<br />

SQUID measurements.<br />

These results are correlated with bright- and dark field high-resolution transmission<br />

electron microscopy measurements that show the repartition of the<br />

Mn 4 decoration on the CNTs. Its elemental analysis capabilities, energydispersive<br />

x-ray spectroscopy and electron energy loss spectroscopy, proof the<br />

existence of Mn on the CNTs. Investigating several oxidation strengths we<br />

can show that already a mild oxidation that leaves the nanotubes intact in<br />

terms of a finite electrical conductance is sufficient for functionalization. This<br />

is important for the future application of this material in transport devices.<br />

80


Posters Tuesday February 5<br />

Poster 36:<br />

Analysis of quantum transport features in complex carbon nanotube structures<br />

Robert Frielinghaus<br />

We have investigated two carbon nanotubes (CNTs) both in quantum transport<br />

and in the transmission electron microscope by means of a novel sample<br />

design. This enables us to determine the device structure unambiguously as<br />

a two-fold single-walled CNT bundle and an individual triple-walled CNT,<br />

respectively. The corresponding low-temperature transport experiments are,<br />

to our knowledge, the first ones unambiguously conducted on these very<br />

systems. The stability diagrams exhibit complex features as anti-crossings,<br />

Fano-shaped coulomb peaks, and regular sawtooth patterns. The origin of<br />

these features is only found with the detailed knowledge about the atomic<br />

structure, which cannot be obtained with standard sample layouts. More precisely,<br />

we measure capacitive and molecular interactions between the various<br />

elements of the devices and the environment.<br />

Poster 37:<br />

Nanomechanical read-out of a single spin<br />

Philipp Struck<br />

The spin of a single electron in a suspended carbon nanotube can be read<br />

out by using its coupling to the nano-mechanical motion of the nanotube. To<br />

show this, we consi<strong>der</strong> a single electron confined within a quantum dot formed<br />

by the suspended carbon nanotube. The spin- orbit interaction induces a<br />

coupling between the spin and one of the bending modes of the suspended<br />

part of the nanotube. We calculate the response of the system to pulsed<br />

external driving of the mechanical motion using a Jaynes-Cummings model.<br />

To account for resonator damping, we solve a quantum master equation, with<br />

parameters comparable to those used in recent experiments, and show how<br />

information of the spin state of the system can be acquired by measuring<br />

its mechanical motion. The latter can be detected by observing the current<br />

through a nearby charge detector.[1]<br />

[1] P. R. Struck, H. Wang, G. Burkard, arXiv:1212.1569<br />

81


Posters Tuesday February 5<br />

Poster 38:<br />

Cotunneling renormalization in carbon nanotube quantum dots<br />

Kirsanskas Gediminas<br />

We determine the level shifts induced by cotunneling in a Coulomb blockaded<br />

carbon nanotube quantum dot using leading-or<strong>der</strong> quasi-degenerate<br />

perturbation theory within a single nanotube “shell.” It is demonstrated<br />

that otherwise degenerate and equally tunnel coupled K and K’ states are<br />

mixed by cotunneling and therefore split up in energy except at the particle-hole<br />

symmetric midpoints of the Coulomb diamonds. In the presence<br />

of an external magnetic field, we show that cotunneling induces a gate dependent<br />

g-factor renormalization, and we outline different scenarios which might<br />

be observed experimentally, depending on the values of both intrinsic KK’-<br />

mixing and spin-orbit coupling.<br />

Poster 39:<br />

Kondo effect in graphene with Rashba spin-orbit coupling<br />

Diego Matrogiuseppe<br />

We study the effect of Rashba spin-orbit coupling in graphene with an<br />

adsorbed magnetic impurity. We model the system starting with a multiband<br />

An<strong>der</strong>son Hamiltonian, which is reduced to a single channel problem through<br />

suitable fermionic redefinitions. Then we map it to a Kondo Hamiltonian<br />

through a proper Schrieffer-Wolff transformation. The energy dependence<br />

of the Kondo exchange coupling follows the functional form of the density<br />

of states, giving rise to interesting phenomena as a function of the band filling.<br />

Compared to plain graphene, the presence of Rashba spin-orbit induces a<br />

finite density of states at the charge neutrality point. Therefore, a Kondo<br />

phase is expected for any finite value of the Rashba parameter, even for<br />

the particle-hole symmetric case. Finally, we compare these findings to recent<br />

results of magnetic impurities on bilayer graphene without spin-orbit coupling.<br />

Coauthors<br />

S. Ulloa and N. Sandler<br />

82


Posters Tuesday February 5<br />

Poster 40:<br />

Magnetic field effects on the finite-frequency noise and ac conductance of a<br />

Kondo quantum dot out of equilibrium<br />

Sarah Müller<br />

We present analytic results for the finite-frequency current noise and the<br />

nonequilibrium ac conductance for a Kondo quantum dot in presence of a<br />

magnetic field. We determine the line shape close to resonances and show<br />

that while all resonances in the ac conductance are broadened by the transverse<br />

spin relaxation rate; the noise at finite field additionally involves the<br />

longitudinal rate as well as sharp kinks resulting in singular <strong>der</strong>ivatives. Our<br />

results provide a consistent theoretical description of recent experimental<br />

data [Phys. Rev. Lett. 108, 046802 (2012)] for the emission noise at zero<br />

magnetic field, and we propose the extension to finite field for which we<br />

present a detailed prediction.<br />

Poster 41:<br />

Electron entanglement in Cooper pair beam splitter with magnetic fields<br />

Stephan Weiss<br />

We develop a theory that suggests the efficient manipulation of entangled<br />

electrons provided by a Cooper pair beam splitter. The splitting of coherent<br />

electrons forming a spin singlet is present if the superconductor is tunnel<br />

coupled to a double quantum dot [1]. In or<strong>der</strong> to probe entanglement, we<br />

allow for an inhomogeneous and, in general, non-collinear magnetic field in<br />

both dots. If the DQD-SC system is embedded in a transport setup, non-local<br />

current and noise properties are obtained within the real-time diagrammatic<br />

method [2]. As a small parameter we use the hybridization between splitter<br />

and normal leads. The tunnel coupling to the superconductor is taken into<br />

account non-perturbatively. Furthermore, we provide a detailed investigation<br />

of the violation of Bell’s inequality for various parameter regimes.<br />

[1] J. Eldridge, M. Governale, and J. König, Phys. Rev. B 82 184507, (2010).<br />

[2] M. Governale, M. Pala, and J. König, Phys. Rev. B 77 134513, (2008).<br />

83


Posters Tuesday February 5<br />

Poster 42:<br />

Current correlations in the interacting Cooper-pair beam-splitter<br />

Jerome Rech<br />

We propose an approach allowing the computation of currents and their correlations<br />

in interacting multi-terminal mesoscopic systems involving quantum<br />

dots coupled to normal and/or superconducting leads [1]. The formalism<br />

relies on the expression of branching currents and noise crossed correlations in<br />

terms of one- and two-particle Green’s functions for the dots electrons, which<br />

are then evaluated self-consistently within a conserving approximation [2].<br />

We illustrate our method with the Cooper-pair beam-splitter setup recently<br />

proposed [3], which we model as a double quantum dot with weak interactions,<br />

connected to a superconducting lead and two normal ones. Our method<br />

not only enables us to take into account a local repulsive interaction on the<br />

dots, but also to study its competition with the direct tunneling between<br />

dots. Our results suggest that even a weak Coulomb repulsion tends to favor<br />

positive current cross correlations in the antisymmetric regime (where the<br />

dots have opposite energies with respect to the superconducting chemical<br />

potential).<br />

Poster 43:<br />

Controlling entanglement and spin-correlations in double quantum dots using<br />

non-equilibrium currents<br />

Carlos Busser<br />

We study the non-equilibrium dynamics in a parallel double-quantum dot<br />

structure induced by a large bias voltage. By applying both a magnetic flux<br />

and a voltage, it is possible to generate spin-spin-correlations between the two<br />

quantum dots, whose sign and absolute value can be controlled by changing<br />

the bias voltage. Our study is based on the An<strong>der</strong>son-impurity model and<br />

we use time-dependent density matrix renormalization group simulations to<br />

obtain currents and spin-correlations in the non-equilibrium regime.<br />

84


List of participants<br />

1. Yulieth Cristina Arango, Forschungszentrum Jülich, Germany<br />

y.arango@fz-juelich.de<br />

2. Christian Bartsch, TU Braunschweig, Braunschweig, Germany<br />

c.bartsch@tu-braunschweig.de<br />

3. Bernd Beschoten, <strong>RWTH</strong> <strong>Aachen</strong> University, <strong>Aachen</strong>, Germany<br />

bernd.beschoten@physik.rwth-aachen.de<br />

4. Stefan Blügel, Forschungszentrum Jülich, Germany<br />

s.bluegel@fz-juelich.de<br />

5. Aldo Brunetti, Heinrich Heine Univerität - Düsseldorf, Düsseldorf, Germany<br />

brunetti@thphy.uni-duesseldorf.de<br />

6. Carlos Busser, LMU Munich, Munich, Germany<br />

C.Buesser@physik.uni-muenchen.de<br />

7. Hernan Calvo, <strong>RWTH</strong> <strong>Aachen</strong> University, <strong>Aachen</strong>, Germany<br />

hcalvo@physik.rwth-aachen.de<br />

8. Theo Costi, Research Centre Jülich GmbH, Jülich, Germany<br />

t.costi@fz-juelich.de<br />

9. Silvano De Franceschi, CEA, Grenoble, France<br />

silvano.defranceschi@cea.fr<br />

10. Manuel dos Santos Dias, Forschungszentrum Jülich, Jülich, Germany<br />

m.dos.santos.dias@fz-juelich.de<br />

11. Reinhold Egger, Heinrich Heine Univerität- Düsseldorf, Düsseldorf, Germany<br />

egger@thphy.uni-duesseldorf.de<br />

12. Sigurdur I. Erlingsson, Reykjavik University, Reykjavik, Iceland<br />

sie@ru.is<br />

13. Vladimir Falko, Lancaster University, Lancaster, United Kingdom<br />

v.falko@lancaster.ac.uk<br />

14. Robert Frielinghaus, Forschungszentrum Jülich, Jülich, Germany<br />

r.frielinghaus@fz-juelich.de<br />

15. Robert Frielinghaus, Forschungszentrum Jülich, Jülich, Germany<br />

r.frielinghaus@fz-juelich.de<br />

16. Kirsanskas Gediminas, University of Copenhagen, Copenhagen, Denmark<br />

gedikirs@nano.ku.dk<br />

17. Thomas Gerster, Fz-Jülich, Jülich, Germany<br />

t.gerster@fz-juelich.de<br />

85


18. Domenico Giuliano, Universita‘ della Calabria - Italy, Rende, Italy<br />

domenico.giuliano@fis.unical.it<br />

19. Stephan Grap, <strong>RWTH</strong> <strong>Aachen</strong> University, <strong>Aachen</strong>, Germany<br />

stephan.grap@rwth-aachen.de<br />

20. Kasper Grove-Rasmussen, University of Copenhagen, Copenhagen, Denmark<br />

k_grove@fys.ku.dk<br />

21. Jan-Christian Gunia, Forschungszentrum Jülich, Germany<br />

j-c.gunia@fz-juelich.de<br />

22. René Hammer, University Graz, Graz, Austria<br />

rene.hammer@uni-graz.at<br />

23. Fe<strong>der</strong>ica Haupt, <strong>RWTH</strong> <strong>Aachen</strong> University, Germany<br />

fe<strong>der</strong>ica.haupt@gmail.com<br />

24. Sebastian Heedt, Forschungszentrum Jülich, Jülich, Germany<br />

s.heedt@fz-juelich.de<br />

25. Fabian Heidrich-Meisner, LMU Munich, Munich, Germany<br />

heidrich-meisner@lmu.de<br />

26. Stefan Heinze, University of Kiel, Kiel, Germany<br />

heinze@physik.uni-kiel.de<br />

27. Michael Hell, Research Center Jülich, Jülich, Germany<br />

m.hell@fz-juelich.de<br />

28. Carsten Honerkamp, <strong>RWTH</strong> <strong>Aachen</strong>, Germany,<br />

honerkamp@physik.rwth-aachen.de<br />

29. Christoph Hörig, <strong>RWTH</strong>, <strong>Aachen</strong>, German<br />

hoerig@physik.rwth-aachen.de<br />

30. Julen Ibanez, University of the Basque Country, Leioa (Bizkaia), Spain<br />

julen.ibanez@ehu.es<br />

31. Henrik Johannesson, University of Gothenburg, Gothenburg, Sweden<br />

henrik.johannesson@physics.gu.se<br />

32. Marvin Junk, <strong>RWTH</strong> <strong>Aachen</strong>, <strong>Aachen</strong>, Germany<br />

Marvin.Junk@rwth-aachen.de<br />

33. Pascal Kaienburg, <strong>RWTH</strong>, <strong>Aachen</strong>, Germany<br />

pascal.kaienburg@rwth-aachen.de<br />

34. Vladislav Kataev, IFW Dresden, Dresden, Germany<br />

v.kataev@ifw-dresden.de<br />

35. Michael Kinza, <strong>RWTH</strong> <strong>Aachen</strong> University, <strong>Aachen</strong>, Germany<br />

kinza@physik.rwth-aachen.de<br />

86


36. Jürgen König, University of Duisburg-Essen, Duisburg, Germany<br />

koenig@thp.uni-due.de<br />

37. Francois Konschelle, <strong>RWTH</strong> - <strong>Aachen</strong>, <strong>Aachen</strong>, Germany<br />

konschelle@physik.rwth-aachen.de<br />

38. Andor Kormanyos, University of Konstanz, Konstanz, Germany<br />

andor.kormanyos@uni-konstanz.de<br />

39. Martin Leijnse, Copenhagen University, Copenhagen, Denmark<br />

leijnse@fys.ku.dk<br />

40. Andrei Manolescu, Reykjavik University, Reykjavik, Iceland<br />

manoles@ru.is<br />

41. Charles Marcus, University of Copenhagen, Copenhagen, Denmark,<br />

marcus@nbi.dk<br />

42. Diego Matrogiuseppe, Ohio University, United States,<br />

mastrogiuseppe@ifir-conicet.gov.ar<br />

43. Volker Meden, <strong>RWTH</strong> <strong>Aachen</strong>, <strong>Aachen</strong>, Germany<br />

meden@physik.rwth-aachen.de<br />

44. Sebastian Mehl, Forschungszentrum Jülich, Jülich, Germany<br />

s.mehl@fz-juelich.de<br />

45. Lukas Merker, Forschungszentrum Jülich GmbH, Jülich, Germany<br />

l.merker@fz-juelich.de<br />

46. Maciej Misiorny, Forschungszentrum Jülich, Germany<br />

m.misiorny@fz-juelich.de<br />

47. Markus Morgenstern, <strong>RWTH</strong>, <strong>Aachen</strong>, Germany<br />

mmorgens@physik.rwth-aachen.de<br />

48. André Müller, <strong>RWTH</strong> <strong>Aachen</strong>, Germany<br />

andre.mueller@physik.rwth-aachen.de<br />

49. Sarah Müller, Universität Wien, Wien, Austria<br />

sarah.mueller@univie.ac.at<br />

50. Amin Naseri Jorshari, Heinrich Heine University, Dusseldorf, Germany<br />

nasseri.amin@gmaul.com<br />

51. Christoph Neumann, <strong>RWTH</strong> <strong>Aachen</strong>, <strong>Aachen</strong>, Germany<br />

christoph.neumann@rwth-aachen.de<br />

52. Hoa Nghiem, Forschungszentrum Jülich, Jülich, Germany<br />

h.nghiem@fz-juelich.de<br />

53. Christoph Ohm, <strong>RWTH</strong> <strong>Aachen</strong>, <strong>Aachen</strong>, Germany<br />

ohm@physik.rwth-aachen.de<br />

54. San<strong>der</strong> Otte, TU Delft, Delft, The Netherlands<br />

a.f.otte@tudelft.nl<br />

87


55. Jens Paaske, Copenhagen University, Copenhagen, Denmark<br />

paaske@nbi.ku.dk<br />

56. Andras Palyi, Eotvos University Budapest, Budapest, Hungary<br />

andraspalyi@caesar.elte.hu<br />

57. Mikhail Pletyukhov, <strong>RWTH</strong>, <strong>Aachen</strong>, Germany<br />

pletmikh@physik.rwth-aachen.de<br />

58. Vlad Pribiag, TU Delft, Delft, The Netherlands<br />

v.s.pribiag@tudelft.nl<br />

59. Benedikt Probst, TU Braunschweig, Braunschweig, Germany<br />

b.probst@tu-braunschweig.de<br />

60. Jerome Rech, Aix Marseille Université, Marseille, France<br />

jerome.rech@cpt.univ-mrs.fr<br />

61. Maria-Theresa Rie<strong>der</strong>, Freie Universität Berlin, Berlin, Germany<br />

rie<strong>der</strong>m@physik.fu-berlin.de<br />

62. Stephan Rojek, Universität Duisburg-Essen, Duisburg, Germany<br />

strojek@thp.uni-due.de<br />

63. Achim Rosch, University of Cologne, Cologne, Germany<br />

rosch@thp.uni-koeln.de<br />

64. Julia Samm, University of Basel, Basel, Switzerland<br />

julia.samm@unibas.ch<br />

65. Nancy Sandler, Freie Universitat/Ohio University, Berlin, Germany<br />

sandler@ohio.edu<br />

66. Roman Saptsov, Forschungszentrum Jülich, Jülich, Germany<br />

r.saptsov@fz-juelich.de<br />

67. Thomas Schäpers, Forschungszentrum Jülich and <strong>RWTH</strong> <strong>Aachen</strong>, Jülich,<br />

Germany<br />

th.schaepers@fz-juelich.de<br />

68. Thomas Schmidt, Universität Basel, Basel, Switzerland<br />

thomas.schmidt@unibas.ch<br />

69. Michael Schnee, Forschungszentrum Jülich, Jülich, Germany<br />

m.schnee@fz-juelich.de<br />

70. Herbert Schoeller, <strong>RWTH</strong> <strong>Aachen</strong> University, <strong>Aachen</strong>, Germany<br />

schoeller@physik.rwth-aachen.de<br />

71. Christian Schönenberger, University of Basel, Basel, Switzerland<br />

Christian.Schoenenberger@unibas.ch<br />

72. Llorens Serra, University of Balearic Islands, Palma de Mallorca, Spain<br />

llorens.serra@uib.es<br />

88


73. Janine Splettstoesser, <strong>RWTH</strong> <strong>Aachen</strong>, <strong>Aachen</strong>, Germany<br />

splett@physik.rwth-aachen.de<br />

74. Christoph Stampfer, <strong>RWTH</strong> <strong>Aachen</strong>, <strong>Aachen</strong>, Germany<br />

christoph@stampfer.com<br />

75. Philipp Stegmann, Universität Duisburg-Essen, Duisburg, Germany<br />

philipp.stegmann@uni-due.de<br />

76. Robin Steinigeweg, TU Braunschweig, Braunschweig, Germany<br />

robin@robin-st.de<br />

77. An<strong>der</strong>s Ström, TU Braunschweig, Braunschweig, Germany<br />

an<strong>der</strong>s.p.strom@gmail.com<br />

78. Philipp Struck, University of Konstanz, Konstanz, Germany<br />

philipp.struck@uni-konstanz.de<br />

79. Arturo Tagliacozzo, Universita’ di Napoli "Fe<strong>der</strong>ico II", Napoli , Italy<br />

arturo@na.infn.it<br />

80. Seigo Tarucha, University of Tokyo, Tokyo, Japan<br />

tarucha@ap.t.u-tokyo.ac.jp<br />

81. Jonckheere Thibaut, CNRS , Marseille, France<br />

thibaut.jonckheere@cpt.univ-mrs.fr<br />

82. Carsten Timm, Technische Universität Dresden, Dresden, Germany<br />

carsten.timm@tu-dresden.de<br />

83. Mircea Trif, UCLA, Los Angeles, United States<br />

mtrif@physics.ucla.edu<br />

84. Sergio Ulloa, Ohio University, Athens, Ohio, USA<br />

ulloa@ohio.edu<br />

85. Herre van <strong>der</strong> Zant, Delft University of Technology, Delft, The Netherlands<br />

h.s.j.van<strong>der</strong>zant@tudelft.nl<br />

86. Ilse van Weperen, Delft University of Technology, Delft, The Netherlands<br />

I.vanWeperen@tudelft.nl<br />

87. Christian Volk, <strong>RWTH</strong> <strong>Aachen</strong>, <strong>Aachen</strong>, Germany<br />

c.volk@fz-juelich.de<br />

88. Stephan Weiss, Universität Duisburg-Essen, Duisburg, Germany<br />

weiss@thp.uni-due.de<br />

89. Luzie Weithofer, TU Braunschweig, Braunschweig, Germany<br />

luzie.weithofer@tu-bs.de<br />

90. Ireneusz Weymann, Adam Mickiewicz University, Poznan, Poland<br />

weymann@amu.edu.pl<br />

89

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