2009 CARBON ALLOTROPESEdge fingerprints and magneto-conductance in graph<strong>en</strong>e nanoribbonsThe control of the curr<strong>en</strong>t flow in gated graph<strong>en</strong>e nanoribbons(GNR) constitutes a fascinating chall<strong>en</strong>ge for the futureof carbon-based electronic devices. The combinationof the extraordinary electronic properties of the Diracfermions in graph<strong>en</strong>e, like their outstanding mobility atroom temperature, with a sizeable <strong>en</strong>ergy gap, op<strong>en</strong>s a routeto outperform the ultimate scaling of silicon field effecttransistors [Wang et al, Phys. Rev. Lett. 100 206803(2008)]. However, the lateral confinem<strong>en</strong>t goes along witha problematic decay of the mobility. Low temperaturetransport measurem<strong>en</strong>ts performed on nano-lithographedGNR also unveil a ubiquitous <strong>en</strong>ergy gap, irrespective ofthe edges ori<strong>en</strong>tation and exceeding the expected confinem<strong>en</strong>tgap.Drawing a parallel betwe<strong>en</strong> GNR and carbon nanotubes(CNT) is certainly tempting. The pres<strong>en</strong>ce of edges in GNRimposes Dirichlet boundary conditions and results in a lossof one conducting channel at the Charge Neutrality Point(CNP), compared to armchair CNT.obtained on high quality GNR is sorely lacking. Applyinga large transverse magnetic field is also a suitable tool toboth explore the expected 1D-electronic band structure andthe disorder induced localization.In this work, we pres<strong>en</strong>t evid<strong>en</strong>ce of 1D-subbands signatureson the electronic transport on an 11 nm wide GNR.Comparison to band structures calculations of a set ofGNRs in a width window of 11±0.3 nm allows an assignationof the carbon atoms arrangem<strong>en</strong>t at the edges and th<strong>en</strong>umber of dimers (figure 7).The application of a 60 T perp<strong>en</strong>dicular magnetic field inducesa drastic increase of the conductance, whose magnitudedep<strong>en</strong>ds on the doping level (figure 8(left). At zero<strong>en</strong>ergy, we demonstrate that the large positive magnetoconductanceoriginates from the onset of the first Landaustate accompanying the closing of the <strong>en</strong>ergy gap (figure8(right). Landauer-Buttiker simulations of the conductanceof GNR including bulk and edge disorder (and curr<strong>en</strong>tlyin progress) demonstrate that the magnetoconductanceresults from a subtle combination of magnetic bandformations and quantum interfer<strong>en</strong>ce effects in pres<strong>en</strong>ce ofdisorder.Figure 7: Conductance versus back-gate voltage at 80 K measuredon the 11 nm wide GNR for two V bias , 50 mV and 1 mV(respectively red and blue curve). Superimposed is the calculatedd<strong>en</strong>sity of states (black curve) as a function of V g , for four distinctGNRs : (a,b,c) aGNR, N = 90,91,92 and (d) zGNR, N = 52.Non-perfect edges are also source of short range pot<strong>en</strong>tialdisorder responsible for inter-valley backscattering. Drasticconsequ<strong>en</strong>ces on the electronic transport have be<strong>en</strong> theoreticalanticipated with the formation of a mobility gap at zero<strong>en</strong>ergy, ev<strong>en</strong> in the pres<strong>en</strong>ce of an ultra-smooth edge roughness.However, a direct comparison with experim<strong>en</strong>tal dataFigure 8: (Left) Magnetoconductance measured on the 11 nmwide GNR for various back gate voltages at 80 K. For comparison,the black dashed curve is the magnetoconductance measuredon a 90 nm GNR varying from 0.6 to 0.4G 0 under 55 T. (Right)Magnetoconductance at the CNP measured at 80,50 and 20 K.The black dashed curves are the simulated magnetoconductanceassuming a thermally activated regime and a magnetic field inducedclosing of the <strong>en</strong>ergy gap along with the onset of the firstLandau level at zero <strong>en</strong>ergy.J-M Poumirol, W. Escoffier, M. Goiran, J-M Broto, B. RaquetS. Roche, A. Cresti (Commissariat à l’Energie Atomique, INAC, SP2M, Gr<strong>en</strong>oble), X. Wang, H. Dai (Physics departm<strong>en</strong>tand Chemistry Laboratory, Stanford, US)9
CARBON ALLOTROPES 2009Using Landau quantization to suppress Auger scattering in graph<strong>en</strong>eCarrier-carrier scattering due to the Coulomb interactionis the dominant process which governs the dynamics ofhot carriers in solids at very short time scales. Thisis true for conv<strong>en</strong>tional (semiconductor) two-dim<strong>en</strong>sionalsystems, ev<strong>en</strong> wh<strong>en</strong> their <strong>en</strong>ergy bands are quantized intodiscrete Landau levels by the application of a magneticfield. This is because Auger-type scattering processes betwe<strong>en</strong>equidistant Landau levels, formed from bands withparabolic dispersions, are extremely effici<strong>en</strong>t. Indeed,Auger scattering has long be<strong>en</strong> considered as the main obstaclefor the fabrication of tunable far-infrared laser basedon inter-Landau level emission. However, the application ofa magnetic field should considerably influ<strong>en</strong>ce the electronelectronscattering process in strongly non parabolic electronicsystems such as graph<strong>en</strong>e.Here we investigate the dynamics of the non-equilibriumcarriers in graph<strong>en</strong>e measured using a deg<strong>en</strong>erate pumpprobetechnique which directly probes the occupancy ofstates well above the Fermi level. The differ<strong>en</strong>tial transmission∆T /T as a function of delay betwe<strong>en</strong> the pumpand probe pulses, is pres<strong>en</strong>ted in figure 9(a-d) for magneticfields in the range 0 − 6 T. Two characteristic relaxationtimes are observed, a fast process (∼ 50 fs) which broad<strong>en</strong>sthe photo-created distribution and a slower process (∼ 4 ps)due to thermalization. At low temperature (T = 18 K), themagnetic field has a considerable influ<strong>en</strong>ce on both the fastand slow relaxation processes.This can be se<strong>en</strong> more clearly in figure 10 which plotsln(∆T /T ) versus delay time to highlight the expon<strong>en</strong>tialcharacter of the relaxation. The characteristic time of thedecay (τ r ) can be extracted from the slope of such a plot.For the slow relaxation at zero magnetic field there is littlediffer<strong>en</strong>ce betwe<strong>en</strong> the high and low temperature datawith a relaxation time of τ r ∼ 4 ps at both 18 K and 250 K.The relaxation becomes slower by a factor of 3–4, changingfrom τ r ∼ 4 ps at B = 0 T to τ r ∼ 12–14 ps for magneticfields above 3 T. For the fast decay, without magnetic fieldthere is little differ<strong>en</strong>ce betwe<strong>en</strong> the high and low temperaturedata with a relaxation time of τ r ∼ 55 fs at 18 K andτ r ∼ 70 fs at 250 K. However, at low temperatures, the applicationof a mo<strong>des</strong>t magnetic field ∼ 3–6 T doubles therelaxation time to τ r ∼ 110 fs, providing direct experim<strong>en</strong>talevid<strong>en</strong>ce that the electron-electron scattering is significantlyless effective in the pres<strong>en</strong>ce of Landau quantization.This slow down, which is common for both the slowand fast relaxation processes, can be se<strong>en</strong> as a proof that inboth cases the electron–electron scattering or thermalizationof the hot plasma with the cold electrons is reduced inthe pres<strong>en</strong>ce of Landau quantization which limits the possible<strong>en</strong>ergy of the initial and final states.This is interpreted as a reduction of electron-electron(Auger) scattering due to the unusual Landau quantizationof Dirac fermions in graph<strong>en</strong>e. Our measurem<strong>en</strong>ts, whichprobe Landau levels with a high index (n ≈ 100), suggestthat for lower Landau levels, Auger processes may be completelysuppressed. This makes graph<strong>en</strong>e a promising systemfor the implem<strong>en</strong>tation of the long ago proposed tunablefar infrared Landau level laser [Plochocka et al. Phys.Rev. B 80, 245415 (2009)].Figure 9: The differ<strong>en</strong>tial transmission ∆T /T as a function of thedelay betwe<strong>en</strong> the pump and probe pulses measured at a temperatureof (a-b) 250 K and (c-d) 18 K for magnetic fields in the range0 − 6 T.Figure 10: (a-b) Natural log of the differ<strong>en</strong>tial transmission as afunction of a delay betwe<strong>en</strong> pump and probe pulses measured formagnetic fields (0 − 6 T) at 18K. The B = 0 T data measured at250 K is plotted using op<strong>en</strong> circles. The relaxation times τ r extractedfrom linear fits are indicated. The inset of (a) shows thecalculated <strong>en</strong>ergy mismatch for Auger processes for carriers in th<strong>en</strong> = 10 and n = 100 Landau level versus change in Landau levelindex mP. Plochocka, P. Kossacki, M. PotemskiA. Golnik, T. Kazimierczuk (Institute of Experim<strong>en</strong>tal Physics, University of Warsaw), C. Berger, W. A. de Heer (GeorgiaTech., Atlanta, USA)10
- Page 1 and 2: LABORATOIRE NATIONAL DES CHAMPS MAG
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- Page 6 and 7: Coexistence of closed orbit and qua
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- Page 12 and 13: 2009 CARBON ALLOTROPESInvestigation
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METALS, SUPERCONDUCTORS... 2009High
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METALS, SUPERCONDUCTORS... 2009Angu
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METALS, SUPERCONDUCTORS... 2009Magn
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METALS, SUPERCONDUCTORS... 2009Meta
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2009 MAGNETIC SYSTEMSY b 3+ → Er
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2009 MAGNETIC SYSTEMSMagnetotranspo
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2009 MAGNETIC SYSTEMSHigh field tor
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2009 MAGNETIC SYSTEMSNuclear magnet
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2009 MAGNETIC SYSTEMSStructural ana
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2009 MAGNETIC SYSTEMSEnhancement ma
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2009 MAGNETIC SYSTEMSInvestigation
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2009 MAGNETIC SYSTEMSField-induced
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2009 MAGNETIC SYSTEMSMagnetic prope
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2009Biology, Chemistry and Soft Mat
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BIOLOGY, CHEMISTRY AND SOFT MATTER
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2009 APPLIED SUPERCONDUCTIVITYMagne
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2009 APPLIED SUPERCONDUCTIVITYPhtha
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2009Magneto-Science105
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MAGNETO-SCIENCE 2009Study of the in
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MAGNETO-SCIENCE 2009Magnetohydrodyn
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MAGNETO-SCIENCE 2009112
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 MAGNET DEVELOPMENT AND INSTRUM
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2009 PROPOSALSProposals for Magnet
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2009 PROPOSALSSpin-Jahn-Teller effe
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2009 PROPOSALSQuantum Oscillations
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2009 PROPOSALSThermoelectric tensor
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2009 PROPOSALSDr. EscoffierCyclotro
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2009 PROPOSALSHigh field magnetotra
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2009 THESESPhD Theses 20091. Nanot
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2009 PUBLICATIONS[21] O. Drachenko,
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2009 PUBLICATIONS[75] S. Nowak, T.
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Contributors of the LNCMI to the Pr
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Institut Jean Lamour, Nancy : 68Ins
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Lawrence Berkeley National Laborato