STM - Boulder School for Condensed Matter and Materials Physics

Scanning Tunneling Microscopy & Spectroscopyof Correlated Electronic SystemsAli YazdaniDepartment of PhysicsPrinceton Universityhttp://wwwphy.princeton.edu/~yazdaniweb/Boulder Summer School on Condensed Matter PhysicsYazdani-Boulder 08 lectures

Why do we need local measurements?• Conventional wisdom in solid state physics: band theory• Past: Understanding things in momentum space is enough!• New wisdom?: for correlated or nanoscale systems this may not be enoughExamples:• Randomly doped systems are not spatially homogenous• Systems close to a transition may segregate in to different phases(ex: last conducting link in a metal-insulator transition)• Can learn about correlated system by study of their response to defects (impurities,vortices, boundaries)• “Fluctuating order”--search for “propensity” for organization of electrons• Complimenting spatially average measurements is also criticalYazdani-Boulder 08 lectures

Length Scales:• Inter-atomic distances: few Å• Electron wavelength: depending on density; “good metals” few Å, “Unconventionalmetals” about 10-15 Å, semiconductors 100-200 Å• Correlation lengths: conventional superconductors 100-1000 Å; unconventional onebelow 20 typically (size of a vortex or a defect state)• “Phase separation lengths”: depends on the model from 10s of Å to 1000 ÅYazdani-Boulder 08 lectures

Plan for LecturesLecture I• Brief history of tunneling: tunneling through insulating barriers• Basics of scanning tunneling microscopy• Some comments on construction of an STM• STM on simple metals--quantum interference of electronic states• STM on semiconductors--imaging and probing single dopants• STM on conventional superconductors--impurity effects in a BCS superconductorLecture II• STM on high-Tc superconductors• Local signatures of d-wave pairing• Quasi-particle Interference• Local Pairing above Tc and the phase diagram• Clues on the mechanism: electron-boson or not?Yazdani-Boulder 08 lectures

Leo EsakiIvar GiaeverShared Nobel Prize in Physics(with B. Josephson 1973)Yazdani-Boulder 08 lectures

Giaever Tunneling: Aluminum-oxide the key to tunneling1963Yazdani-Boulder 08 lectures

Giaever Tunneling: Aluminum-oxide the key to tunnelingPinhole free tunnel barrierYazdani-Boulder 08 lectures

Giaever Tunneling: Tunneling into a superconductorYazdani-Boulder 08 lectures

Giaever Tunneling: Tunneling into a superconductor (1963)Yazdani-Boulder 08 lecturesAl-AlOx-Pb junction: Pb goes superconducting at 7.2K

Basics of Tunneling• Giaever tunneling: conducting electrodes separated by an insulating barrier• Apply a voltage bias across the barrier to get a net tunneling current I• First consider elastic tunneling: electrons get across without change in E• Tunneling current depends on density of states (DOS) of the electrodes• If one of the electrodes has a simple DOS, we can use this technique to measurethe unknown DOS. (Except can not forget the influence of T)I(V, r ! ) = 4" 2" dE M(E) # tip(E) f (E)# 2 sample(E $ eV, r !++ %)(1$ f (E $ eV )) (, '$# tip(E)(1$ f (E))# sample(E $ eV, r ! *$+ &) f (E $ eV ))M 2 "e #z / z 0!Yazdani-Boulder 08 lecturesVery low T limit

Basics of Tunneling• Giaever tunneling: conducting electrodes separated by an insulating barrier• Apply a voltage bias across the barrier to get a net tunneling current I• First consider elastic tunneling: electrons get across without change in E• Tunneling current depends on density of states (DOS) of the electrodes• If one of the electrodes has a simple DOS, we can use this technique to measurethe unknown DOS. (Except can not forget the influence of T)I(V, r ! ) = 4" 2" dE M(E) # tip(E) f (E)# 2 sample(E $ eV, r !++ %)(1$ f (E $ eV )) (, '$# tip(E)(1$ f (E))# sample(E $ eV, r ! *$+ &) f (E $ eV ))M 2 "e #z / z 0I(V, ! r ) = 4" 2"+%&$%dE M(E) 2 # tip(E)# sample(E $ eV, ! r ) f (E) $ f (E $ eV )( )!Yazdani-Boulder 08 lecturesVery low T limit

Basics of Tunneling• Giaever tunneling: conducting electrodes separated by an insulating barrier• Apply a voltage bias across the barrier to get a net tunneling current I• First consider elastic tunneling: electrons get across without change in E• Tunneling current depends on density of states (DOS) of the electrodes• If one of the electrodes has a simple DOS, we can use this technique to measurethe unknown DOS. (Except can not forget the influence of T)I(V, r ! ) = 4" 2" dE M(E) # tip(E) f (E)# 2 sample(E $ eV, r !++ %)(1$ f (E $ eV )) (, '$# tip(E)(1$ f (E))# sample(E $ eV, r ! *$+ &) f (E $ eV ))M 2 "e #z / z 0I(V, ! r ) = 4" 2"+%&$%dE M(E) 2 # tip(E)# sample(E $ eV, ! r ) f (E) $ f (E $ eV )( )E F +V%I(V, r ! ) " M 2 dE# tip(E)# sample(E F$ eV, r ! )E F!Yazdani-Boulder 08 lecturesVery low T limit

Principles of Tunneling SpectroscopyA la J. Bardeen, Phys. Rev. Lett. 6, 57 (1960).E F +V%I(V, r ! ) " M 2 # tipdE# sample(E F$ eV, r ! )E F!In the limit of low temperature, theFermi functions can be replaced by stepfunctions. If the tip DOS and thetunneling matrix M are constant in theenergy range of interest, then thisexpression reduces to:dI(V,! dVr ) " M 2 # tip# sample(E F$ eV, r ! )So far consider elastic tunneling only!Yazdani-Boulder 08 lectures!

Vacuum Tunneling: Binning & Rohrer (IBM-1980)• Tunneling exponential with distance• In vacuum: order of magnitude I/Angstrom• With a tip perform local tunneling• First idea was to do local spectroscopy• Imaging was a secondary realizationYazdani-Boulder 08 lectures

Yazdani-Boulder 08 lectures

Yazdani-Boulder 08 lecturesThe First Scanning Tunneling Microscope

Commonly used piezo-electric element for an STM ScanHeadYazdani-Boulder 08 lectures

Various Coarse Approach MechanismPan WalkerBesoke/Bettle WalkerYazdani-Boulder 08 lectures

TipBasics of STM:Vacuum• Tunnel not from a macroscopic electrode butfrom a sharp tip• The barrier is vacuum• Since tunneling is exponential in distance--allcurrent happens with a tunneling cone under thetipcurrentSurface• If the tip is sharp, the spatial extent isroughly the height of the tip• Typical condition: 5-6 Å, 1V, you get a 1 nano-Amp of current (easy to measure with room tempelectrometer)Yazdani-Boulder 08 lectures

Block Diagram of an STMVibrationIsolationCurrentAmplifierSampleTipPiezoVoltageControlledEnvironmentBiasVoltageSystemControlYazdani-Boulder 08 lectures

Basics II: STM topography• The most typical use of the STM is to record a constant current image• A feedback loop adjusts the height of the tip to keep I constant• As another circuit scans the tip across an area (typically 100 Å)• Computer record and displays the trajectory of the tip• Constant-I topograph is a map of contours of constant DOS in vacuumTipTipVacuumTip Trajectory forconstant currentcurrentSurfaceYazdani-Boulder 08 lectures

Atomic Scale Imaging with STM• Binning & Rohrer realized how local tunneling can be usedas an atomic scale imaging tool• First example: Si 7X7 surface reconstructionFirst “STM Topograph”--Binning& Rohrer 1983Si (111) SurfaceYazdani-Boulder 08 lectures

Yazdani-Boulder 08 lecturesRohrer & BinnigIBM Lab in ZurichInvented STM in 1981Nobel Prize awarded 1986

Construction of an STM• Scanning with piezoelectric elements: 1A/V• Tips: “hard” metals such as W, Pt, Ir• Coarse (mm range) and fine motion (0.1um range) are separate• Need clean surfaces: UHV environment (10 -6 Torr about 1 monolayer/sec)• Need low vibrations: floating table, rigid construction, acoustic rooms• Need low electrical noise: Rf shielding, low noise high voltage amplification• Need to measure small currents: Large gain, low noise, electrometers• Most important of all you need the sample surface to cooperate!• It can be a pain to make all these work at the same time!Yazdani-Boulder 08 lectures

Scanning Tunneling Microscopy Laboratory:(1.5K

The schematic of a UHV low temperature STMLoad LockSputter GunAugerMass SpectrometerScanner AssemblyEvaporatorVibrationIsolationLEEDOpticalTableMicroscopeLiquid Helium DeWar and10 Tesla MagnetVacuum PumpsYazdani-Boulder 08 lectures

The schematic of a Variable Temperature UHV STM systemVacuum PumpsYazdani-Boulder 08 lectures

VT-STM HeadDesigned for highertemperatures• Thermal compensation• Compact design• Result :• Extremely low drift athightemperaturesYazdani-Boulder 08 lectures

Trouble with a movable vacuum tunnel junction:Yazdani-Boulder 08 lectures

Princeton Nanoscale Microscopy Lab:• Floating 30T slab of concrete supporting an acoustic/rf enclosure• For operation high resolution scanning probe microscopes• Outcome: better than 30ng of floor vibrationYazdani-Boulder 08lectures

STM on Simple MetalsElectron Waves & QuantumInterferenceYazdani-Boulder 08 lectures

Electron Waves:Surface waves onnoble metal surfaceCu(111)1000Å x 1000ÅYazdani-Boulder 08 lectures

Substrate: Au(111) on MicaReconstructedSurface &adsorbatesYazdani-Boulder 08 lecturesConstant current image, V=100 mV, I=90 pA1000 Å x 1000 Å

Simple Examples of Spectroscopy• Surface state on noble metal surfaces (Au, Cu, Ag);where bulk states are forbidden• Au(111) surface has a two-dimensional surface state• Measured previously with photoemission• STM spectroscopy can probe these statesBulk band structureYazdani-Boulder 08 lectures

Yazdani-Boulder 08 lecturesScattering from chemical impurities

Standing Waves in Simple Metals• Scattering from step edges and defect creates a situation for wave interference• At each energy electrons have different wavelength and hence a satisfy slightlydifferent interference conditiondI/dV maps Ag(111)500Å x 500ÅYazdani-Boulder 08 lectures500Å x 500Å

Standing Waves in Simple Metals• Scattering from step edges and defect creates a situation for wave interference• At each energy electrons have different wavelength and hence a satisfy slightlydifferent interference conditiondI/dV maps Ag(111)500Å x 500ÅYazdani-Boulder 08 lectures500Å x 500Å

Standing Waves in Simple Metals• Elastic scattering electron from k 1 to k 2allows mapping the Fermi Surface• A standing wave occur with Q=k1 - k2• At different energies different Q’sFourier Transform of the dI/dV maps Ag(111)STM & ARPES E(!) forAu111Yazdani-Boulder 08 lectures

Standing Waves in Simple Metals• Elastic scattering electron from k 1 to k 2allows mapping the Fermi Surface• A standing wave occur with Q=k1 - k2• At different energies different Q’sFourier Transform of the dI/dV maps Ag(111)STM & ARPES E(!) forAu111Yazdani-Boulder 08 lectures

Scattering of Electrons from a Hard WallYazdani-Boulder 08 lectures


Particle in a boxSurface waves : states that decay into the bulk of the sampleAdsorbates at 4K can be used to confine these states into artificial boxesYazdani-Boulder 08 lecturesExample: Iron atom corrals onCu(111) Crommie and Eigler1992-3

Spectroscopy Fabrication of of a device: particle Quantum in a box Corrals statesIron atom corrals on Cu(111)Yazdani-Boulder 08 lecturesCrommie and Eigler- 1992-93Particle in a box states.Complete description by two quantum numbers

Spectroscopy Fabrication of of a device: particle Quantum in a box Corrals statesIron atom corrals on Cu(111)Yazdani-Boulder 08 lecturesCrommie and Eigler- 1992-93Particle in a box states.Complete description by two quantum numbers

STM on SemiconductorsImaging Single DopantsYazdani-Boulder 08 lectures

STM on GaAs (110) surface•Easily cleaved (110) surface—exposed in UHV•Simple buckling of the surface bonds•Ga or As atoms via empty or filled states•STM can be used to image individual acceptors &donorsGa atoms on GaAs surfaceEmpty states, +1.6V100Å x 100Å[1-10][001]AsGa

STM on GaAs (110) surface•Easily cleaved (110) surface—exposed in UHV•Simple buckling of the surface bonds•Ga or As atoms via empty or filled states•STM can be used to image individual acceptors &donorsGa atoms on GaAs surfaceEmpty states, +1.6V100Å x 100Å[1-10][001]AsGaAs atoms on GaAs surfaceFilled States, -1.6V100Å x 100Å

STM on GaAs (110) surface•Easily cleaved (110) surface—exposed in UHV•Simple buckling of the surface bonds•Ga or As atoms via empty or filled states•STM can be used to image individual acceptors &donorsGa atoms on GaAs surfaceEmpty states, +1.6V100Å x 100ÅGa atoms on GaAs surfaceEmpty states, +1.6V30Å x 30Å[1-10][001]AsGaAs atoms on GaAs surfaceFilled States, -1.6V100Å x 100Å

STM on GaAs (110) surface•Easily cleaved (110) surface—exposed in UHV•Simple buckling of the surface bonds•Ga or As atoms via empty or filled states•STM can be used to image individual acceptors &donorsGa atoms on GaAs surfaceEmpty states, +1.6V100Å x 100ÅAs atoms on GaAs surfaceFilled States, -1.6V30Å x 30Å[1-10][001]AsGaAs atoms on GaAs surfaceFilled States, -1.6V100Å x 100Å

STM on GaAs (110) surface•Easily cleaved (110) surface—exposed in UHV•Simple buckling of the surface bonds•Ga or As atoms via empty or filled states•STM can be used to image individual acceptors &donorsAs atoms on GaAs surfaceFilled States, -1.6V30Å x 30Å[1-10][001]AsGaSi dopant in n-typeGaAsFilled states, -2 VZn dopants in p-typeGaAsEmpty states, +1.5 V

Substrate: n-type GaAs(110) Single Si-donorsFeesntra et al 2002Conduction bandValance bandSi Gae -E fSTMTipYazdani-Boulder 08 lectures

Substrate: n-type GaAs(110) Single Si-donorsFeesntra et al 2002Yazdani-Boulder 08 lectures

High-Temperature Ferromagnetism inGaAs with Mn doping• Mn-doping makes GaAs ferromagnetic• Mn contributed spins & holes• Mn in Ga site an acceptor• Holes make GaAs both conducting andcouples the spins• Low T-MBE various defects presentReview by MacDonald et al, Nat. Mat. (2005)

High-Temperature Ferromagnetism inGaAs with Mn doping• Mn-doping makes GaAs ferromagnetic• Mn contributed spins & holes• Mn in Ga site an acceptor• Holes make GaAs both conducting andcouples the spins• Low T-MBE various defects presentReview by MacDonald et al, Nat. Mat. (2005)

Mn-Acceptor State in GaAs (Kitchen et al. 2006)Yazdani-Boulder 08 lectures• Mn modifies DOS of neighboring atoms inducing changes to valence band• Modifications are anisotropic, modifying strongly along directions• Large in-gap acceptor level shows wavefunction of highly anisotropic characterImage of Mn’s acceptor state4.0Å0Empty states, 40Å 2Kitchen, A. Richardella, J.-M. Tang, M. E. Flatté, A. Yazdani, Nature 442, 436 (2006)

Mn-Acceptor State in GaAs• Mn modifies DOS of neighboring atoms inducing changes to valence band• Modifications are anisotropic, modifying strongly along directions• Large in-gap acceptor level shows wavefunction of highly anisotropic characterH = H 0 + V• Bulk calculation viewed inthe 110 direction• Tang et al PRL (2004)Yazdani-Boulder 08 lectures

X-STM of Ga1-xMnxAs Heterostructures(Ga,Mn)As (200nm)p-type GaAs buffer (150nm)n-type GaAs buffer (150nm)n-type GaAs substrate150!m




GaAs/Ga1-xMnxAs Hetrostructures• 1.5% doped sample• Tc~ 25K as grownGrownEmpty states (+1.6V )at UCSB

GaAs/Ga1-xMnxAs Hetrostructures• 1.5% doped sample• Tc~ 25K as grownGrownEmpty states (+1.6V )Mn doped GaAsx=1.5%P-typeGaAsat UCSB

dI / dV measurements acrossGaAs / Mn 0.015Ga 0.985As JunctionValence BandIn-gap statesConduction BandEnergyDistance (Å)

1300Å

Yazdani-Boulder 08 lecturesSTM on Superconductors

Giaever Tunneling:Planar Tunneling into a superconductor (1963)Yazdani-Boulder 08 lectures

BCS Density of StatesYazdani-Boulder 08 lectures

BCS Density of StatesYazdani-Boulder 08 lectures

Quantum Tunneling of Electrons as a probe ofsuperconductivity & pairing:Planar Tunneling into a superconductor Giaever (1963)"

Quantum Tunneling of Electrons as a probe ofsuperconductivity & pairing:Planar Tunneling into a superconductor Giaever (1963)

Quantum Tunneling of Electrons as a probe ofsuperconductivity & pairing:Planar Tunneling into a superconductor Giaever (1963)2"(0)k BT C= 3.5 # 4.3

Tunneling Spectroscopy and thePairing InteractionYazdani-Boulder 08 lectures

Electron Boson Coupling & FrequencyDependent of the Pairing Interaction:Ns(V)/Nn is a function of Vand can be less than 1A simple model:• # must have some $dependence• #($)= #R($) + i #I($)Scalapino (1969)


Application of STM to Superconductors• Probing superconductivity on the nanoscale• Imaging defects and vortices• Can we detect the influence of a single impurity?• Impurities in conventional s-wave superconductors• High-Tc Superconductors: defects, inhomogeneity, phase diagram,clues to the mechanismYazdani-Boulder 08 lectures

STM Spectroscopy of a SuperconductorNiobium Diselenide(NbSe 2 )Yazdani-Boulder 08 lecturesH.F. Hess et al. Phys. Rev. Lett. 64, 2711 (1990).

STM Spectroscopy of Flux Vortices in NbSe 2H.F. Hess et al. Phys. Rev. Lett. 64, 2711 (1990).Localized states are observed at the center of vortices in spectroscopy measurementsYazdani-Boulder 08 lectures

Yazdani-Boulder 08 lecturesH.F. Hess et al.


PURE S-WAVE BCS SUPERCONDUCTORCooper pairDDfQuasiparticle excitation spectrumES-WAVE SUPERCONDUCTOR WITH MAGNETIC IMPURITYE = -J S sexchange impurity conductionelectronWeak and staticmagnetic impurityTcExchange interaction breaks pairs!Impurity ConcentrationYazdani-Boulder 08 lectures

Impurity-Induced States in SuperconductorsShiba 1968, Yu 1965, Rusinov 1969S-wave SuperconductorJS! EnergyTotal (Not Local) Density of Electronic StatesSee Review by Balatsky et al.arXiv:cond-mat/0409474Yazdani-Boulder 08 lecturesEvidence for these states from Thermodynamicand Tunneling Measurements:D. Ginsburg in the 80’s.

Nb(110) with Magnetic Impurities200Å x 200Å AreaYazdani-Boulder 08 lecturesA. Yazdani et al., Science 275, 1767 (1997)

STM Spectra: Resolution limited by temperature1.5dI/dV [10 7 # $1 ]10.5BCS Fit"=1.48 meVT= 3.85K0-0.008 -0.004 0 0.004 0.008Yazdani-Boulder 08 lecturesVoltage [V]A. Yazdani et al., Science 275, 1767 (1997)

Yazdani-Boulder 08 lecturesA. Yazdani et al., Science 275, 1767 (1997)

Tunneling Spectra on Nb near a magnetic defectsYazdani-Boulder 08 lectures

Yazdani-Boulder 08 lecturesMn on Nb(110)

STM Spectra on&off the Mn Atom1.41.2dI/dV [10 7 # $1 ]10.80.60.4Mn in Nb:Large Spin: No Kondo effect,i.e. T k

Shiba State Localized Near Mn Atom1.2r=14!Difference dI/dV [10 7 # $1 ]A. Yazdani et al., Science 275, 1767 (1997)0.80.40Offsetr=12!r=9!r=7!r=5!r=3!r=0!-0.008 -0.004 0 0.004 0.008Voltage [V]Yazdani-Boulder 08 lectures

1.2Shiba State in the Gap near Gd AtomGd in Nb:Difference dI/dV [10 7 # $1 ]1r=10!0.8r=8!0.6r=6!0.4r=4!0.2r=2!0r=0!-0.2-0.008 -0.004 0 0.004 0.008Voltage [V]Large Spin: No Kondo effect,A. Yazdani et al., Science 275, 1767 (1997)i.e. T k

Shiba State nearGd Atoms on NbYazdani-Princeton 06 lectures

Yazdani-Boulder 08 lecturesA. Yazdani et al., Science 275, 1767 (1997)

What happens near a magnetic atom?! A Simple ViewAttractive Potential! Unpaired electron can!t go far in a" " superconductorWave function of anunpaired electronLocal Theory of Shiba state in s-wave superconductors:Flatte and Byers, PRL 78, 3761 (1997); PRB 56, 11213 (1997)Solkola, Balatsky, and Shrieffer, PRB 55, 12648 (1997)Yazdani-Princeton 06 lectures

Bound state wavefunction"(r) 20.2J=0.2Weak Scattering"(r) 20.2J=0.76E FStrong Scattering0.10.1Electron PartHole Part!0Electron partHole partA. Yazdani et al., Science 275, 1767 (1997)Yazdani-Boulder 08 lectures

A. Yazdani et al., Science 275, 1767 (1997)Yazdani-Boulder 08 lectures

SummaryLecture I• Brief history of tunneling: tunneling through insulating barriers• Basics of scanning tunneling microscopy• Some comments on construction of an STM• STM on simple metals--quantum interference of electronic states• STM on semiconductors--imaging and probing single dopants• STM on conventional superconductors--impurity effects in a BCS superconductorOther basic things I could have talk about:spin polarized measurementsInelastic Tunneling Spectroscopy79

STM - Boulder School for Condensed Matter and Materials Physics

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