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Wittenberg 2: Tunneling Spectroscopy

Wittenberg 2: Tunneling Spectroscopy. Andreas Heinrich heinrich@almaden.ibm.com. Wittenberg 2: Spectroscopy. Spectroscopy with STM Example: quantum corral Example: BCS superconductor Inelastic Tunneling Spectroscopy CO on Cu(111): vibrational spectroscopy

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Wittenberg 2: Tunneling Spectroscopy

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  1. Wittenberg 2: Tunneling Spectroscopy Andreas Heinrich heinrich@almaden.ibm.com

  2. Wittenberg 2: Spectroscopy • Spectroscopy with STM • Example: quantum corral • Example: BCS superconductor • Inelastic Tunneling Spectroscopy • CO on Cu(111): vibrational spectroscopy • Measuring the g-value of single atoms • H2 physisorbed on Cu (111)

  3. STM Imaging & Spectroscopy z-servo ~1nm Tip Keep I constant V V+Vac turn off servo add Vac measure dI/dV I , R I +Iac, R Sample

  4. V V σ eV LDOS dI/dV σe V STM Spectroscopy Barrier EF EF LDOS Sample Tip

  5. Standing Waves on the Cu (111) Surface M.F. Crommie, C.P. Lutz and D.M. Eigler, Nature363, 524 (1993)

  6. Vacuum Metal Z Shockley-Type Surface States on Cu (111) • Gap in bulk band structure in the <111> direction • Surface breaks symmetry resulting in localized states • ‘Free’ 2-d electron gas at the surface

  7. Spectroscopy of Surface State • Compare spectra of step edge vs. terrace • Step in conductance at V = -0.45V • Bottom of band is close to EF

  8. Dispersion Relation • Scattering from step edge • Energy resolved wavelength • Free electron gas • Modified electron mass • meff = 0.38 me, λF = 30 Å

  9. Construction of Circle • Fe on Cu(111) • 48 atom circle

  10. Quantum Corral vertical [Å] lateral [nm] • Same corral built with CO  more stable • ‘topograph’ measures purely electronic structure: orbits • peaked in center for l=0 state – ‘s-like’ • 71Å radius circle 20nm × 20nm R = 27 unit cells V = 10mV I = 1nA

  11. Corral Spectroscopy • Spectra in circle center • From I/V to dI/dV • Particle in a box ×

  12. QM: 1d Particle in a Box Schroedinger: for 0 < z < a Ansatz: Solution: with n=1,2,3,… • Infinite walls at z=0 and z=a • Schroedinger equation between z=0 and z=a • Wavefunction is zero outside for z<0 and z>a • The energy spacing is non-linear in 1d

  13. QM: 2d Particle in a Circle • 2d solutions are Bessel functions • l=0 and l=1 are energy separated • l=2 is same energy as l=0… EF

  14. Eigenstates of Circle • Fit using l=0,2,7 • The surprising details of the spectrum can be reproduced • High n’s and l’s contribute…

  15. Identifying States • s-states in circle • l=0 states are peaked in center • n counts number of nodes

  16. Off-Center Spectroscopy • higher l states contribute to the spectrum • lx and ly do not have fixed phase, no nodes in angular pattern center of corral 10 Å off center

  17. Wittenberg 2: Spectroscopy • Spectroscopy with STM • Example: quantum corral • Excitation spectrum of superconductor • Inelastic Tunneling Spectroscopy • CO on Cu(111): vibrational spectroscopy • Measuring the g-value of single atoms • H2 physisorbed on Cu (111)

  18. Superconductor Excitation Spectrum Iridium Niobium

  19. How to get T<4K? 3He pump P≈0.01Torr UHV l-4He 4.2K STM 0.5K l-3He l-3He 0.35K Vacuum

  20. Schematic of Dewar UHV Chamber 3He @ 2 atm 3He Exhaust to Pump 0.5 K, 7T UHV STM Dewar Vibration free Joule-Thompson 3He refrigerator Counter flow heat exchanger l-4He Shutter Vacuum 7T Split coil magnet 3He expansion H STM

  21. Niobium BCS Thermometer Iridium Niobium • temperature of tip is really T=0.5K • radio frequency noise is less than 0.5K

  22. Wittenberg 2: Spectroscopy • Spectroscopy with STM • Example: quantum corral • Excitation spectrum of superconductor • Inelastic Tunneling Spectroscopy • CO on Cu(111): vibrational spectroscopy • Measuring the g-value of single atoms • H2 physisorbed on Cu (111)

  23. Inelastic Electron Tunneling Spectroscopy (IETS) V LDOS Barrier elasticσe +inelasticσie Sample Tip dI/dV σe+ σie σe σe V Vmode

  24. IETS of CO on Cu (111) 35meV 4meV O O C C B.C. Stipe et al.Science280, 1732 (1998).

  25. IETS Mapping of C Isotopes 12C16O 13C16O Topograph dI/dV image 11nm×11nm, 513 CO I=3.55nA, V=35.5mV, VAC=1.5mVRMS

  26. Isotope Controlled Assembly Topograph dI/dV image I=3.55nA, V=35.5mV, VAC=1.5mVRMS

  27. Isotope Graffiti Topograph dI/dV image 4.6nm×5.8nm, 160 CO I=3.55nA, V=35.5mV, VAC=1.5mVRMS

  28. Timing Linked Chevrons Manual move 12C16O 13C16O 0 1 2 3 4 5 • Only 1 molecule hops • Mixed isotope cascade?

  29. Mixed-Isotope Cascade 13C16O 12C16O 13C16O dI/dV image 12C16O 13C16O

  30. Tunneling from Excited State A=1012 /s × 10-7 • Great fit at all T • Prefactor is product of attempt rate and tunnel probability Shared activation energy E 9.5 meV A 12C 105.8/s A 13C 105.4/s

  31. New Vibrational Mode in Chevron? x Continuous 3 overlayer Center of stabilized chevron Stabilized chevron

  32. Vibrational Modes in Circle • flat top spectrum • ± 4mV vibrational mode ×

  33. Wittenberg 2: Spectroscopy • Spectroscopy with STM • Example: quantum corral • Excitation spectrum of superconductor • Inelastic Tunneling Spectroscopy • CO on Cu(111): vibrational spectroscopy • Measuring the g-value of single atomssubmitted: A.J. Heinrich et. al (2004) • H2 physisorbed on Cu (111)submitted: J.A. Gupta et. al (2004)

  34. An externally applied magnetic field to split the spin states of the atom H 5 kBT re + rie r= dI/dV re Bias Voltage B=1T g=2: T=1K IETS of Magnetic Atoms A non-magnetic tip Magnetic atom eV=gμBH A non-magnetic surface

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