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 Measuring the g-value of single atoms H2 physisorbed on Cu (111)

STM Imaging & Spectroscopy Tip Keep I constant V+Vac V z-servo turn off servo add Vac measure dI/dV ~1nm I +Iac, R I , R also mention meaning of R (i.e. moving in 0.1nm = Rx10, Ix10 or Vx10) Sample

STM Spectroscopy Barrier V V σ Tip Sample V dI/dV σe EF eV EF LDOS let me now take you on a quick tour of vibrational spectroscopy normal channel is elastic, density of final states add inelastic channel at all energies that are high enough

Standing Waves on the Cu (111) Surface M.F. Crommie, C.P. Lutz and D.M. Eigler, Nature 363, 524 (1993) Tell audience this is an STM image of a copper surface Comment abount "images of a new world": A world which was unknown but somehow is intimate in the sense that it is just a close up of our everyday world. It is us.

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

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

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

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

Quantum Corral Same corral built with CO  more stable lateral [nm] vertical [Å] 20nm × 20nm R = 27 unit cells V = 10mV I = 1nA 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

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

QM: 1d Particle in a Box with n=1,2,3,… Schroedinger: for 0 < z < a Schroedinger: Ansatz: with n=1,2,3,… Solution: 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

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

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…

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

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

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)

Superconductor Excitation Spectrum Niobium Iridium

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

Schematic of Dewar 0.5 K, 7T UHV STM UHV Chamber Dewar 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

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

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)

Inelastic Electron Tunneling Spectroscopy (IETS) Barrier V LDOS elastic σe + inelastic σie Tip Sample let me now take you on a quick tour of vibrational spectroscopy normal channel is elastic, density of final states add inelastic channel at all energies that are high enough dI/dV σe+ σie σe σe V Vmode

B.C. Stipe et al. Science 280, 1732 (1998). IETS of CO on Cu (111) here is an example of vibrational excitations CO has 4 modes, but we only see 2 modes here frustrated translation at 4meV and frustrated rotation at 35meV different carbon isotopes show identical curves except for the frustrated rotation 4meV C O 35meV C O B.C. Stipe et al. Science 280, 1732 (1998).

IETS Mapping of C Isotopes 12C16O 13C16O show only the frustrated rotation around 35meV clear shift in dI/dV use that shift to image at 35meV, regular array find natural composition of carbon Topograph dI/dV image 11nm×11nm, 513 CO I=3.55nA, V=35.5mV, VAC=1.5mVRMS

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

Isotope Graffiti Topograph dI/dV image 4.6nm×5.8nm, 160 CO take it one step further build structures with controlled isotopes start with array of random distribution image and rearrange a couple of times so we have absolute control over the carbon isotope in the cascades Topograph dI/dV image 4.6nm×5.8nm, 160 CO I=3.55nA, V=35.5mV, VAC=1.5mVRMS

Timing Linked Chevrons 12C16O 13C16O 1 Manual move 5 2 3 4 we were interested in understanding the hopping mechanism in cascades can’t image continuously, tip influence to start the cascade one atom is moved, then tip is parked wait for cascade to finish and repeat Only 1 molecule hops Mixed isotope cascade?

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

Tunneling from Excited State A=1012 /s × 10-7 Shared activation energy E 9.5 meV A 12C 105.8/s A 13C 105.4/s Great fit at all T Prefactor is product of attempt rate and tunnel probability Schematic: add chevron vs root 3 as symbols and add final state

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

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

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 submitted: A.J. Heinrich et. al (2004) H2 physisorbed on Cu (111) submitted: J.A. Gupta et. al (2004)

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