1. Wittenberg 2: Tunneling Spectroscopy
Andreas Heinrich

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
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

4. 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

5. 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.

6. 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

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 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

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

12. 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

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
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

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
Niobium
Iridium

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

20. Schematic of Dewar 0.5 K, 7T UHV STM UHV Chamber Dewar
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
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)
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

24. 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).

25. 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

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
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

28. 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?

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

30. Tunneling from Excited State
A=1012 /s × 10-7
Shared activation energy
E meV
A 12C /s
A 13C /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

31. New Vibrational Mode in Chevron?
Continuous 3 overlayer
Center of stabilized chevron x
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 atoms submitted: A.J. Heinrich et. al (2004)
H2 physisorbed on Cu (111) submitted: J.A. Gupta et. al (2004)

34. 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