Wittenberg 2: Tunneling Spectroscopy

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Wittenberg 2 Tunneling Spectroscopy
Andreas Heinrich heinrich_at_almaden.ibm.com
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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)

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STM Imaging Spectroscopy
Tip
Keep I constant
V
VVac

• turn off servo
• add Vac
• measure dI/dV

I , R
I Iac, R
Sample
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STM Spectroscopy
Barrier
EF
EF
LDOS
Sample
Tip
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Standing Waves on the Cu (111) Surface
M.F. Crommie, C.P. Lutz and D.M. Eigler, Nature
363, 524 (1993)
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Shockley-Type Surface States on Cu (111)

• Gap in bulk band structure in the lt111gt direction
• Surface breaks symmetry resulting in localized
  states

• Free 2-d electron gas at the surface

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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

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Dispersion Relation

• Scattering from step edge
• Energy resolved wavelength
• Free electron gas
• Modified electron mass
• meff 0.38 me, ?F 30 Å

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Construction of Circle

• Fe on Cu(111)
• 48 atom circle

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Quantum Corral
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 l0 state s-like
• 71Å radius circle

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Corral Spectroscopy

• Spectra in circle center
• From I/V to dI/dV
• Particle in a box

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QM 1d Particle in a Box

• Infinite walls at z0 and za
• Schroedinger equation between z0 and za
• Wavefunction is zero outside for zlt0 and zgta
• The energy spacing is non-linear in 1d

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QM 2d Particle in a Circle

• 2d solutions are Bessel functions
• l0 and l1 are energy separated
• l2 is same energy as l0

EF
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Eigenstates of Circle

• Fit using l0,2,7
• The surprising details of the spectrum can be
  reproduced
• High ns and ls contribute

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Identifying States

• s-states in circle
• l0 states are peaked in center
• n counts number of nodes

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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

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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)

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Superconductor Excitation Spectrum
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How to get Tlt4K?
3He pump P0.01Torr
UHV
l-4He
4.2K
STM
0.5K
l-3He
l-3He
0.35K
Vacuum
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Schematic of Dewar
UHV Chamber
3He _at_ 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
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Niobium BCS Thermometer

• temperature of tip is really T0.5K
• radio frequency noise is less than 0.5K

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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)

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Inelastic Electron Tunneling Spectroscopy (IETS)
Barrier
elastic se
inelastic sie
Sample
Tip
dI/dV
se sie
se
se
V
Vmode
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IETS of CO on Cu (111)
B.C. Stipe et al. Science 280, 1732 (1998).
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IETS Mapping of C Isotopes
Topograph
dI/dV image
11nm11nm, 513 CO I3.55nA, V35.5mV, VAC1.5mVRMS
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Isotope Controlled Assembly
Topograph
dI/dV image
I3.55nA, V35.5mV, VAC1.5mVRMS
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Isotope Graffiti
Topograph
dI/dV image
4.6nm5.8nm, 160 CO I3.55nA, V35.5mV,
VAC1.5mVRMS
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Timing Linked Chevrons

• Only 1 molecule hops
• Mixed isotope cascade?

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Mixed-Isotope Cascade
13C16O
12C16O
13C16O
dI/dV image
12C16O 13C16O
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Tunneling from Excited State
A1012 /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

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New Vibrational Mode in Chevron?
Continuous ?3 overlayer Center of stabilized
chevron
Stabilized chevron
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Vibrational Modes in Circle

• flat top spectrum
• 4mV vibrational mode

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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)

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IETS of Magnetic Atoms
A non-magnetic tip
Magnetic atom
eVgµBH
A non-magnetic surface