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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 - PowerPoint PPT Presentation
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Wittenberg 2: Tunneling Spectroscopy
Andreas Heinrichheinrich@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 & SpectroscopySTM Imaging & Spectroscopy
Sample
I , Rz-se
rvo
~1nm
Keep I constant V
Tip
I +Iac, R
V+Vac
turn off servo add Vac
measure dI/dV
σ
SampleTip
Barrier
STM SpectroscopySTM Spectroscopy
V
dI/dV
σe
V
LDOS
eVEF
EF
V
LDOS
M.F. Crommie, C.P. Lutz and D.M. Eigler, Nature 363, 524 (1993)
Standing Waves on the Cu (111) Surface
Shockley-Type Surface States on Cu Shockley-Type Surface States on Cu (111)(111)
Metal Vacuum
Z
Gap in bulk band structure in the <111> direction Surface breaks symmetry resulting in localized states
‘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
0 2 4 6 8 10 120
0.1
0.2
0.3
0.4
0.5
X[nm]Z[Å]
lateral [nm]ve
rtic
al [
Å]
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 × 20nmR = 27 unit cellsV = 10mVI = 1nA
Corral Spectroscopy
Spectra in circle center From I/V to dI/dV Particle in a box
-400 -200 0 200 400-4-3-2-101234
Cur
rent
[nA
]
Voltage [mV]
-400 -200 0 200 400-20
0
20
40
60
80
100
dI/d
V [a
.u.]
Voltage [mV]
×
QM: 1d Particle in a Box
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
for 0 < z < a zEz
dz
d
m nnn 2
22
2
Schroedinger:
zcCzcCzn 2211 cossin Ansatz:
za
nAzn
sin with n=1,2,3,…Solution:
22
22
2n
maEn
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…
-0.4 -0.2 0.0 0.2 0.40
1
2
3
4
5
dI/d
V
Voltage [V]
Identifying States
s-states in circle l=0 states are peaked in center n counts number of nodes
-400 -200 0 200 400-20
0
20
40
60
80
100
dI/d
V [a
.u.]
Voltage [mV]
-0.4 -0.2 0.0 0.2 0.40
1
2
3
4
5
dI
/dV
Voltage [V]
Off-Center Spectroscopy
-0.4 -0.2 0.0 0.2 0.40
1
2
3
4
5
dI/d
V
Voltage [V] 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
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 SpectrumSuperconductor Excitation Spectrum
21
22Re
E
EDOSBCS
Niobium
Iridium
How to get T<4K?How to get T<4K?
l-3HeVacuum
STM
UHV
3He pump
P≈0.01Torr
0.35K
0.5K
4.2K
l-3He
l-4He
H
UHV Chamber3He Exhaust to Pump
3He @ 2 atm
l-4He
7T Split coil magnet
Vacuum
3He expansion
Counter flow heat exchanger
Dewar
STM
0.5 K, 7T 0.5 K, 7T UHV STMUHV STM
Shutter
Vibration free Joule-Thompson 3He refrigerator
Schematic of Dewar
Niobium BCS ThermometerNiobium BCS Thermometer
-5 -4 -3 -2 -1 0 1 2 3 4 50
1
2
3
dI/d
V [
a.u
.]
Voltage [mV]
calculated curve T=0.5K measured curve
temperature of tip is really T=0.5K radio frequency noise is less than 0.5K Niobium
Iridium
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)
IInelastic nelastic EElectron lectron TTunneling unneling SSpectroscopy (pectroscopy (IETSIETS))
+inelastic σie
elastic σe
SampleTip
Barrier
V
dI/dV
σe σe+ σie
σe
V
LDOS
Vmode
IETS of CO on Cu (111)IETS of CO on Cu (111)
4meV
CO
35meV
CO
B.C. Stipe et al. Science 280, 1732 (1998).
IETS Mapping of C IsotopesIETS Mapping of C Isotopes
Topograph dI/dV image11nm×11nm, 513 CO
I=3.55nA, V=35.5mV, VAC=1.5mVRMS
12C16O13C16O
Isotope Controlled AssemblyIsotope Controlled Assembly
Topograph dI/dV imageI=3.55nA, V=35.5mV, VAC=1.5mVRMS
Isotope GraffitiIsotope Graffiti
4.6nm×5.8nm, 160 CO
I=3.55nA, V=35.5mV, VAC=1.5mVRMS
Topograph dI/dV image
Timing Linked ChevronsTiming Linked Chevrons
0
1
Manualmove
5
2
3
4
12C16O13C16O
Only 1 molecule hops Mixed isotope cascade?
Mixed-Isotope CascadeMixed-Isotope Cascade
13C16O12C16O
13C16O
dI/dV image12C16O13C16O
Tunneling from Excited StateTunneling from Excited State
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/sA 13C 105.4/s
TkEARR
BQTtotal exp
A=1012 /s × 10-7
New Vibrational Mode in New Vibrational Mode in Chevron?Chevron?
x
Stabilized chevron
Continuous 3 overlayerCenter of stabilized chevron
Vibrational Modes in Circle
flat top spectrum ± 4mV vibrational mode
× -150 -100 -50 0 50 100 15020
40
60
80
100
120
dI/d
V [a
.u.]
Voltage [mV]
-20 -15 -10 -5 0 5 10 15 20
80
90
100
110
dI/d
V [a
.u.]
Voltage [mV]
-400 -200 0 200 400-20
0
20
40
60
80
100
dI/d
V [a
.u.]
Voltage [mV]
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)
A non-magnetic surface
IETS of Magnetic Atoms IETS of Magnetic Atoms
Magnetic atom
A non-magnetic tip
H An externally applied magnetic field to split the spin states of
the atom
Hg BE
H
e
e + ie
=
dI/d
V
Bias Voltage
HgΤk BΒ
5 kBT
eV=gμBH
g=2: T=1Kg=2: T=1K B=1TB=1T
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