Wittenberg 2: Tunneling Spectroscopy

Wittenberg 2: Tunneling Spectroscopy

Andreas [email protected]

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




Excitation spectrum of superconductor





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









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



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

Documents

Wittenberg 2: Tunneling Spectroscopy