Probing electronic interactions using electron tunneling
description
Transcript of Probing electronic interactions using electron tunneling
![Page 1: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/1.jpg)
Probing electronic interactions using electron tunneling
Pratap Raychaudhuri
![Page 2: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/2.jpg)
Electrons in a solidFormation of energy bands
E1
E2
E3
Free atoms
Solid
Energy
Individual levelsto nearly continuous bands
Allowed energy for an electron InsulatorsMetals
![Page 3: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/3.jpg)
Electrons in a metal
Energy
~1-50meV
eV
Give rise to electrical
conduction
Superconductivity
(Nb,Pb,Al,Sn)
Novel quantum phenonmenon
Quantum criticality, Unconventional superconductivity
EF
Understanding the nature of electrons close to EF
Itinerant
Magnetism
(Fe,Co,Ni)
Quantum Hall effect
2D systems
V
![Page 4: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/4.jpg)
Leo Esaki, b. 1925Nobel Prize, 1973
Tunneling in Solid State systems
The award is for their discoveries regarding tunneling phenomena in solids. Half of the prize is divided equally between Esaki and Giaever for their experimental discoveries regarding tunneling phenomena in semiconductors and superconductors respectively. The other half is awarded to Josephson for his theoretical predictions of properties in a supercurrent flowing through a tunnel barrier, in particular the phenomena generally known as the Josephson effects.
Ivar Giaever, b. 1929Nobel Prize, 1973
Brian Josephson, b. 1940Nobel Prize, 1973
![Page 5: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/5.jpg)
Electron tunneling in solids
N1 N2
T(12) e-kd N1N2d(E1-E2)
d
Metal A Insulator Metal B
EF+d EF-d
E
Metal 1Metal 2
Electrons close to the Fermi level can tunnel from one metal to another
![Page 6: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/6.jpg)
Electron tunneling does happen!!!
Fermi Energy(EF)
IntrinsicSemiconductor
n-dopedSemiconductor
p-dopedSemiconductor
Conduction band
Valence band
Heavily doped: >1019 cm-3
Leo Esaki, b. 1925Nobel Prize, 1973
![Page 7: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/7.jpg)
The Esaki (Tunnel) dioden-doped p-doped
Potential barrier
n-doped p-doped
Potential barrier
No Bias Reverse bias: Electrons will tunnel from p-doped to n-
doped region
![Page 8: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/8.jpg)
The Esaki (Tunnel) diode: Forward bias
n-doped p-doped
Potential barrier
Small forward bias
Electrons will tunnel from n-doped to p-doped region
Intermediate forward bias
No states available to tunnel to
Electrons will tunnel from n-doped to the conduction band of p-doped
region
Large forward bias
0dIdVRd
![Page 9: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/9.jpg)
How to use tunneling as a spectroscopic probe?
Ivar Giaever, b. 1929Nobel Prize, 1973
What do we want to know about electrons?
E
N(E)
The number of electronic states available in an energy interval E to E+dE: Density of states: N(E)
Free electronsE
N(E)
Free electrons+ periodic potential
Bandgap
![Page 10: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/10.jpg)
Principle of Tunneling spectroscopy as an energy resolved probe
( ( ( (
dEEfeVEfeVENENTAI 21
2
Metal A Insulator Metal B
EF
EFV=0
V>0
V<0
In a realistic situation V is limited to few hundred mV
In simple metals such as Cu, Ag, Au, Al, N(E) is almost constant over this range
( ( ( ( ( ( eVKNeVNNTAdVdIVGdEENNTAI
eV
1122
012
2 0 0
![Page 11: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/11.jpg)
Superconductivity
The resistance is as close to zero as measurable
K Onnes (1911)
Perfect diamagnet:Meissner –Ochsenfeld effect
![Page 12: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/12.jpg)
Superconductors
k
-kk -k
kBTc ~1-20meVT<Tc
2D
E
T>Tc
EF
E
T<TcNormal state DOS
Superconducting state DOS
Energy
N(E)3-4 meV
D 22Re
E
E
x0~5-50nm
![Page 13: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/13.jpg)
Tunneling: ExperimentFabrication of a tunnel junction
Step 1: Deposit a metal such as Al, Pb, Nb which forms native surface oxide
Step 2: The surface of the metal is oxidized through controlled exposure to air
Step3: Deposit the counter-electrode
Step 4: Put gold pads for electrical contacts
Tunnel junction formed here
![Page 14: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/14.jpg)
Tunneling measurement
I
V
Differential conductance measurement
Current: I=Idc+Iacsinwt
Voltage: Vdc+Vacsinwt
d.c. bias V=Vdc
G(V)=dI/dVIac/Vac
Advantage of this technique:
Direct measurement of differential conductance
Vac can be measured with a lock-in amplifier which greatly improves the sensitivity
![Page 15: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/15.jpg)
Tunneling spectroscopy in superconductorsNormal metal/Superconductor tunneling
-6 -4 -2 0 2 4 6
0
1
2
3
4
5T = 0 K
Z = 3
G(V
)/Gn
V (mV)
VCalculated conductance Vs voltage
2D
-6 -4 -2 0 2 4 60.0
0.3
0.6
0.9
1.2
1.5
dI/d
V (
1
V (mV)
2.5K4K5.5K8.5K10 K11.5K12.9K14.4K15K
NbN/I/AgMadhavi Chand
![Page 16: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/16.jpg)
Interactions of electrons with other excitations
Phonon density of states
-10 -5 0 5 100.0
0.4
0.8
1.2
1.6
2.21K
G(V)
/GN
V(mV)
Al/AlOx/Pb
![Page 17: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/17.jpg)
“Clean” junction
Propionic acidCH3(CH2)COOH
Acetic acidCH3COOH
The Al/AlOx layer was exposed to a small amount of organic molecules before depositing the Pb counter-electrode
![Page 18: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/18.jpg)
Tunneling through a nanometer sized particleQuantized levels of particles in a box
AtomNanoparticle Solid
Discrete energy levels
CB
VB
Atomic levels
Ralph et al, Phys. Rev. Lett., 1996
![Page 19: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/19.jpg)
Superconductor-Superconductor TunnelingDissimilar superconductor
2D2
V=0
V>|(D1D2|/e
V>(D1+D2/e
2D1
Onset for the 1st channel of current is at
V=|(D1-D2)|/e
Onset for the 2nd channel of current is at
V=(D1+D2)/e
T0Thermally excited quasiparticle
-5 0 50.00.20.40.60.81.01.21.4
2.26K 5.5K 6.5K 7K 8K 12.5K
dI/dV
(
-1)
V (mV)NbN/Insulator/Pb junction
![Page 20: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/20.jpg)
T0( ( ( (
dEEfeVEfeVENENTAI 21
2
(
D
22,1
22,1 ReE
EEN
Townsend & Sutton, PR128, 591 (1962)
(D1+D2)/e
|(D1-D2)|/e
0dIdVRd
![Page 21: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/21.jpg)
The Josephson Effect
Dissipation-less current up to a certain current Ic
Current flows in a Josephson junction even
at V=02D2
V=0
2D1
T=0
Predicted: 1961-62, Nobel Prize in 1973
![Page 22: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/22.jpg)
Macroscopic Quantum State
Random Phase approximation
+
Eti
ertr )(),(
Since energy/momentum of the electron is altered statistically after travelling a distance l does not matter
Superconductor
iertr )(),(
Phase important for Cooper pair tunneling
![Page 23: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/23.jpg)
Josephson effect…
This effect is over and above the single particle tunneling current.
![Page 24: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/24.jpg)
Where is the Josephson effect???
Anderson & Rowell, PRL10, 230 (1963)
![Page 25: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/25.jpg)
I realized that actually doing physics is much more enjoyable than just learning it. Maybe 'doing it' is the right way of learning, at least as far as I am concerned.
Gerd Binnig, b. 1947Nobel Prize: 1986
Heinrich Rohrer, b. 1933Nobel Prize: 1987
The scanning tunneling microscope
7X7 reconstruction of Si (111)
![Page 26: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/26.jpg)
Vacuum tunneling between two planar electrodes
V
I f(V) exp (-2k d)
For low bias voltage (eV << ):
hm /2]2[ 2/1 k
STM basis
V
![Page 27: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/27.jpg)
Piezoceramic tube
![Page 28: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/28.jpg)
Scanning Tunneling Spectroscopy
Graphite
![Page 29: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/29.jpg)
![Page 30: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/30.jpg)
The TIFR (low temperature high vacuum) STM
With active design help from Dr. Sangita Bose
Sourin Mukhopadhyay(currently post-doc in Cornell)
Anand Kamlapure and Garima Saraswat
![Page 31: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/31.jpg)
V
Topographic image/spectroscopy
FeSe0.5Te0.5 single crystal: Grown by P. L. Paulose
Atomic steps on grapite surface GaAs epilayer by MOVPE: Grown by Arnab Bhattacharya
![Page 32: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/32.jpg)
NbNTc~16K
x~5nm l~200nm
Grows as epitaxial thin film on (100) MgO substrate using reactive magnetron sputtering:
NaCl structure
MgO
NbN
Thickness of our films ~ 50nm >> x
![Page 33: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/33.jpg)
Topographic image
Atomic step edges on a 6nm thick film
Strain relaxed structure on a 50 nm thick film
![Page 34: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/34.jpg)
Superconducting tunneling using STM
-4 -2 0 2 40.0
0.3
0.6
0.9
1.2
1.5
G(V)
/G N
Bias (mV)
V (mV)
150nm
Bias
(mV)
G(V)/GN
G(V)
![Page 35: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/35.jpg)
Superconducting Tunneling
-4 -2 0 2 40.0
0.5
1.0
1.5
G(V)
/GN
Bias (mV)
0 2 4 6 8 10 120.0
0.5
1.0
1.5
2.0
BCS D D (m
ev)
T (K)
150 nm
-4.55
0.00
4.55
0
1
2
3
4
08
162432dI
/dV
(arb
)
Point
Num
ber
V(mV)
![Page 36: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/36.jpg)
The superconducting gap map
Topographic image
Superconducting gap map
![Page 37: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/37.jpg)
Combining Spectroscopy with ImagingMapping inhomogeneities in a superconductor: BSCCO
A Pushp et al. Science 320, 196(2008)
![Page 38: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/38.jpg)
Observation of shell effects in superconducting nanoparticles
Atomic shell structureMagic number of electrons : closed shells : Inert gas atoms
Superconducting nanoparticles : formation of shells
Discrete energy levels have a degeneracy depending on the symmetry of the grainEach degenerate energy level : SHELL
EFE+ED-ED
Discrete Energy level
d = mean energy level spacing
hi
EF
Pairing Region ED
Manifestation of shell structure : oscillation in the ionization energy
0 nm
11 nm
V
It
STM : single nanoparticle
Sangita Bose et al., Nature Materials (in press)
5 10 15 20 25 300.0
0.4
0.8
D 0 (m
eV)
Particle height (nm)
![Page 39: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/39.jpg)
10 15 20 25 300.4
0.6
0.8
1.0
1.2
1.4
1.6
Experimental data Theory
Gap
(meV
)
Particle height (nm)
Sangita Bose et al., Nature Materials (in press)
![Page 40: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/40.jpg)
Particle in a box (again)
M.F.Crommie et al. Nature 363, 524 (1993)
M.F.Crommie et al., Science (1993)
![Page 41: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/41.jpg)
Imaging in the momentum space
20nm
1mV
Courtesy: Sangita Bose, MPI Stuttgart
7.3nmAu surface: Topography
![Page 42: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/42.jpg)
How to accentuate spacial variation of the Local Density of States
E
N(E)
eV
( ( eV
dEeVENENTAI0
21
2
( (
( ( ( ( eVKNeVNNTAdVdIVG
dEENNTAIeV
112
2
012
2
0
0
![Page 43: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/43.jpg)
1.6{1/nm}
k = 1.5 nm-1
( ( rkierur
Fourier Transform
Courtesy: Sangita Bose, MPI Stuttgart-2 -1 0 1 2
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4 subK STM; B = 0T subKSTM; B = 5T subKSTM; B = 8T
E [e
V]
k|| [nm]
dI/dV image
xikFAexikFBe
![Page 44: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/44.jpg)
Unusual Superconducting states: Ca2−xNaxCuO2Cl2
Difference of conductance map +6 and -6 meV
Hanaguri et al.
![Page 45: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/45.jpg)
Exploring Molecules: Homo Lumo gapPentacene
Theory
Repp and Meyer
![Page 46: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/46.jpg)
Resolving spins: Spin polarized STMTip coated with ferromagnetic material
![Page 47: Probing electronic interactions using electron tunneling](https://reader033.fdocuments.net/reader033/viewer/2022042616/56816937550346895de098f5/html5/thumbnails/47.jpg)
Make your own STM (Rs.50000/-)http://www.e-basteln.de/
http://sxm4.uni-muenster.de/introduction-en.html
http://web.archive.org/web/20021219052018/http://www.peddie.k12.nj.us/Research/STMProject/
Simple STM Project
http://www.geocities.com/spm_stm/
AMATEUR STM
http://www.angelfire.com/electronic2/spm/index.html