Probing electronic interactions using electron tunneling Pratap Raychaudhuri.
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Transcript of Probing electronic interactions using electron tunneling Pratap Raychaudhuri.
Probing electronic interactions using electron tunneling
Pratap Raychaudhuri
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
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
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
Electron tunneling in solids
N1 N2
T(12) e-kd N1N2 (d 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
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
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
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
0dI
dVRd
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
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
eVKNeVNNTAdV
dIVGdEENNTAI
eV
112
2
0
12
20 0
Superconductivity
The resistance is as close to zero as measurable
K Onnes (1911)
Perfect diamagnet:Meissner –Ochsenfeld effect
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
22Re
E
E
x0~5-50nm
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
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
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
)/G
n
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
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
)/G
N
V(mV)
Al/AlOx/Pb
“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
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
Superconductor-Superconductor TunnelingDissimilar superconductor
2D2
V=0
V>|(D1-D2)|/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 50.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
2.26K 5.5K 6.5K 7K 8K 12.5K
dI/d
V (
-1)
V (mV)
NbN/Insulator/Pb junction
T0
dEEfeVEfeVENENTAI 21
2
2
2,1
22,1 Re
E
EEN
Townsend & Sutton, PR128, 591 (1962)
(D1+D2)/e
|(D1-D2)|/e
0dI
dVRd
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
Macroscopic Quantum State
Random Phase approximation
Et
i
ertr )(),(
Since energy/momentum of the electron is altered statistically after travelling a distance l f does not matter
Superconductor
iertr )(),(
Phase important for Cooper pair tunneling
Josephson effect…
This effect is over and above the single particle tunneling current.
Where is the Josephson effect???
Anderson & Rowell, PRL10, 230 (1963)
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)
Vacuum tunneling between two planar electrodes
V
I f(V) exp (-2 d)
For low bias voltage (eV << ):
hm /2]2[ 2/1
STM basis
V
Piezoceramic tube
Scanning Tunneling Spectroscopy
Graphite
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
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
NbNTc~16K
~5x nm ~200l nm
Grows as epitaxial thin film on (100) MgO substrate using reactive magnetron sputtering:
NaCl structure
MgO
NbN
Thickness of our films ~ 50nm >> x
Topographic image
Atomic step edges on a 6nm thick film
Strain relaxed structure on a 50 nm thick film
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)
Superconducting Tunneling
-4 -2 0 2 40.0
0.5
1.0
1.5
G(V
)/G
N
Bias (mV)
0 2 4 6 8 10 120.0
0.5
1.0
1.5
2.0
BCS
(m
ev)
T (K)
150 nm
-4.5
5
0.00
4.55
0
1
2
3
4
08
162432dI
/dV
(ar
b)
Poi
nt N
umbe
r
V(mV)
The superconducting gap map
Topographic image
Superconducting gap map
Combining Spectroscopy with ImagingMapping inhomogeneities in a superconductor: BSCCO
A Pushp et al. Science 320, 196(2008)
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
0 (
me
V)
Particle height (nm)
10 15 20 25 300.4
0.6
0.8
1.0
1.2
1.4
1.6
Experimental data Theory
Gap
(m
eV)
Particle height (nm)
Sangita Bose et al., Nature Materials (in press)
Particle in a box (again)
M.F.Crommie et al. Nature 363, 524 (1993)
M.F.Crommie et al., Science (1993)
Imaging in the momentum space
20nm
1mV
Courtesy: Sangita Bose, MPI Stuttgart
7.3nmAu surface: Topography
How to accentuate spacial variation of the Local Density of States
E
N(E)
eV
eV
dEeVENENTAI0
21
2
eVKNeVNNTAdV
dIVG
dEENNTAIeV
112
2
0
12
2
0
0
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 [
eV]
k|| [nm]
dI/dV image
xikFAexikFBe
Unusual Superconducting states: Ca2−xNaxCuO2Cl2
Difference of conductance map +6 and -6 meV
Hanaguri et al.
Exploring Molecules: Homo Lumo gapPentacene
Theory
Repp and Meyer
Resolving spins: Spin polarized STMTip coated with ferromagnetic material
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