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Probing Superconductors using Point Contact Andreev Reflection
Pratap RaychaudhuriPratap Raychaudhuri
Tata Institute of Fundamental ResearchTata Institute of Fundamental Research
MumbaiMumbai
Collaborators:
Gap anisotropy in YNi2B2C
G. Sheet, S. Mukhopadhyay, D. Jaiswal, S. Ramakrishnan, H. Takeya (Japan)
Phys. Rev. Lett. 93, 156802 (2004).
Nanostructured Nb
S. Bose, P. Vasa, P. Ayyub, R. Bannerjee (Ohio)
Free path: the electron accelerates
V
Scattering Centre (elementary excitation, defects): the electron loses energy
K.E imparted to the electron=
Mean free path
Sample size eV
Lattice
a<<l
e V= (1/2)mv2
T
Ballistic Transport
• Statistically no scattering
• Electrons kinetic energy=eV
• Spectroscopic Probe
Experiment
L He
I=Idc
+Iac
sint
V=Vdc
+Vac
sint
I
Iac
<<Idc
Vdc
-dc bias voltage on the junction
Iac
/Vac
~dI/dV: the differential conductance of the junction
Spectroscopy using Point Contact
Electron phonon interaction
(Au foil/ Au tip)
-6 -4 -2 0 2 4 60.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
G(V
)/G
n
V(mV)
Nb film / Pt-Ir Tip
T= 4.2K Z=0.6 delta=0.9meV Superconducting energy gap
Superconductor
Normal Metal
1
0ikx
inc e
0
0
ikx
refl ikx
eb a
e
iqx iqxtrans
u vc e d e
v u
Normal Reflection
Andreev reflection 0( ) ( )V x V x
Fitting parameters:
superconducting gap
Z-barrier height parameter
-broadening parameter
N(E)
E(meV)
BCS density of states
2 2(0) Re
E iN
E i
Superconducting Energy Gap
Angle resolved probe capable of probing different k directions on the Fermi surface
-6 -4 -2 0 2 4 60.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
G(V
)/G
n
V(mV)
Nb film / Pt-Ir Tip
T= 4.2K Z=0.6 delta=0.9meV
Fitting parameters:
superconducting gap
Z-barrier height parameter
-broadening parameter
Superconducting gap anisotropy in YNi2B2C
Discovered in TIFR in 1994
Tc~14.6K
Type II Supserconductor:
BCS Superconductor with conventional electron phonon coupling
Unusual Vortex Symmetries evolving with temperatureThermal Conductivity
Izawa et al., PRL 89, 137006 (2002)
Specific Heat
Park et al., PRL 92, 237002 (2004)
Angular variation in magnetic field
Unusual gap function symmetry
s+g(mixed angular
momentum symmetry)
)4sin(cos12
1)( 4
0
k
K Maki, P Thalmeier and others
Purely Geometrical with no microscopic origin
k of YNi2B2C
S-wave superconductivity
s+g symmetry of the order parameter
Multiband superconductivty???
Crystal used for this study
Susceptibility
Primary Secondary
Sample
Intervortex spacing: 1500ÅÅ
Very low defect density
-8 -6 -4 -2 0 2 4 6 8
0.98
1.05
1.12
1.19
1.26
14.5 K
1.75 KI || c-axis
YNi2B
2C/Ag tip
G(V
)/Gn
V (mV)
-3 -2 -1 0 1 2 30.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
6.0 K
2.32 KYNi
2B
2C/Ag tip
I || a-axis
G (
V)
/ Gn
V (mV)
Gap anisotropy
||2~ 3.6I c
B ck T
c
a
I||a
I||c/I||a ~ 7
at 1.75 K
c
a
I||c
Temperature dependence
0 2 4 6 8 10 12 140.00
0.05
0.10
0.15
0.20
0.25
0.30
I || c (meV)
I |
| a (m
eV)
T (K)
0.0
0.3
0.6
0.9
1.2
1.5
1.8
)4sin(cos2
1)( 4
00 gsk
)4sin(cos1
2
1)( 4
0
k
Two Band SuperconductorTwo Band Superconductor
Suhl et al, PRL 3, 552 (1959)
No Interband scattering
Weak Interband Scattering
TT
T
sg
g
Tc
Temperature dependent Temperature dependent s+gs+g
Yuan and Thalmeier
PRB 68, 174501 (2003)
Magnetic field dependence
-10 -5 0 5 100.9
1.0
1.1
1.2
1.3
1.4
1.5
1.6
YNBC/AgI||c
0 T0.25 T0.75 T1.25 T1.75 T2.25 T2.75 T3.25 T
G(V
)/Gn
V (mV)-3 -2 -1 0 1 2 3
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.14
1.16YNBC/AgI || a
0 T0.25 T0.375 T0.5 T0.75 T0.875 T0.9 T1.25 T1.5 T1.75 T2.25 T
G(V
)/Gn
V (mV)0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
0.15
0.20
0.25
0.30
0.35
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0
0.5
1.0
1.5
2.0
2.5
H||a
H||c(b)
(m
eV)
H (T)
(a)H||a
x 5
H||c
(m
eV)
H(T)
0.0
0.4
0.8
1.2
1.6
2.0
0 2 4 6 8 10 12 14 160
1
2
3
4
5
6
H||c
H||a
HC
2(T)
T (K)
2 3 4 5 6 7
-1.0
-0.8
-0.6
-0.4
-0.2
0.0T= 2 K
H||a
H||c
' (n
orm
alis
ed)
H (T)
Zero bias density of States
2 2( 0) ~ Re
( )
E iN E
E i
Comparison with theoretical predictions for a two band superconductor
Zero bias density of states
Superconducting energy gap
Koshelev & Golubov, PRL 90,177002 (2003)
Two band superconductivity in MgB2
Gonnelli et al., PRL 89, 247004 (2002).
Band Structure of YNi2B2C
3 bands crossing the FS produce 5 FS sheets
Cylindrical FS
Square FS
Ellipsoidal FS
I||a
I||c
Mostly fast electrons:responsible for small gapMostly slow electrons:
responsible for large gap
Encloses only 0.3% of the Fermi surface volume. Not important in PC expt.
Epilogue
What is special about MgB2 (or YNi2B2C)?
The clear demonstration of multiband superconductivity in MgB2 calls for a closer look at all
the known superconductors.
Under what limiting condition will a multiband superconductor behave like a single band superconductor?
Interband scattering
Size effect in nanoscale superconductors
Complete
destruction of superconductivity
Open Questions
How does the superconducting properties evolve at small sizes?
In Al, Sn, Tc gets enhanced by a factor of 2 before destruction of superconductivity
In Pb, Nb Tc decreases monotonically
Softening of the (surface) Phonon modes vs. quantum size effect?
Softening of Phonon Modes increased electron phonon coupling
Quantum size effect N(0) will decrease
2/kBTc
Evolution of Superconducting properties in nanostructured Nb
Mechanism of destruction of Tc
Magnetization
Resistivity
Nature of the grain boundary
Weakly coupled Josephson Junction
Evolution of Energy Gap with Particle size
2~ 3.7
ckT
45nm
15nm10nm
8nm
Remains in the weak coupling limit down to
the lowest size
Temperature variation of
Summary
In Nb,
Tc decreases monotonically with decreasing particle size.
2/kBTc remains constant down to the Anderson limit.
The suppression of Tc in nanocrystalline Nb is possibly governed by quantum size effects rather than phonon softening.
YNi2B2C: Superconducting properties
0 2 4 6 8 10 12 14 160
1
2
3
4
5
6
H||c
H||a
HC
2(T
)
T (K)
2 3 4 5 6 7
-1.0
-0.8
-0.6
-0.4
-0.2
0.0T= 2 K
H||a
H||c
'
(no
rma
lise
d)H (T)
Critical fields
Tc~14.6K
Type II Supserconductor:
Coherence length:
BCS Superconductor with conventional electron phonon coupling
Tuson Park et al. PRL92, 237002(2004)
Specific heat
CH1/2
Thermal Conductivity
Izawa et al., PRL 89, 137006 (2002)
Specific Heat
Park et al., PRL 92, 237002 (2004)
Angular variation in magnetic fieldUnusual Vortex Symmetries evolving with temperature