Probing Superconductors using Point Contact Andreev Reflection Pratap Raychaudhuri Tata Institute of Fundamental Research Mumbai Collaborators: Gap anisotropy.

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