Point contact Andreev reflection as a probe to study superconductors and ferromagnets

Introduction to Point contact Andreev Reflection (PCAR)

• Probing supercondonductors with PCAR: (i) Gap anisotropy in YNi

2B

2C

(ii) Evolution of the superconducting energy gap in nanostructured Nb films

• Probing Ferromagnets with PCAR: SrRuO3

• Good versus bad spectra

Pratap RaychaudhuriTIFR Mumbai

Collaborators

Goutam SheetSangita Bose

Sour in MukhopadhayayPushan Ayyub

Rajarshi Baner jeeSwati Soman

D. JaiswalS Ramakr ishnan

H Takeya

Electron flow in metals

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≈0≈0≈0≈0

Ballistic Flow

The electron will lose energy only if it has sufficient energy to excite an elementary excitation in the solid.

The resistance of such a contact can therefore be used as an energy resolved spectroscopic probe to investigate the interaction of the electron with other elementary excitations in the solid.

Experiment

L He

I=Idc+I

acsinωt

V=Vdc+V

acsinωt

I

Iac<<I

dc

Vdc-dc bias voltage on the junction

Iac/V

ac~dI/dV: the differential conductance of the junction

Example: Electron-Phonon Interaction in Au

Angle resolved information?

xI

k

IS

F

N k EF vk xdS

4 3

1k E k

1

4 3k E k

dSk dSxk

IS

F

dSxk Sx

[010]

Modelling a ballistic superconductor-normal metal contact

el10

ei kx

Good w.f. in normal metals

ho01

e

� i kx

Electron Hole

a<<l

eV

Normal metal Superconductor

Good w.f. in superconductors

0uv

eiqx1

vu

e

� iqx

u2 � 12

1

� E2 �

� 2

E2v2 � 1

21 �

E2 �

� 2

E2

For E>>∆∆∆∆u=1 v=0

�

inc

� 10

ei kx

Andreev reflection

Normal reflection

n x 0 s x 0

s' x 0 n ' x 02mV

2 x 0

V x V 0 x

�

refl

� b e

� i kx

0

�

a 0ei k x

�

trans

� c uS

vSeiqu x �

d vS

uSe

� iqv x

Z=V0/ v

F

Projected Density of States

Completely Transparent junction

Junctions with finite potential barrier

Typical “good” PCAR spectra

-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

-10 -8 -6 -4 -2 0 2 4 6 8 10

1.00

1.05

1.10

1.15

1.20 I // c

14.0 K13.0 K12.0 K10.0 K8.00 K6.00 K3.54 K2.66 KYNBC/Au

G(V

)/Gn

V (mV)

Fe/Nb

0 0.001 0.002 0.003 0.004 0.0050

1

2

3

Broadening of the PCAR spectra

eV

N(E)

BCS Density of States

Broadened density of states

Γ/∆ ~ 0.33Γ/∆ ~ 0.023

T = 2.62KZ= 0.575∆∆∆∆ = 1.0meVΓΓΓΓ = 0.315meV

Measurement of Gap Anisotropy in superconducting YNi

2B

2C

Gap anisotropy in Superconductors kz

kx

kz

kx

∆(k)

kx

Isotropic gap

Ansotropic gap

kz

kz

kx

Fermi Surface

Unconventional Superconductors

Gap function zero at certain points (lines) on the Fermi surface

Directional PCAR: Principle

kz

kx

[001]

[100]

dSxk

dSzk

k

I a

SF

k dSxk

I c

SF

k dSzk

2

SF

k I

�

c2 dSzk

Variance

Point contact Spectroscopy in YNi2B

2C

Tc~14.5K

Unconventional superconductor?

T2 dependence of resistivity at low temperatures: Fermi liquid

Power law temperature dependence of specific heat at low temperatures: Zeros in the gap function

4 fold anisotropy in the a-b plane in the superconducting state (Hc2):

Anisotropy in superconducting order parameter

Indirect evidence from thermal conductivity

∆(k) very small in certain crystallographic directions:[100] [010] [-100] [0-10]

YNi2B2C (Tc~14.5K)

-10 -8 -6 -4 -2 0 2 4 6 8 10

1.00

1.05

1.10

1.15

1.20 I // c

14.0 K13.0 K12.0 K10.0 K8.00 K6.00 K3.54 K2.66 KYNBC/Au

G(V

)/Gn

V (mV)

-6 -4 -2 0 2 4 6

1.000

1.025

1.050

1.075

1.100

1.125 2.688 K3.470 K4.150 K5.000 K6.000 K7.000 K

YNBC/Au I // a

G(V

)/G n

V (mV)

∆≈1.8±0.1 meV at T=2.7KΓ / ∆∼ 0.32±0.3Γ / ∆∼ 0.32±0.3Γ / ∆∼ 0.32±0.3Γ / ∆∼ 0.32±0.3

∆≈0.42±0.08 meV at T=2.7KΓ / ∆ ∼ 0.53±0.04Γ / ∆ ∼ 0.53±0.04Γ / ∆ ∼ 0.53±0.04Γ / ∆ ∼ 0.53±0.04

c

a

c

a

I ||a

I ||c

No observation of zero bias anomaly

Point contact spectra for I ||c and I ||aCrystal 1 Crystal 1

Crystal 2Crystal 2

Temperature dependence of superconducting energy gap

Different temperature variation in different directions

Proposed Gap anisotropy

[100]

[010]

[100]

[010]

[001] [001]

k12 0 1 sin4 cos 4 k

12 0 1 sin 2

anisotropic s-waves+g

d-wave

+

_

_

+

s: L=0g: L=4

d: L=2

k12 0 1 sin4 cos 4 k

12 0 1 sin 2

anisotropic s-waves+g

d-wave

Temperature dependence from ∆

0 alone

k12 s0 g0sin4 cos 4 s0 g0 Fine tuned

No symmetry reason

∆∆∆∆s0 and ∆∆∆∆g0 could have different temperature dependences giving r ise to a temperature dependent shape of gap anisotropy.

Measurement of Spin Polar isation in a fer romagnet using PCAR

Spin polar isation in fer romagnets

J

E

N↑(E) N↓(E)

N↓(EF)

N↑(EF)

PN � EF N � EF

N � EF N � EF

Andreev reflection across a fer romagnet/superconductor inter face

inc10

ei kx

refl b e

� i kx

0a 0

e

� x

Evanescent wave

trans c uS

vSe

iqu

xd vS

uSe

� iqv

x

Pt=1

I=Iu (1-P

t)+I

p P

t J

E

N↑(E) N↓(E)

N↓(EF)

N↑(EF)

...for finite spin polarisation

Will undego Andreev reflection

Evanescent wave

G=dI/dV

-10 -5 0 5 10

0.0

0.5

1.0

1.5

2.0

T=4.2K, Pt=0.4

T=4.2K, Pt=1

G

(V)/G

n

V (mV)

T=0, Pt=0 T=4.2K, Pt=0

Ferromagnet/superconductor interface

Spin polarisation of Iron

Τ=3.5Κ ∆=1.5 meV Z=0.28

Pt=0.43

Fe foil/Nb tip Co film/Pb tip

Τ=3.4Κ ∆=1.15 meV Z=0.345Γ=0.31

Pt=0.4

Transport spin polarisation SrRuO3

1. Clean system with large mean free path: ~ 400Å � Easy to realise a ballistic limit in point contact.

2. One of the very few oxide ferromagnets where quantum oscillations could be observed.

3. P~0.091-0.2 N↓(ΕF)≈N↑(Ε

F)

4. vF↓>>v

F↑

4d ferromagnet with Tc~160K.

Ms=1.6µ

B/Ru

SrRuO3

Fitting parameters

∆, Z, Pt

Pt as a function of Z

0.0 0.1 0.2 0.3 0.4 0.5 0.60.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55P t

Z

2.7 3.0 3.3 3.6 3.9 4.2

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

T (K)

|Pt|=0.51±±±±0.02

Evolution of Superconducting energy gap in nanostructured Nb films

Nanocrystalline thin films of Nb: Prepared by DC magnetron sputtering

XRD showing the [ 110 ] line of Nb

Lattice expansion as a function of particle size

Banerjee et. al. APL 82, 4250 (2003)

BulkSuperconductor

Insulator

Superconductor with suppressed Tc

Suppression of superconductivity

Mechanism of destruction of superconductivity

Multi gap Two gaps

Power of Point Contact to probe multi gap features

Single gap

Evolution of Superconducting Gap with particle size

Temperature variation of Gap

2 ∆ / kB

TC

~ 3.5

Linear variation of gap with Tc

“ Good” versus “ bad” spectra

Destruction of superconductivity at the point contact

“Bad” SpectraNb/AuFe

PtIr/V3Si Pt-Ir/

Y2PdGe3

MgCNi3/Pt

Unconventional Superconductivity Mao et al. (2003)

Nb/Cu

Proximity induced Superconductivity Strijkers et al. (2001)

UBe13/AuAndreev Bound StatesWalti et al. (1994)

Thermal Regime

Ballistic regime

Intermediate Regime

a<<l

eV

R=Rk/(ak

F)2 Rs

a>>l

eV

R=ρ(Teff

)/a RM

Teff=(T2+V2/4L)1/2

At T=0, Teff=3.2K/mV

a ≈ l

eV

Rs+RM

For RM<R

s

local heating is small

Ni-Ni

Heating in a point contact

Duif et al., JPCM (1989)

Tc

Thermal coupling with the external bath very weak → ��������������

VM=IRM∝∝∝∝ρρρρ����

Vs=IRs

YNi2B

2C – gold tip

ρρρρN large

Pt-Ir/Y2PdGe3

In the normal state RM>>R

s

Subham Majumdar and E. V. Sampathkumaran, (2001)

Summary

JoyPoint contact Andreev Reflection is a powerful tool to obtain energy and angle resolved information in both superconductors and ferromagnets.

PitfallThe usefulness of this technique is crucially dependent on the quality of the sample and sample processing. Samples with high defect densities can lead to misleading results even if the bulk properties are not very different from the best quality single crystals.

Hysteresis in critical current