Point contact Andreev reflection as a probe to study
superconductors and ferromagnets
Pratap Raychaudhuri
TIFR Mumbai
Introduction to Point contact Andreev Reflection (PCAR)
• Probing supercondonductors with PCAR:
(i) Gap anisotropy in YNi2B2C
(ii) Evolution of the superconducting energy gap in
nanostructured Nb films
• Probing Ferromagnets with PCAR: SrRuO3
• Good versus bad spectra
Collaborators
Goutam Sheet
Sangita Bose
Sourin Mukhopadhayay
Pushan Ayyub
Rajarshi Banerjee
Swati Soman
D. Jaiswal
S Ramakrishnan
H Takeya
Electron flow in metals
V
Scattering Centre
(elementary excitation,
defects):
the electron loses energy
K.E imparted to the electron=
Mean free path
eV
Sample size
Free path: the
electron accelerates
Lattice
Ballistic Flow
a<<l
e V=(1/2)mv2
T≈0
≈0
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
I=Idc+Iacsinωt
L He
Iac<<Idc
V=Vdc+Vacsinωt
I
Vdc-dc bias voltage on the junction
Iac/Vac~dI/dV: the differential conductance of the junction
Example: Electron-Phonon Interaction in Au
Angle resolved information?
I
x
I
N k EF
S
dS k
dS xk
k
4
k
1
k
E k
I
dS xk
S
[010]
dS
4 3
F
1
3
vk x
F
Sx
E k
Modelling a ballistic superconductor-normal metal contact
Normal
metal
Superconductor
a<<l
eV
Good w.f. in superconductors
u eiqx
v
0
Electron
Hole
1
iqx
i kx
E
2
v
2
1
1
2
E
For E>>∆
∆
u=1
2
2
E2
1
1
2
u
2
ho
0 e
1
el
1 ei kx
0
v e
u
Good w.f. in normal metals
v=0
E2
2
i kx
0
a
u
x
S
v
d S e
u
S
iq
u
c S e
v
trans
refl
b e
inc
1 e i kx
0
iq v x
0
e
ik x
Projected Density of States
Normal
reflection
Andreev
reflection
V x
n
s
' x 0
x 0
n
V0
s
' x 0
x
x 0
2mV
2
Z=V0/ vF
x 0
Completely Transparent junction
Junctions with finite potential barrier
Typical “good” PCAR spectra
1.35
Nb film / Pt-Ir Tip
2.66 K
3.54 K
6.00 K
8.00 K
10.0 K
12.0 K
13.0 K
14.0 K
T= 4.2K Z=0.6
delta=0.9meV
G(V)/Gn
1.25
1.20
G(V)/Gn
YNBC/Au
I // c
1.20
1.30
1.15
1.10
1.15
1.10
1.05
1.05
1.00
1.00
0.95
-6
-4
-2
0
V(mV)
2
4
6
-10
-8
-6
-4
-2
0
2
V (mV)
Fe/Nb
4
6
8
10
Broadening of the PCAR spectra
T = 2.62K
Z= 0.575
∆ = 1.0meV
Γ = 0.315meV
BCS Density of States
3
Broadened density of
states
Γ/∆ ~ 0.33
Γ/∆ ~ 0.023
N(E)
2
1
0
0
0.001
0.002
0.003
eV
0.004
0.005
Measurement of Gap Anisotropy in superconducting
YNi2B2C
Gap anisotropy in Superconductors
kz
kz
∆(k)
kx
kx
Isotropic gap
Fermi Surface
kz
kz
kx
kx
Ansotropic gap
Unconventional Superconductors
Gap function zero at certain points (lines) on the Fermi surface
Directional PCAR: Principle
k dS zk
I c
SF
[001]
dSzk
kz
Variance
2
dSxk
k
kx
2
k
S
I
dS zk
F
k dS xk
I a
SF
[100]
c
Point contact Spectroscopy in YNi2B2C
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)
a
YNBC/Au
I // a
1.125
2.688 K
3.470 K
4.150 K
5.000 K
6.000 K
7.000 K
G(V)/G
n
1.100
1.075
c
I||a
1.050
∆≈0.42±0.08 meV at T=2.7K
Γ / ∆ ∼ 0.53±0.04
1.025
1.000
-6
-4
-2
0
2
4
6
V (mV)
G(V)/Gn
1.20
I||c
YNBC/Au
I // c
2.66 K
3.54 K
6.00 K
8.00 K
10.0 K
12.0 K
13.0 K
14.0 K
1.15
1.10
1.05
1.00
-10 -8
-6
-4
-2
0
2
V (mV)
4
6
8
a
c
∆≈1.8±0.1 meV at T=2.7K
Γ / ∆∼ 0.32±0.3
10
No observation of zero bias anomaly
Point contact spectra for I||c and I||a
Crystal 1
Crystal 2
Crystal 1
Crystal 2
Temperature dependence of superconducting energy gap
Different temperature
variation in different
directions
Proposed Gap anisotropy
[001]
[001]
+
[010]
[010]
_
_
+
[100]
k
1
2
0
1 sin
4
cos 4
anisotropic s-wave
s+g
s: L=0
g: L=4
[100]
k
1
2
0
1 sin 2
d-wave
d: L=2
d-wave
anisotropic s-wave
s+g
k
1
2
0
1 sin
4
k
cos 4
1
2
0
1 sin 2
Temperature dependence from
∆0 alone
k
1
2
s0
g0
sin
4
cos 4
s0
g0
Fine tuned
No symmetry reason
∆s0 and ∆g0 could have different temperature dependences giving rise
to a temperature dependent shape of gap anisotropy.
Measurement of Spin Polarisation in a ferromagnet using PCAR
Spin polarisation in ferromagnets
E
N↑(EF)
N↑(E)
P
N↓(E)
N EF
N EF
N EF
N EF
J
N↓(EF)
Andreev reflection across a
ferromagnet/superconductor interface
Pt=1
refl
b e
i kx
0
a
0
e x
Evanescent wave
trans
S
u
c S
v
e
iq x
u
S
v
d S
u
inc
1 ei kx
0
e
iq x
v
...for finite spin polarisation
E
N↑(EF)
J
N↑(E)
N↓(EF)
I=Iu (1-Pt)+Ip Pt
N↓(E)
Will undego
Andreev reflection
G=dI/dV
Evanescent
wave
Ferromagnet/superconductor interface
2.0
T=0, Pt=0
T=4.2K, Pt=0
G(V)/Gn
1.5
T=4.2K, Pt=0.4
1.0
0.5
T=4.2K, Pt=1
0.0
-10
-5
0
V (mV)
5
10
Spin polarisation of Iron
Fe foil/Nb tip
Τ=3.5Κ ∆=1.5 meV Z=0.28
Pt=0.43
Co film/Pb tip
Τ=3.4Κ ∆=1.15 meV Z=0.345
Γ=0.31
Pt=0.4
Transport spin polarisation SrRuO3
4d ferromagnet with Tc~160K.
Ms=1.6µB/Ru
1. Clean system with large mean free path: ~ 400Å
ballistic limit in point contact.
Easy to realise a
2. One of the very few oxide ferromagnets where quantum oscillations could
be observed.
3.
4.
P~0.091-0.2
N↓(ΕF)≈N↑(ΕF)
vF↓>>vF↑
SrRuO3
Fitting parameters
∆, Z, Pt
Pt as a function of Z
T (K)
Pt
0.55
2.7
3.0
3.3
3.6
3.9
4.2
0.55
0.50
0.50
0.45
0.45
0.40
0.40
0.35
0.35
0.30
0.30
0.25
0.25
0.20
0.0
0.20
0.1
0.2
0.3
0.4
Z
|Pt|=0.51±
±0.02
0.5
0.6
Evolution of Superconducting energy gap in nanostructured Nb films
Nanocrystalline thin films of Nb: Prepared by DC magnetron sputtering
Lattice expansion as a function
of particle size
Superconductor with
suppressed Tc
XRD showing the [ 110 ] line of Nb
Bulk
Superconductor
Insulator
Banerjee et. al. APL 82, 4250 (2003)
Suppression of superconductivity
Mechanism of destruction of
superconductivity
Power of Point Contact to probe multi gap features
Multi gap
Two gaps
Single gap
Evolution of Superconducting Gap with particle size
Linear variation of gap with Tc
Temperature variation of Gap
2 ∆ / kB TC ~ 3.5
“Good” versus “bad” spectra
Destruction of superconductivity at the point contact
“Bad” Spectra
Nb/AuFe
PtIr/V3Si
Pt-Ir/
Y2PdGe3
MgCNi3/Pt
Unconventional Superconductivity
Mao et al. (2003)
Nb/Cu
Proximity induced Superconductivity
Strijkers et al. (2001)
UBe13/Au
Andreev Bound States
Walti et al. (1994)
Ballistic regime
Intermediate
Regime
Thermal Regime
a<<l
R=Rk/(akF)2 Rs
eV
a≈l
Rs+RM
For RM<Rs
local heating
is small
eV
Teff=(T2+V2/4L)1/2
a>>l
eV
R=ρ(Teff)/a RM
At T=0,
Teff=3.2K/mV
Heating in a point contact
Ni-Ni
Tc
Duif et al., JPCM (1989)
Thermal coupling with the external bath very weak →
Vs=IRs
VM=IRM∝ρ
YNi2B2C – gold tip
ρN large
In the normal state RM>>Rs
Pt-Ir/
Y2PdGe3
Subham Majumdar and E. V. Sampathkumaran, (2001)
Summary
Joy
Point contact Andreev Reflection is a powerful tool to obtain energy and
angle resolved information in both superconductors and ferromagnets.
Pitfall
The 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