Point contact Andreev reflection as a probe to study ...pratap/Andreev.pdf · Point contact Andreev...
Transcript of Point contact Andreev reflection as a probe to study ...pratap/Andreev.pdf · Point contact Andreev...
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