Superconducting proximity effect in graphene: Injecting ... - GDR Meso

Superconducting proximity effect in graphene:
Injecting Cooper pairs into quantum Hall regime
Katsuyoshi Komatsu, Chuan Li, Sandrine Autier-Laurent,
Alik Kasumov, Sophie Gueron and Helene Bouchiat
Theory: Lih-King Lim, Jean-Noel Fuchs, and Mark-Oliver Goerbig
LPS University Paris Sud XI

Outline
- Introduction and purpose
- Superconducting proximity effect in
graphene with long junction
- Superconducting proximity effect in
quantum Hall regime
- Summary and outlook

What is the superconducting
proximity effect?
Andreev reflection (S/N interface)
N
e
h
Super
conductor
An electron from N is reflected on the N/S interface as a hole.
A Cooper pair is injected into S.
Supercurrent (SNS junction)
S
N
e
h
L < L T , L φ

What material?
INSULATOR
S
S
Insulator (~1nm)
NORMAL METAL
LONG!!
S
Normal metal (~ 1µm)
Au, Cu, Ag, etc
S
MOLECULE
S S S S S S
Carbon nanotube DNA Fullerene
GRAPHENE?
S
S
Morpurgo (2007)
E. Andrei (2009)
C. Ojeda (2010)

Special Andreev reflection in graphene
Doped graphene
Close to Dirac point
ε
ε
E F
ε < E F
ε > E F
δk∝-v hole in conduction band δk∝v hole in valence band
ky and ε are conserved ε = ⎮⎮E F ±(δkx 2 +δky 2 ) 1/2 ⎮⎮
v y
v y
x
y
v y
v y
Andreev retroreflection
Specular Andreev reflection
Not observed yet
Charge inhomogeneity

Superconducting proximity
effect in graphene
Previous work:
Morpurgo (2007), Andrei (2008): Ti/Al
L = 200 to 500 nm
Ojeda-­‐ArisHzabal (2010): Pt/Ta
Joeng (2011): PbIn, Borzenets (2011): Pd/Pb
Our work: Long juncHon, L=1.2 µm, Pd/Nb (Tc ≈ 8K)
L >> ξ Nb ≈100nm (ξ Al ≈300nm)
More than two times longer than those in
previous works
Long junction limit may be
a way to observe specular
reflection...

Results (Nb electrodes, 1.2 μm distance)
V (V)
I (µA)
dV/dI
Ic
Ic*
Idc
Supercurrent (~200 nA) was
observed at 200 mK
Supercurrent is “tunable”
by back gate

Question:
Why does Ic fall off too fast?
Theory for long junction Ic=10ETh/Rn ETh=Dħ/L 2
Ic, ETh/Rn (A) Ic, ETh∕Rn
dV/dI
Ic
Ic*
Idc
Ic is much smaller than expectation
and decreases faster than ETh/Rn

Possible explanation
Role of charge inhomogeneity
Carrier density
distribution is gausian
and has a maximum
at zero carrier density
A. Yacoby et al, 2008

Possible explanation
Doped
Super
conductor
W > LT
Zero doping
S
L < LT
S

Possible explanation
Undoped
W > LT
ε ≈ k B T
Zero doping
S
S
Coherent propagation of Andreev pairs destroyed by
charge inhomogeneity Ic suppressed at CNP

Can Cooper pairs go through
the Quantum Hall regime?
Bz
Edge states
e
h
Edge states
Theory
A. Ma and A. Yu Zyuzin, Europhys. Lett. 21, 941 (1993).
A. Yu Zyuzin Phys. Rev. B 50, 323 (1994).
Experiments in 2DEG systems
H. Takayanagi and T. Akazaki, Physica B 249-251, 462 (1998).
T. D. Moore and D. A. Williams, Phys. Rev. B 59, 7308 (1999).
High Hc superconductor is required!!
Bz
Bz
S
Retroreflection
S
Specular reflection

Preliminary result of a sample
with high Hc superconductor
electrodes
Electrodes: ReW (Hc > 7T, Tc ~ 5K),
contact distance ~ 0.7μm
ReW
graphene
ReW wire resistance
2 wire measurement

Results (ReW, 0.7μm distance)
Ic ~ 130 nA with Vg=-25V at 55mK in H=0T
Ic can be tuned by back gate similar to the
sample with Nb electrodes

QHE with S electrodes
H=7.5T
No obvious sign of
supercurrent in QHE
regime
Is this because ρ xy is
mixed with ρ xx ? (2wire
measurement)
H=0T

QHE with S electrodes
H=7.5T
No obvious sign of
supercurrent in QHE
regime
Is this because ρ xy is
mixed with ρ xx ? (2wire
measurement)
Takayanagi (2002),
AlGaAs/GaAs
NS
G N (2e 2 ∕h)∑2t 2 ∕(2-t) 2
H=0T

Is shape of plateaux
differenet with S electrodes?
H=7.5T
No obvious sign of
supercurrent in QHE
regime
Is this because ρ xy is
mixed with ρ xx ? (2wire
measurement)
H=0T
Small oscillations are
related to supercurrent?

Andreev reflection in QH regime
Most of dV/dI show peak
at Idc = 0 A.
But three Vgs give dips
at Idc = 0 A.
H=7.5T at 55 mK
These dips may be sign of
constructive interference in
Andreev reflection.

Looking for signature of interference
d 3 V/dI 3 (x10 -6 a.u.)
200
100
0
Vg = 0
T=55mK
0
10
20
30
40
50
60
70
Magnetic field (x10 3 G)
2000
150
d 3 V/dI 3 (x10 -6 a.u.)
100
50
0
-50
42.5
43.0
43.5
Maginetic field (x10 3 G)
44.0
d 3 V/dI 3 < 0 gives a dip in dV/dI
AB type effect in the edge state?
dV/dI (Ohm)
1950
1900
Min Harm3 Vg=0V h=42806G
Max Harm3 Vg=0V h=42498G
iac=2nA
-100
0
Idc (x10 -9 A)
e
100
h
Edge states
BEdge states

Summary
- We succeeded to observe supercurrent with both
Nb and ReW electrodes in long junctions (~1µm).
- Andreev reflection in QH regime was observed.

Open questions
- Which configuration is the best to observe
supercurrent in QH regime?
A. Yu Zyuzin geometry
Edge states
Bz
e
h
Edge states
small contact < ξs