andreev reflection in quantum hall effect regime h. takayanagi 髙柳 英明 tokyo university of...
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Andreev Reflection in Quantum Hall Effect Regime
H. Takayanagi 髙柳 英明
Tokyo University of Science,TokyoInternational Center for Materials NanoArchitechtonics (MANA),
National Institute for Materials Science, Tsukuba
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Superconducting Junctions using AlGaAs/GaAs Heterostructures
with High H c2 NbN Electrodes
Hideaki Takayanagi,
Tatsushi Akazaki & Yuichi Harada , NTT Basic Research Laboratories
Minoru Kawamura, RikenJunsaku Nitta, Tohoku University
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Andreev Reflection
Electron
HoleCooper pair
EF
SuperconductorNormal conductor
An incident electron from the normal conductor is reflected as a hole and a Cooper pair is created in the superconductor.
The differential resistance of the S/N interface decreases or increases within the superconducting energy gap depending on the Andreev reflection probability (A) and normal reflection probability (B).
0.4
0.6
0.8
1.0
1.2
1.4
1.6
2-2
A << B
A >> B
dV
/dI
Voltage
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Andreev Reflection in High Magnetic Field
• A 2DEG exhibits QHE in a strong perpendicular magnetic field. The QHE is represented in terms of edge states.
• Andreev reflection between superconductor and edge states was first proposed by Zyuzin[1] and have been investigated theoretically and experimentally by several authors.
[1] A. Yu Zyuzin Phys. Rev. B 50(1994) 323. [2] H. Takayanagi and T. Akazaki, Physica B 249-251(1998)462. [3] T. D. Moore and D. A. Williams, Phys. Rev. B 59(1999)7308.
Superconductingelectrode
Superconductingelectrode
2DEG
Edge states
B
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SNS junction withNbN sueprconducting electrodes
&a 2DEG in a AlGaA/GaAs single heterostructure
• Advantages of these materials– NbN
• High Hc2 > 18T– 2DEG in AlGaAs/GaAs heterostructure
• High electron mobility• Low carrier density
• Problem– High Schottky barrier between NbN and GaAs
Sample
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Sample Fabrication
AuGeNi layer is inserted between NbN and GaAs.
The samples are annealed at 450 in N℃ 2 atmosphere.
S.I. GaAs Substrate
n-GaAs:cap
n-AlGaAs:Si doped
i-AlGaAs:spacer
i-GaAs
AuGeNi
NbN
AuGeNi
NbN
600 nm
5 nm
35 nm10 nm
50 nm
1500 nm
S.I. GaAs Substrate
n-GaAs:cap
n-AlGaAs:Si doped
i-AlGaAs:spacer
i-GaAs
NbN NbN
Alloyedohmicregion
Alloyedohmicregion
2DEG
Before annealing After annealing
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0 2 4 6 8 10 12 140.0
0.5
1.0
1.5
2.0
2.5
0
2
4
6
8
10
12
14
T~35 mK
Rxx (
k)
Magnetic field (T)
RH (k
)
Properties of 2DEG &NbN
n=7.36x1015m-2
=18.3m2/Vs
8 9 10 11 12 13 14 15 160.00
0.05
0.10
0.15
0.20NbN(150 nm)/AuGeNi(50 nm) on S.I.-GaAs
without annealing 400℃ - 1 min. 450℃ - 1 min. 500℃ - 1 min.
(m
cm
)
Temperature (K)
Magnetic field dependence of a Hall-bar shaped sample with normal conductor electrode (left). Temperature dependence of the resistance of NbN thin film (right).
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V Dependence of dV/dI
The differential resistance of a SNS junction. A decrease of a resistance (about 6%) is observed within V ~ 5mV, which corresponds to 2. is the superconducting energy gap of NbN.
-20.0 -10.0 0.0 10.0 20.0
96
98
100
102
104
106
108
110
T ~ 30 mK
W=50 m, L = 3m: NbN electrode
dV
/dI
()
Voltage (mV)
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Magnetic Field Dependence I
dV/dI v.s. V curves at weak magnetic fields. As magnetic field is increased, the Hall voltage arises in the 2DEG. So the voltage drop mainly occurs in the 2DEG rather than S/N interface. This causes the energy gap structure moves to higher voltages.
ne
IBV
VVV
H
HS/Ntot
-30.0 -20.0 -10.0 0.0 10.0 20.0 30.0
100
150
200
250
300
350
0.10 T
0.20 T
0.40 T
0.30 T
0.50 T
0.60 T
0.68 T
0.00 T
dV
/dI
()
Voltage (mV)
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Magnetic Field Dependence II
Magnetic field dependence of zero-bias resistance. The inset shows the junction length L dependence of R.
8 9 10 11 12 13 14 155
6
7
8
9
10
11
12
13
14
0.20
0.25
0.30
0.35
0.40
0.45
0.50
2 4 6 8 100
1
1
2
W = 50 m, L = 3 mT ~35 mK
R (
k)
Magnetic field (T)
Superconducting electrode Normal electrode
=2
=3
=4
R
R(h
/e2 )
L (m)
R (
k)
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Remarkable Features– The SNS junctions with superconducting electrodes
show deep resistance minima between =4 and =3.– The minima does not appear in the junction with normal
electrode.– The resistance minima become smaller as the junction
length L become longer.– Resistance of the SNS junctions are almost same as
the usual value h/e2, when the filling factor is integer.
These resistance minima can be explained by Andreev reflection.
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A Simple Explanation
top
2
][ Gh
eG
2
22
top )2(
2
T
T
h
eG
Imported from a model of S/N junctions at zero magnetic field.
SN2N1
B=8.0T B=9.2T
T=0 T≠ 0
B=12.5T
T≠ 0
Holes cannot propagate Holes can propagate Holes of spin down are not created
(1)
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L-dependence
The transmission probability T is calculated using Eq.(1) for several samples with different junction length L. T is almost proportional to 1/L as same as diffusive case.
0.0 0.1 0.2 0.3 0.4 0.50.75
0.80
0.85
0.90
0.95
T
1/L (m-1)
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Summary
• The SNS junction using a 2DEG in an AlGaAs/GaAs single heterostructure and High Hc2 superconductor NbN was fabricated.
• The transport properties of the SNS junctions have been investigated in the quantum Hall regime.
• Large resistance minima appear between the quantum Hall plateau, which are explained in terms of Andreev reflection between NbN and extended states at the center of the Landau level.
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How we can use graphene for this experiment ?