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

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

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

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

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

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

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).

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)

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)

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)

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.

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)

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)

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.

How we can use graphene for this experiment ?