1

Ｓｕｐｒｃｏｎｄｕｃｔｉｎｇ Ｔｒａｎｓｐｏｒｔ ｉｎ ａｎ ＬＥＤ with Nb Electrodes

H. Takayanag 高柳英明 Tokyo University of Science,Tokyo

International Center for Materials NanoArchitechtonics (MANA), National Institute for Materials Science, Tsukuba

CREST, Japan Science and Technology Agency, Kawaguchi I. Suemune Hokkaido University

R. Inoue Tokyo University of Science T. Akazaki NTT Basic Research Laboratories K. Tanaka Hamamatsu Photonics

2

Background [I] -Superconducting proximity effect-

A cooper pair can penetrate into the normal metal with a decay length ξN.

Spatial dependence of the Cooper pair density F(x) at the Super/Normal interface

Superconducting proximity effect

TkD

BN π

ξ2

=

D : the diffusion constant in the N film

S N

Thermal bath

ξNCoherent electron pair

1

2Cooper pair

3

A cooper pair can penetrate into the normal metal with a decay length ξN.

Superconducting Proximity Effect

Ic ∝ exp(−L/ξN) /ξN

ξN = (D/2πk T)1/2B

Super Semicon. Super

Ic Superconducting critical current

L

coherence length

Metal (Semiconductor) : Dirty System ξN >

NL ξ≤

4 H. Takayanagi & T. Kawakami, Phys. Rev. Lett. 54 (1985) 2449

Superconductor

Cooper pair

Supercurrent through the 2DG

Wavw-function control by gate potential

Superconducting proximity effect

5

0 x

N S Electron

Hole E F

E

Cooper pair

∆ 0

θie0∆

Background II; Andreev Reflection

A. F. Andreev, Sov. Phys. JETP 19 (1964) 1228.

6

S N

S

EF

EF

2∆0

eV

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5

規格化された微分抵抗

バイアス電圧 V (mV)

Z

= 0.6

n =1

23

4= 0.85

Z

Multiple Andreev reflection

Subiharmonic gap structures

V =(2∆0 /e)

n(n =1,2,)

Bias voltage

Nor

mal

ized

dV/

dI

7 0.6

0.7

0.8

0.9

1

1.1

1.2

-4 -2 0 2 4

規格化された微

分抵

抗

V

n = 1

23

4

(mV)

dV/d

I T= 0.33 KL= 0.6

バイアス電圧

µm

多重アンドレーエフ反射

InGaAsInAlAs Nb

InGaAsInAlAs

n − InAlAs

InP Substrate

+

L

InAlAs

W

InAs 2DEG

L = 0.3 µm, Lg < 0.1 µm, W = 10 µm

Lg

Gate (Al)

NbInGaAsInAlAs

Nb Nb

InGaAsInAlAs

n − InAlAs

InP 基板

+

InAs (2DEG)

L

InAlAs

分割形ゲート

Lg

超伝導量子トランジスタと超伝導量子ポイントコンタクト

8

Superconductor-Based Quantum-Dot Light-Emitting Diodes

Injection of Electron Cooper pairs

p-type semiconductor

n-type semiconductor

Injection of hole pairs

QD Injection of Electron Cooper pairs

p-type semiconductor

n-type semiconductor

Injection of hole pairs

QD

Electron Cooper pairs are evanescently injected into the conduction band of the QD from the n-type semiconductor

When the Cooper-pair state energy in the n-type semiconductor is resonant with the QD lowest state in the conduction band, electron Cooper pairs are injected by the tunneling through thin barrier.

I. Suemune et al., Japn.J Appl. Phys. 45 (2006) 9264.

E. Hanamura: Phys. Status Solidi B 234 (2002) 166.

“Superradiance from p–n Junction of Hole- and Electron- Superconductors”

SQ-LED is based on the theory by

R. Recher Y. V. Nazarov,and L. P. Kouwenhoven arXiv:0902.4468v1(2009) “The Josephson light-emitｔing diode”

9

Tc

Superconductor-Based Light-Emitting Diodes 1

p-InP (substrate)

p-InP (1×1017 cm-3) : 500nm

n-In0.53Ga0.47As (5×1018 cm-3) : 30nm

n-In0.7Ga0.3As (5×1018 cm-3) : 10nmNb (800 Å) Nb (800 Å)

p-InP (substrate)

p-InP (1×1017 cm-3) : 500nm

n-In0.53Ga0.47As (5×1018 cm-3) : 30nm

n-In0.7Ga0.3As (5×1018 cm-3) : 10nmNb (800 Å) Nb (800 Å)

photon

p-n junction

Y. Hayashi et al., Appl.Phys. Express 1 (’08) 011701

EL intensity enhances below Tc of Nb.

10

SiN

Au

Nb Au

Nb Nb InGaAs

110nm

B A

eV

EFn

EFp

EC

EV

Nb n-InGaAs (40 nm)

p-InP sub

Normal Holes

Electron Cooper Pairs C

11

ON (250 µA) OFF (offset bias)

I. Suemune et al, Applied Physics Express, 3 (2010) 054001.

12

T > Tc T < Tc

Nb Nb

n-InGaAs

p-InP

Nb Nb

n-InGaAs

p-InP

Electron

Hole

Cooper pair

Superconductor-Based Light-Emitting Diodes 2

How is the enhancement of EL intensity explained ?

Electron and hole recombination Cooper-pair and hole recombination

Y. Asano, I. Suemune, H. T., and E. Hanamura, : Phys. Rev. Lett. 103 (2009) 187001.

“The second order perturbation theory for electron-photon interaction shows that the recombination of a Cooper with two p-type carriers causes drastic enhancement of the luminescence intensity.”

13

Superconductor-Based Light-Emitting Diodes 2

How is the enhancement of EL intensity explained ?

Y. Asano, I. Suemune, H. T., and E. Hanamura, : Phys. Rev. Lett. 103 (2009) 187001.

14

Ordinary emission spectra per unit time are described well by the Fermi’s golden rule within the first order expansion with respect to the dipole interaction between an electron and a photon.

)2(

)(2)( 21

µω

ζξδπω

++−=Ω

−−Ω= −∑vcqq

qkkqk

q

EE

Bn

B: the amplitude of the dipole interaction.

In a superconducting pn junction, the final state of a superconductor after emitting a pair of photons is very similar to the initial state before emitting. This is the background of resonant-like emission process of a pair of photons. The emission spectra of a superconducting pn junction is calculated by the second order perturbation .

222242 )/()(2)( ∆+∆−Ω= −∑ kqkq

kq Bn ξξδπω

2212 /)(/)( ∆≈ Bnn qq ωω

Resonant-like emission enhancement

kξ

15

Junction Structure

Single-hetero structure (Type J)

p-InP (substrate)

p-InP (1×1017 cm-3) : 500nm

n-In0.53Ga0.47As (5×1018 cm-3) : 30nm

n-In0.7Ga0.3As (5×1018 cm-3) : 10nm

Nb (800 Å) Nb (800 Å)

Nb Nb

20 µm

20 µm

Nb slit~0.15 µm

p-InP

In order to confirm further the cooper pair effect on the recombination in the active layer, the I-V characteristics between two Nb electrodes were measured.

In0.53Ga0.47As InP

0.810 eV 1.408 eV

Positive bias

Zero bias

Depletion layer~ 10 nm

16

I-V characteristics at 30 mK

InGaAs Mean free path

0.3Katμm4.0~kT2D

N πξ

=

Coherence length

Clear supercurrent

Injected cooper pairs can reach the InGaAs active layer and help to enhance EL below Tc

Nb Nb Nb Nb

supercurrent Cooper pair

-0.2 -0.1 0.0 0.1 0.2-4

-2

0

2

4

Curre

nt (µ

A)

Voltage (mV)

@ 30 mK

m076.0 µ≈

17

-40 -30 -20 -10 0 10 20 30 40

0

30

60

90

120

@32 mK

Res

ista

nce

(Ohm

)

Current (µA)

-4 -3 -2 -1 0 1 2 3 40

30

60

90

120

Diff

eren

tial R

esist

ance

(Ohm

)

Voltage (mV)

@ 32 mK

dV/dI-V characteristics dV/dI-I characteristics

Structures due to multiple Andreev reflection

Differential resistance characteristics at 30 mK

Large reduction of Rn

18

AC Josephson effect

-100 -75 -50 -25 0 25 50 75 100-3

-2

-1

0

1

2

3

RF Off RF 8 GHz RF 12 GHz RF 16 GHz RF 20 GHz

Curre

nt (µ

A)

Voltage (µV)

2.1 µV/GHz

19

pn Junction Characteristics

V, I -V, -I

Vp

A Ip

-1.0 -0.5 0.0 0.5 1.0

0

20

40

60

80

100

Injec

tion C

urren

t Ip (n

A)

Gate Voltage Vp (V)

0.0 0.2 0.4 0.6 0.8 1.00.001

0.01

0.1

1

10

100

1000

20

-6

-4

-2

0

2

4

6

Gate Voltage+1.0 V+0.8 V

+0.6 V+0.4 V

+0.2 V0 V

-0.2 V-0.4 V

-0.6 V-0.8 V

-1.0 V

Curre

nt (µ

A)

Voltage (0.1 mV/div)

Ic and Rn Change with Gate Voltage Vp.

V, I -V, -I

Vp

A Ip

Gate voltage control

21

Gate Voltage Dependence Ic and Rn

0

25

50

75

100

125

150

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0

1.5

2.0

2.5

Criti

cal C

urren

t Ic (µ

A)

Gate Voltage (V)

Norm

al Re

sistan

ce R

n (Ohm

)

0.001 0.01 0.1 1 10 1001.5

1.6

1.7

1.8

1.9

2.0

Criti

cal C

urren

t Ic (µ

A)

Injection Current (nA)

Ic increases by gate voltage with no Ip. IC shows saturation (or decrease) when Ip >0.

IC starts to decrease at Ip > 1nA and disappear at Ip>1 µA.

0.0 0.2 0.4 0.6 0.8 1.0 0.001

0.01

0.1

1

10

100

1000

p-n junction

Vp (V)

Ip (n

A)

22

0.001 0.01 0.1 1 10 1001.5

1.6

1.7

1.8

1.9

2.0

Criti

cal C

urren

t Ic (µ

A)

Injection Current (nA)

Three regions for gate effect on the supercurrent

Region I

Region II

Region II

Region III

III

I

Region Vp Ip Behaviour of Ic I Vp< 0.35 V Ip ～0 increases with Vp, Ip II 0.35 V < Vp< 0.88 V 0 < Ip < 10 nA constant III 0.88 V < Vp 10 nA < Ip decreases with Vp, Ip Three regions in gate voltage Vp and injection current Ip.

0

25

50

75

100

125

150

-1.0 -0.5 0.0 0.5 1.0 0.0

0.5

1.0

1.5

2.0

2.5

Crit

ical

Cur

rent

I c ( µ A

)

Gate Voltage (V)

Nor

mal

Res

ista

nce

R n (O

hm)

23

Region I

Region I for gate effect on the supercurrent

Region I

No injection current Ip = 0

Ic increases with decreasing Vp. It is because the channel for the supercurrent increases with the decrease of the depletion layer.

V, I -V, -I

Vp

A Ip

-2 V < Vp < 0.4 V

Nb Nb

Nb Nb

Depletion layer

IC increases

Cooper pairs can reach at the end of the depletion layer.

0

25

50

75

100

125

150

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0

1.5

2.0

2.5

Criti

cal C

urre

nt I

c (µA

)

Gate Voltage (V)

Nor

mal

Res

istan

ce R

n (O

hm)

24 H. Takayanagi & T. Kawakami, Phys. Rev. Lett. 54 (1985) 2449

超伝導体

クーパー対

純２次元系に超伝導電流が流れた

巨視的波動関数をゲートポテンシャル で制御

超伝導近接効果

25

InGaAsInAlAs Source

(Super- conductor Nb)

Drain

InGaAsInAlAs

n − InAlAs

InP Substrate

+

L

InAlAs

W

InAs 2DEG

L = 0.3 µm, Lg < 0.1 µm, W = 10, 40 µm

Lg

Gate (Al)

Ns = 2.3 x 10 cm12 -2 µ = 111,000 cm /Vs2 at 4.2 K

– 3 µm >> L, >> ξ Ν = vF /2πkBT

-8

-6

-4

-2

0

2

4

6

8

-0.1 -0.05 0 0.05 0.1

Curre

nt (

µA)

Voltage (mV)

Vg = 0 V-0.4 V-0.6 V-0.7 V

-0.8 V

-0.9 V-1.1 V

T = 1 K

Josephson Field Effect Transistor (JOFET)

It has a voltage gain. T. Akazaki, H. Takayanagi & J. Nitta, Appl. Phys. Lett. 68 (1996) 418.

26

Region I

Region I for gate effect on the supercurrent

Nb Nb

Nb Nb

Depletion layer IC increases

0

25

50

75

100

125

150

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0

1.5

2.0

2.5

Criti

cal C

urre

nt I

c (µA

)

Gate Voltage (V)

Nor

mal

Res

istan

ce R

n (O

hm)

-1.0 -0.5 0.0 0.5 1.00

50

100

150

200

250

I cR n prod

uct (

µV)

Gate Voltage (V)

Region I Why do IcRn product as well as Ic increase with gate voltage ?

27

Region III for gate effect on the supercurrent

Region III

Cp II ≥ or Cp II >>

IC goes to disappear due to non-equilibrium effect.

0

25

50

75

100

125

150

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0

1.5

2.0

2.5

Criti

cal C

urren

t Ic (µ

A)

Gate Voltage (V)

Norm

al Re

sistan

ce R

n (Ohm

)

0.001 0.01 0.1 1 10 1001.5

1.6

1.7

1.8

1.9

2.0

Criti

cal C

urren

t Ic (µ

A)

Injection Current (nA)

Region III

III

28

Region II for gate effect on the supercurrent

Region II Measured Ic is almost constant but real Ic seems to decrease. It is because Rn still decreases by gate voltage in Region II. 0 < Ip < 100 nA

Why ?? Photon emiｔtion starts

0

25

50

75

100

125

150

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0

1.5

2.0

2.5

Criti

cal C

urren

t Ic (µ

A)

Gate Voltage (V)

Norm

al Re

sistan

ce R

n (Ohm

)

0.001 0.01 0.1 1 10 1001.5

1.6

1.7

1.8

1.9

2.0

Criti

cal C

urren

t Ic (µ

A)

Injection Current (nA)

Region II

Region II

29

-1.0 -0.5 0.0 0.5 1.00

50

100

150

200

250

I cR n prod

uct (

µV)

Gate Voltage (V)-1.0 -0.5 0.0 0.5 1.0

0.0

0.5

1.0

1.5

2.0

2.5

Criti

cal C

urren

t Ic (µ

A)

Gate Voltage (V)

extrapolated

fixed IcRn

extrapolated

fixed IcRn

0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.801.8

1.9

2.0

2.1

2.2

2.3

Critical

Curr

ent

Ic (µ

A)

Gate Voltage (V)

Ic should increase because Rn still decreases in Region II.

Real IcRn or Ic in Region II

Josephson junction characteristics has an extraordinary sensitivity to the radiative recombination process.

30

Nb Nb

n-InGaAs

p-InP

Cooper pair carried in the injection current Ip.

Cooper pair carried in the form of the supercurrent.

Cooper pairs carried in the form of supercurrent are destroyed by a photon emitted from the p-n junction.

31

n-InGaAs

Hot electron

Elecreons

The recombination efficviency is about 100 ~ 800/

32

Measurements of a new sample

Check of the reproducibility using a new sample(80C). Cool down of both samples.

(new one 80C and old one 90C)

Heavily-filtered measurement system

Temperature dependence

Magnetic field dependence

33

New sample

-1.0 -0.5 0.0 0.5 1.0-3

-2

-1

0

1

2

3

Curre

nt (µ

A)

Voltage (mV)

30 mK, VG = 0 V

Type J P3 80C

-3 -2 -1 0 1 2 3-10

-5

0

5

10

30 mK, VG = 0 V

Curre

nt (µ

A)

Voltage (mV)

Type J P3 80C

-0.2 -0.1 0.0 0.1 0.2-4

-2

0

2

4

Curre

nt (µ

A)

Voltage (mV)

30 mK, VG = 0 V

Type J P3 90C

Ic(1) 0.6 µA … Vc 1 µV

Ic(2) 1.95 µA … Vc 100 µV

Rn 380 Ω

34

Current Injection Effect for a new sample

-2

-1

0

1

2

+1.1 V+0.9 V

+0.7 V+0.5 V

+0.3 V+0.1 V

-0.1 V-0.3 V

-0.5 V

Curre

nt (µ

A)

Voltage (20 µV/div)

-0.7 V

0 1 20.001

0.01

0.1

1

10

100

1000

10000

-2 -1 0 1 2

0

500

1000

1500

2000

Injec

tion C

urren

t (nA

)

Gate Voltage (V)

0.0

0.5

1.0

1.5

2.0

-2 -1 0 1 2

0.0

0.2

0.4

0.6

0.8

1.0

Criti

cal C

urren

t IC(1

) (µA)

Gate Volatege (V)

Criti

cal C

urren

t IC(2

) (µA)

0.0

0.5

1.0

1.5

2.0

0.0001 0.001 0.01 0.1 1 10 100 1000 10000

0.0

0.2

0.4

0.6

0.8

1.0

Criti

cal C

urren

t IC(1

) (µA)

Injection Current (nA)

Criti

cal C

urren

t IC(2

) (µA)

35

Type J P3 80C Current Injection Effect(2)

300

320

340

360

380

400

-2 -1 0 1 21.2

1.4

1.6

1.8

2.0

Criti

cal C

urren

t IC(2

) (µA)

Gate Volatege (V)

Norm

al Re

sistan

ce R

n (Ω)

300

320

340

360

380

400

-1 0 1 2

0.0

0.2

0.4

0.6

0.8

1.0

Criti

cal C

urren

t IC(1

) (µA)

Gate Volatege (V)

Norm

al Re

sistan

ce R

n (Ω)

0

25

50

75

100

125

150

-1.0 -0.5 0.0 0.5 1.00.0

0.5

1.0

1.5

2.0

2.5

Criti

cal C

urre

nt I

c (µA)

Gate Voltage VG (V)

IIIIII

Norm

al Re

sistan

ce R

n (Ohm

)

36

• Transport properties of a superconductor-based light emitting diode was measured. • A clear supercurrent was confirmed. This indicates that Cooper pairs enhance the EL below Tc. • The supercurrent (critical current Ic) showed first an enhancement and then a

saturation and finally disappear by increasing gate voltage. • The gate effects on Ic can be explained as follows. (i) Vp < 0.4 V : Ic increases due to the enhancement of the semiconductor channel. (ii) 0 < Ip <100 nA : . Ic is almost constant and Josephson current is very sensitive to radiative recombination process. Ic is almost constant. Cooper pairs might be destroyed by emitted photons. (iii) Ip > Ic : Ic disappears due to non-equilibrium effect.

Summary

37

Type J P3 80C Magnetic Field Dependence

-10 -8 -6 -4 -2 0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

1.0

Criti

cal C

urren

t Ic(1

) (µA)

Magnetic Field (G)

-30 -20 -10 0 10 20 301

2

3 -Ic-

Ic+

I c(2) (µ

A)

Magnegic Field (G)

-30 -20 -10 0 10 20 301

2

3 -Ic-

Ic+

I c(2) (µ

A)δB S = Φ0 / δB W = S / L (L = 0.15 µm)

Ic(1) 0.27 G 76.6 µm2 510 µm >> 20 µm

6 G ?? 3.5 µm2 23 µm

Ic(2) 7 G ?? 3.0 µm2 20 µm

Fraunhofer pattern was not observed.

38

Type J P3 90C Magnetic Field Dependence (previous sample)

-2000 -1000 0 1000 20000.0

0.5

1.0

1.5

2.0

2.5

Criti

cal C

urren

t (µA

)

Magnetic Field (G)

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.50.0

0.5

1.0

1.5

Criti

cal C

urren

t (µA

)

Magnetic Field (T)

δB > 2000 G, S = Φ0 / δB < 0.01 µm2, W = S / L< 69 nm

39

Magnetic Field Dependence

-1.0 -0.5 0.0 0.5 1.0-6

-4

-2

0

2

4

6

0 T 1.0 T 2.0 T 3.0 T 4.0 T 5.0 T 6.0 T 7.0 T 10.0 T

Curre

nt (µ

A)

Voltage (mV)0

50

100

150

200

250

0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Criti

cal C

urren

t Ic (

µA)

Magnetic Field (T)

Norm

al Re

sistan

ce (O

hm)

40

Josephson Junction Characteristics

-0.2 -0.1 0.0 0.1 0.2-4

-2

0

2

4

Curre

nt (µ

A)

Voltage (mV)

@ 30 mK

Ic = 1.52 µA , Rn = 102 Ohm @ T = 30 mK, Ip = 0 nA hysterisis