Josepson Current in Four-Josepson Current in Four-Terminal Terminal

Superconductor/Exciton-Superconductor/Exciton-Condensate/Superconductor Condensate/Superconductor

SystemSystem

S. Peotta, M. Gibertini, F. Dolcini, F. Taddei, M. Polini,

L. B. Loffe, R. Fazio, and A. H. MacDonald

Physical Review B 84, 184528 (2011)

Speaker Iryna Kulagina

IntroductionIntroduction1.Exiton-Condensate1.Exiton-Condensate

Exciton – pair of electron and hole.

Attracted by electrostatic Coulomb force.

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IntroductionIntroduction2. Exciton Condensate in two 2. Exciton Condensate in two

layerslayersTransport energy without transporting net electric charge

e - h superconductivity

Y.E.Lozovil, V.I.Yudson, Pis’ma Zh. Eksp. Teor. Fiz. 22, 556 (1975)

(JETP Lett. 22, 274 (1975))

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IntroductionIntroduction3. Property of S/N/S Junction3. Property of S/N/S Junction

Supercurrent induced by phase difference.

Dissipationless flow of suppercurrent

Andreev reflection.

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ModelModel

top layer is negatively charged

bottom layer is positively charged

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EquationsEquationsElectron field operator

Hamiltonian

6

( ) ( )ˆ ˆ ˆ( ) ( ) ( )F Fik x ik xx e x e x

*

* *

*

( ) ( ) 0

( ) 0 ( )

( ) 0 ( )

0 ( ) ( )

F x T

F x B

T F x

B F x

ip v x x

x ip v xH

x ip v x

x x ip v

ˆ ˆ ˆ ˆ ˆ( ) ( ), ( ), ( ), ( )T

p T p B p T p B px x x x x

EquationEquation

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Order parameter in EC region

Superconducting order parameters

( ) , / 2 / 2( )

0,

i qxe L x Lx

otherwise

( ),

( ),

( )

, / 2

( ) 0, / 2 / 2

, / 2

T B L

T B R

i

T B

i

e x L

x L x L

e x L

Four-particle Andreev Four-particle Andreev reflectionreflection

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*

*

T T

B B

a

b

T B

B T

c

d

* * * * 1T T

ac b d ac b d

Long-junction limitLong-junction limit

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Superconducting gap is largest energy scale

Boundary conditions

Josephson current

Dmitrii. L. Maslov et al, Phys. Rev. B 53, 1548 (1996)

SL

,

,

,

,

ˆ ˆ(0) (0)

ˆ ˆ(0) (0)

ˆ ˆ( ) ( )

ˆ ˆ( ) ( )

L

L

R

R

i

i

i

i

i e

i e

L i e L

L i e L

†

, ,

ˆ ˆ ˆ( ) ( )F p pp

I ev p x x

, ,GS TFI I I

Long-junction limitLong-junction limitZero temperatureZero temperature

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Current / 2F T B

T B

evI

L

Long-junction limitLong-junction limitFinite temperatureFinite temperature

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Current

/

sinh( / 2)1 2

2 / 2thF T B

T Bth

qLevI e

L qL

1S ECL L

/F Bv L k T

From the long- to short-junction From the long- to short-junction limit: The scattering approachlimit: The scattering approach

Equilibrium current

Free energy

Density of states

Free energy

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2 JFeI

0

( )JF d

1( ) ln(det )

2S

i

2 2( ) ( ) 2 cos( )

2 4F R L

J

v qLF qL qL

L

ResultsResultsFree energy

For long-junction limit

For short-junction limit

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2 2( ) ( ) 2 cos( )

2 4F R L

J

v qLF qL qL

L

2R LqL n

2

2 2F R R

J

vF

L

/ ( ) 2

J F R LT B

dF eveI

d qL L

2Fv

L

2 / 1SL

sin2 4

R LqL

2 cos4

R LJF

/ sin4

R LT B R L

eI

Crossover regimeCrossover regime

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SL

Josephson Current inJosephson Current in The Tunneling Regime The Tunneling Regime

Hamiltonian

Free energy

where

Current

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, ,, ,

S i EC Ti L R T B

H H H H

, , , ,( ) 2 2 2EC L L T L B R R T R BF F qL F F qL

4 2 2

, ,

4, , cos 2L L T L BF t I

4 2 2

, ,

4, , cos 2 2L R T R BF t I qL

2

2 22 2 2 2

1 1, ,

n p n p n p

I

2( ) ( )2

FEC

vF qL qL

L

/ sin2

T BT B cI I

Topologically protected Topologically protected QUBITSQUBITS

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T B

T B

( ) (2 )T BF F

ConclusionsConclusions In this work, they have calculated the Josephson current between two

pairs of superconducting terminals coupled by a bilayer electron system that is EC. They considered the regime of strong exciton coupling where the bilayer gap is the largest energy scale. In this limit, quasiparticles can not propagate through the bilayer, and the Josephson current is entirely due to the conversion of Cooper-pair current into counterflow excitonic supercurrent.

The superconducting phases enter in Josephson current expression only in combination (ψT - ψB)/2. Electrons are transferred through such a hybrid junction in group of four.

In such structures can appear situation when the Josephson current doesn’t flow through junction (exciton blockade, ψT = ψB); when the Josephson current is maximal (ψT = - ψB) with a critical value equals to half the critical current of ballistic one-channel SNS junction. And such device allows to realize a drag of dissipationless current, when current in different layers equal in magnitude but opposite in direction.

At finite temperature, when EC gap is larger than kBT , the current is essentially unaffected by thermal fluctuations. Andreev reflection processes coherently occurring at the two interfaces transform Cooper pairs into electron-hole pairs of the EC, which are protected from thermal decoherence by the excitonic gap.

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Thank you for

attention

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