josepson current in four-terminal superconductor/exciton- condensate/superconductor system s....
TRANSCRIPT
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.
2
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))
3
IntroductionIntroduction3. Property of S/N/S Junction3. Property of S/N/S Junction
Supercurrent induced by phase difference.
Dissipationless flow of suppercurrent
Andreev reflection.
4
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
7
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
8
*
*
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
9
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
10
Current / 2F T B
T B
evI
L
Long-junction limitLong-junction limitFinite temperatureFinite temperature
11
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
12
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
13
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
Josephson Current inJosephson Current in The Tunneling Regime The Tunneling Regime
Hamiltonian
Free energy
where
Current
15
, ,, ,
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
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.
17