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Josepson Current in Four-Terminal Superconductor/Exciton- Condensate/Superconductor System 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

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Introduction 1.Exiton-Condensate Exciton – pair of electron and hole. Attracted by electrostatic Coulomb force. 2

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Introduction 2. Exciton Condensate in two layers Transport 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

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Introduction 3. Property of S/N/S Junction Supercurrent induced by phase difference. Dissipationless flow of suppercurrent Andreev reflection. 4

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Model top layer is negatively charged bottom layer is positively charged 5

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Equations Electron field operator Hamiltonian 6

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Equation 7 Order parameter in EC region Superconducting order parameters

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Four-particle Andreev reflection 8

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Long-junction limit 9 Superconducting gap is largest energy scale Boundary conditions Josephson current Dmitrii. L. Maslov et al, Phys. Rev. B 53, 1548 (1996)

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Long-junction limit Zero temperature 10 Current

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Long-junction limit Finite temperature 11 Current

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From the long- to short-junction limit: The scattering approach Equilibrium current Free energy Density of states Free energy 12

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Results Free energy For long-junction limit For short-junction limit 13

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Crossover regime 14

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Josephson Current in The Tunneling Regime Hamiltonian Free energy where Current 15

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Topologically protected QUBITS 16

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Conclusions 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 ( ψ T - ψ B )/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, ψ T = ψ B ); when the Josephson current is maximal ( ψ T = - ψ B ) 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 k B T, 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

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Thank you for attention 18

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