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Mouhamadou Driss Badiane

Non-equilibrium properties of topological and multi terminal Josephson junctions

Published on 4 October 2013

Thesis presented October 04, 2013

Abstract:
This PhD thesis manuscript deals with the non equilibrium transport properties of superconducting mesoscopic systems. This study declines in two shutters: i) signatures of Majorana fermions in topological Josephson junctions and ii) current-current correlations in three-terminal Josephson junctions. Majorana fermions appears at the boundaries of topological superconductors. When two topological superconductors are connected to form a Josephson junction, the zero-energy Majorana bound states localized on either side of the junction form an Andreev bound state. As this current carrying state is 4π-periodic in the superconducting phase difference, it was speculated that, at finite dc bias voltage, the junction exhibits a fractional Josephson effect. We show that any finite phase velocity induces a dynamic coupling between the bound state and the continuum of states above the superconducting gap amplitude. This intrinsic coupling provides an unavoidable mechanism that alters the fractional Josephson effect. We discuss, in terms of the circuit parameters, signatures of the fractional Josephson effect that could be relevant for current experimental investigations: the even-odd effect in Shapiro steps and the emergence of a peak at fractional Josephson frequency in the current noise spectrum. Furthermore, other manifestations of the Majorana bound states on the subgap current-voltage characteristic are discussed. In a second step, we discuss the dissipative current fluctuations in three terminal Josephson junctions. Weshow that, current-current cross correlations can be positive and amplified in a coherent regime. This finding opens the possibility for further investigations on quantum entanglement in those systems

Keywords:
Majorana Fermions, Josephson Effect, Quantum Entanglement, Quantum Transport, Superconductors