Tuning Majorana zero modes with temperature in π-phase Josephson junctions

Umberto Borla; Dushko Kuzmanovski; Annica M. Black-Schaffer

doi:10.1103/PhysRevB.97.014507

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Tuning Majorana zero modes with temperature in π-phase Josephson junctions

Umberto Borla, Dushko Kuzmanovski, Annica M. Black-Schaffer

DOI 10.1103/PhysRevB.97.014507 · Physical Review B

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Abstract

We study a superconductor–normal-state–superconductor Josephson junction along the edge of a quantum spin Hall insulator with a superconducting π phase across the junction. We solve self-consistently for the superconducting order parameter and find both real junctions, where the order parameter is fully real throughout the system, and junctions where the order parameter has a complex phase winding. Real junctions host two Majorana zero modes (MZMs), while phase-winding junctions have no subgap states close to zero energy. At zero temperature we find that the phase-winding solution always has the lowest free energy, which we establish as being due to a strong proximity effect into the N region. With increasing temperature this proximity effect is dramatically decreased and we find a phase transition into a real junction with two MZMs.