Interplay of quantum spin Hall effect and spontaneous time-reversal symmetry breaking in electron-hole bilayers II: Zero-field topological superconductivity

TL;DR

This paper proposes a method to realize and detect Majorana zero modes in electron-hole bilayers with spontaneous time-reversal symmetry breaking, using proximity-induced superconductivity and Josephson junctions, without requiring magnetic fields.

Contribution

It introduces an analytical low-energy theory for Majorana modes in time-reversal symmetry broken phases and demonstrates their detection via Josephson current measurements and gate voltage control.

Findings

Majorana zero modes can exist without magnetic fields in electron-hole bilayers.

A good agreement between analytical and numerical results is achieved in weak symmetry breaking.

Detection of Majorana modes is feasible through $4 ext{pi}$ Josephson current and gate voltage tuning.

Abstract

It has been proposed that band-inverted electron-hole bilayers support a phase transition from an insulating phase with spontaneously broken time-reversal symmetry to a quantum spin Hall insulator phase as a function of increasing electron and hole densities. Here, we show that in the presence of proximity-induced superconductivity it is possible to realize Majorana zero modes in the time-reversal symmetry broken phase in the absence of magnetic field. We develop an effective low-energy theory for the system in the presence of time-reversal symmetry breaking order parameter to obtain analytically the Majorana zero modes and we find a good agreement between the numerical and analytical results in the limit of weakly broken time-reversal symmetry. We show that the Majorana zero modes can be detected in superconductor/time-reversal symmetry broken insulator/superconductor Josephson junctions through the measurement of a $4\pi$ Josephson current. Finally, we demonstrate that the Majorana fusion-rule detection is feasible by utilizing the gate voltage dependence of the spontaneous time-reversal symmetry breaking order parameter.