Can Majorana zero modes in quantum Hall edges survive edge reconstruction?

TL;DR

This paper investigates the stability of Majorana zero modes in quantum Hall edges with edge reconstruction, revealing new topological sectors and fractional Josephson effects.

Contribution

It demonstrates that edge reconstruction creates additional topological sectors, affecting the behavior of Majorana zero modes and Josephson currents.

Findings

Edge reconstruction doubles the topological sectors to Z2 x Z2.

The many-body spectrum shows a 4π Josephson periodicity.

Distinct edge velocities influence fractional Josephson current signatures.

Abstract

Parafermion zero modes can be trapped in the domain walls of quantum Hall edges proximitized by superconductors and ferromagnets. The $\nu = 1/3$ fractional quantum Hall side strip arising due to edge reconstruction of a $\nu = 1$ edge doubles the number of topological sectors such that each of them is $Z_{2} \times Z_{2}$ degenerate. The many-body spectrum displays a $4\pi$ Josephson periodicity, with the states in each $Z_{2}$ being energetically decoupled. Signatures of the new states appear in the fractional Josephson current when the edge velocities are taken to be different.