Majorana fermions on the quantum Hall edge

TL;DR

This paper investigates Majorana fermions at the quantum Hall edge in a superconducting Josephson junction, revealing features that could aid in detecting topological phase transitions and the spin properties of Majorana modes.

Contribution

It introduces a combined numerical and analytical study of Majorana modes in quantum Hall-superconductor hybrid structures, highlighting their spectral signatures and topological transitions.

Findings

Distinct features in Andreev levels and Fraunhofer patterns identified

Numerical tight-binding calculations describe the topological transition

A low-energy spinful model captures key transport properties

Abstract

Superconductivity and the quantum Hall effect are considered to be two cornerstones of condensed matter physics. The realization of hybrid structures where these two effects coexist has recently become an active field of research. In this work, we study a Josephson junction where a central region in the quantum Hall regime is proximitized with superconductors that can be driven to a topological phase with an external Zeeman field. In this regime, the Majorana modes that emerge at the ends of each superconducting lead couple to the chiral quantum Hall edge states. This produces distinguishable features in the Andreev levels and Fraunhofer patterns that could help in detecting not only the topological phase transition but also the spin degree of freedom of these exotic quasiparticles. The current phase relation and the spectral properties of the junction throughout the topological transition are fully described by a numerical tight-binding calculation. In pursuance of the understanding of these results, we develop a low-energy spinful model that captures the main features of the numerical transport simulations in the topological phase.