Phase diagram of superconductivity in the integer quantum Hall regime

TL;DR

This paper explores the phase diagram of superconductivity in the quantum Hall regime, revealing transitions from quantum Hall to skyrmion and vortex phases with Majorana modes, using self-consistent mean-field calculations.

Contribution

It presents a detailed theoretical analysis of superconducting phases and topological transitions in a Hofstadter lattice with attractive interactions, highlighting the emergence of Majorana modes.

Findings

Transition from quantum Hall to skyrmion lattice with topological edge currents

Vortex phase with Majorana modes forming a lattice and a low-energy Majorana band

Identification of parameter regimes with no low-energy Majorana modes

Abstract

An interplay between pairing and topological orders has been predicted to give rise to superconducting states supporting exotic emergent particles, such as Majorana particles obeying non-Abelian braid statistics. We consider a system of spinless electrons on a Hofstadter lattice with nearest neighbor attractive interaction, and solve the mean-field Bogoliubov-de Gennes equations in a self-consistent fashion, leading to gauge invariant solutions that display a rich phase diagram as a function of the chemical potential, magnetic field and the interaction. As the strength of the attractive interaction is increased, the system first makes a transition from a quantum Hall phase to a skyrmion lattice phase that is fully gapped in the bulk but has topological chiral edge current, characterizing a topologically non-trivial state. This is followed by a vortex phase in which the vortices carrying Majorana modes form a lattice; the spectrum contains a low-energy Majorana band arising from the coupling between neighboring vortex-core Majorana modes but does not have chiral edge currents. For some parameters, a dimer vortex lattice occurs with no low energy Majorana band. The experimental feasibility and the observable consequences of skyrmions as well as Majorana fermions are indicated.