Multifold Majorana corner modes arising from multiple pairs of helical edge states

TL;DR

This paper demonstrates that quantum spin Hall insulators with multiple pairs of helical edge states can host robust multifold Majorana corner modes when combined with superconductivity and magnetic fields, expanding potential platforms for topological quantum computing.

Contribution

It introduces a model with two pairs of helical edge states supporting multifold Majorana corner modes under specific conditions, highlighting a new platform for topological superconductivity.

Findings

Twofold Majorana corner modes are achievable with magnetic and pairing effects.

Majorana modes are protected by chiral symmetry under magnetic fields.

Heterostructures with multiple helical edge states can host multifold Majorana modes.

Abstract

Quantum spin Hall insulators with a pair of helical edge states and proximity-induced superconductivity have been shown to support second-order topological superconductors with Majorana corner modes. As the Majorana corner modes are originated from the helical edge states of the quantum spin Hall insulators, whether quantum spin Hall insulators with multiple pairs of helical edge states and proximity-induced superconductivity can give rise to second-order topological superconductors with multifold Majorana corner modes is an interesting question to address. In this work, we consider a quantum spin Hall insulator with two pairs of helical edge states. We find robust twofold Majorana corner modes can be achieved when the helical edge states are gapped by a combined action of a magnetic exchange field and an $s$-wave pairing, or an $s+p$ mixed-parity pairing. The stability of two Majorana zero modes per corner under the action of magnetic exchange fields is attributed to the protection from the chiral symmetry. Our study reveals that heterostructures composed of superconductors and quantum spin Hall insulators with multiple pairs of helical edge states could serve as a platform to pursue multifold Majorana corner modes.