Kramers pairs of Majorana corner states in a topological insulator bilayer

TL;DR

This paper demonstrates that a bilayer topological insulator with superconducting proximity effects can host Kramers pairs of Majorana corner states, with phase diagrams influenced by time-reversal symmetry breaking perturbations, confirmed analytically and numerically.

Contribution

It introduces a second-order topological superconducting phase in a bilayer topological insulator system with Majorana corner states, including effects of symmetry-breaking perturbations.

Findings

Presence of Kramers pairs of Majorana corner states at all four corners.

Phase diagram with multiple phases influenced by Zeeman field.

Robustness of Majorana states against disorder and parameter variations.

Abstract

We consider a system consisting of two tunnel-coupled two-dimensional topological insulators proximitized by a top and bottom superconductor with a phase difference of $\pi$ between them. We show that this system exhibits a time-reversal invariant second-order topological superconducting phase characterized by the presence of a Kramers pair of Majorana corner states at all four corners of a rectangular sample. We furthermore investigate the effect of a weak time-reversal symmetry breaking perturbation and show that an in-plane Zeeman field leads to an even richer phase diagram exhibiting two nonequivalent phases with two Majorana corner states per corner as well as an intermediate phase with only one Majorana corner state per corner. We derive our results analytically from continuum models describing our system. In addition, we also provide independent numerical confirmation of the resulting phases using discretized lattice representations of the models, which allows us to demonstrate the robustness of the topological phases and the Majorana corner states against parameter variations and potential disorder.