Majorana and parafermion corner states from two coupled sheets of bilayer graphene

TL;DR

This paper proposes a theoretical setup using coupled bilayer graphene sheets with strong spin-orbit interaction to realize second-order topological phases, including Majorana and parafermion corner states, influenced by electron interactions.

Contribution

It introduces a novel system of coupled bilayer graphene sheets that can host fractional topological phases with exotic corner states, advancing topological quantum matter research.

Findings

Supports a topological insulator phase with gapless helical edge states.

Demonstrates emergence of Majorana corner states under certain conditions.

Shows fractional phases with parafermion corner states influenced by electron interactions.

Abstract

We consider a setup consisting of two coupled sheets of bilayer graphene in the regime of strong spin-orbit interaction, where electrostatic confinement is used to create an array of effective quantum wires. We show that for suitable interwire couplings the system supports a topological insulator phase exhibiting Kramers partners of gapless helical edge states, while the additional presence of a small in-plane magnetic field and weak proximity-induced superconductivity leads to the emergence of zero-energy Majorana corner states at all four corners of a rectangular sample, indicating the transition to a second-order topological superconducting phase. The presence of strong electron-electron interactions is shown to promote the above phases to their exotic fractional counterparts. In particular, we find that the system supports a fractional topological insulator phase exhibiting fractionally charged gapless edge states and a fractional second-order topological superconducting phase exhibiting zero-energy $\mathbb{Z}_{2m}$ parafermion corner states, where $m$ is an odd integer determined by the position of the chemical potential.