Superconductivity in monolayer and few-layer graphene: II. Topological edge states and Chern numbers

TL;DR

This paper investigates topological edge states and Chern numbers in superconducting monolayer, bilayer, and trilayer graphene, revealing how stacking, chemical potential, and normal state properties influence topological phases.

Contribution

It provides a detailed analysis of topological phases in superconducting graphene, highlighting the role of stacking, warping, and normal state band structure in determining Chern numbers.

Findings

Rich Chern phase diagram depends on stacking and parameters.

Unique Chern number region in rhombohedral stacking.

Normal state band structure influences topological properties.

Abstract

We study the emergence of electronic edge states in superconducting (SC) monolayer, bilayer, and trilayer graphene for both spin-singlet and spin-triplet SC order parameters. We focus mostly on the gapped chiral $p+ip'$- and $d+id'$-wave SC states that show a non-zero Chern number and a corresponding number of edge states. For the $p+ip'$-wave state, we observe a rich Chern phase diagram when tuning the chemical potential and the SC order parameter amplitudes, which depends strongly on the number of layers and their stacking, and is also modified by trigonal warping. At small parameter values we observe a region whose Chern number is unique to rhombohedrally stacked graphene, and is independent of the number of layers. Our results can be understood in relation not only to the SC order parameter winding as expected, but also to the normal state band structure. This observation establishes the importance of the normal state characteristics for understanding the topology in SC graphene systems.