Valley Chern Numbers and Boundary Modes in Gapped Bilayer Graphene

TL;DR

This paper investigates boundary modes in gapped bilayer graphene, revealing their topological origins and the effects of intervalley coupling through continuum, lattice, and quantum geometric analyses.

Contribution

It introduces a comprehensive analysis combining continuum models, lattice calculations, and quantum geometry to understand boundary modes and topological transitions in bilayer graphene.

Findings

Boundary modes are explained by topological transitions and gap closures.

Intervalley coupling significantly affects boundary mode properties.

Continuum models capture some features but require lattice calculations for full accuracy.

Abstract

Electronic states at domain walls in bilayer graphene are studied by analyzing their four and two band continuum models, by performing numerical calculations on the lattice, and by using quantum geometric arguments. The continuum theories explain the distinct electronic properties of boundary modes localized near domain walls formed by interlayer electric field reversal, by interlayer stacking reversal, and by simultaneous reversal of both quantities. Boundary mode properties are related to topological transitions and gap closures which occur in the bulk Hamiltonian parameter space. The important role played by intervalley coupling effects not directly captured by the continuum model is addressed using lattice calculations for specific domain wall structures.