Robust one-dimensional wires in lattice mismatched bilayer graphene

TL;DR

This paper demonstrates that lattice mismatched bilayer graphene can host robust one-dimensional topological wires at domain walls, with their existence depending on the wall orientation and Dirac cone positions, generalizing to arbitrary domain wall patterns.

Contribution

It introduces a projection principle for topological zero-energy states in bilayer graphene and generalizes the conditions for their existence across various domain wall configurations.

Findings

Topological zero-energy states depend on domain wall orientation.

Existence of states requires an odd number of domain walls.

Generalized the principle for arbitrary domain wall patterns.

Abstract

We show that lattice mismatched bilayer graphene can realize robust one-dimensional wires. By considering a single domain wall where the masses of the Dirac electrons change their sign, we establish a general projection principle. This determines how the existence of topological zero-energy domain wall states depends on the direction of the domain wall and locations of the massive Dirac cones inside the bulk Brillouin zone. We generalize this idea for arbitrary patterns of domain walls, showing that the topologically protected states exist only in the presence of an odd number of topological domain walls.