Stacking Textures and Singularities in Bilayer Graphene

TL;DR

This paper explores the design and analysis of smooth, topologically interesting stacking textures in bilayer graphene, revealing new patterns and rules for complex stacking configurations.

Contribution

It introduces a framework for constructing and understanding two-dimensional twisted stacking textures and their interactions in bilayer graphene.

Findings

Identified strain-minimizing stacking patterns connecting different ground states.

Developed composition rules for complex stacking textures.

Displayed topological stacking textures and their interactions.

Abstract

We study a family of globally smooth spatially varying two dimensional stacking textures in bilayer graphene. We find that the strain-minimizing stacking patterns connecting inequivalent ground states with local $AB$ and $BA$ interlayer registries are two dimensional twisted textures of an interlayer displacement field. We construct and display these topological stacking textures for bilayer graphene, examine their interactions and develop the composition rules that allow us to represent other more complex stacking textures, including globally twisted graphenes and extended one dimensional domain walls.