General continuum model for twisted bilayer graphene and arbitrary smooth deformations

TL;DR

This paper derives a unified continuum Hamiltonian for bilayer graphene with arbitrary smooth deformations, encompassing twisted bilayer graphene and other extensions, using a real-space approach.

Contribution

It provides a simple, real-space derivation of a general continuum model for bilayer graphene with arbitrary smooth lattice deformations.

Findings

Unifies various continuum models under a single framework.

Enables analysis of arbitrary smooth deformations in bilayer graphene.

Simplifies the derivation process compared to previous methods.

Abstract

We present a simple derivation of a continuum Hamiltonian for bilayer graphene with an arbitrary smooth lattice deformation -- technically in a fashion parametrized by displacement fields with small gradients. We show that this subsumes the continuum model of Bistritzer and Macdonald for twisted bilayer grapheneas well as many generalizations and extensions of it. The derivation is carried out entirely in real space.