General continuum model for twisted bilayer graphene and arbitrary smooth deformations

We present a simple derivation of a continuum Hamiltonian for bilayergraphene with an arbitrary smooth lattice deformation – technically in afashion parametrized by displacement fields with small gradients. Weshow that this subsumes the continuum model of Bistritzer and Macdonaldfor twisted bilayer graphene as well as many generalizations andextensions of it. The derivation is carried out entirely in realspace.