Interlayer interaction in general incommensurate atomic layers

TL;DR

This paper introduces a comprehensive theoretical approach to model interlayer interactions in incommensurate bilayer systems with arbitrary structures, enabling analysis of complex 2D interfaces beyond traditional moiré superlattices.

Contribution

It develops a reciprocal space formulation based on generalized Umklapp processes for arbitrary incommensurate bilayers, extending beyond specific lattice types.

Findings

Successfully applied to large-angle bilayer graphene

Derived quasi band structure and density of states

Demonstrated applicability to complex incommensurate systems

Abstract

We present a general theoretical formulation to describe the interlayer interaction in incommensurate bilayer systems with arbitrary crystal structures. By starting from the tight- binding model with the distance-dependent transfer integral, we show that the interlayer coupling, which is highly complex in the real space, can be simply written in terms of generalized Umklapp process in the reciprocal space. The formulation is useful to describe the interaction in the two-dimensional interface of different materials with arbitrary lattice structures and relative orientations. We apply the method to the incommensurate bilayer graphene with a large rotation angle, which cannot be treated as a long-range moir\'{e} superlattice, and obtain the quasi band structure and density of states within the first-order approximation.