Electronic Density of States for Incommensurate Layers

TL;DR

This paper establishes a rigorous mathematical foundation for the electronic density of states in 2D incommensurate layered materials, providing an explicit formula and a new computational algorithm that avoids traditional supercell methods.

Contribution

It proves the well-definedness of the DOS as a thermodynamic limit and introduces a novel algorithm for electronic structure calculations in incommensurate heterostructures.

Findings

DOS is well-defined as the thermodynamic limit

Explicit integral representation formula for DOS

New algorithm for incommensurate heterostructure computations

Abstract

We prove that the electronic density of states (DOS) for 2D incommensurate layered structures, where Bloch theory does not apply, is well-defined as the thermodynamic limit of finite clusters. In addition, we obtain an explicit representation formula for the DOS as an integral over local configurations. Next, based on this representation formula, we propose a novel algorithm for computing electronic structure properties in incommensurate heterostructures, which overcomes limitations of the common approach to artificially strain a large supercell and then apply Bloch theory.