Incommensurate Heterostructures in Momentum Space

TL;DR

This paper introduces a momentum space computational scheme for incommensurate heterostructures, offering significant efficiency improvements over real space methods, especially for bilayer systems with small rotation angles.

Contribution

It develops and analyzes a momentum space method for electronic structure calculations of incommensurate heterostructures, demonstrating computational advantages over previous real space approaches.

Findings

Momentum space scheme has faster convergence rates.

Method is effective for bilayers with small rotation angles.

Computational experiments confirm theoretical efficiency gains.

Abstract

To make the investigation of electronic structure of incommensurate heterostructures computationally tractable, effective alternatives to Bloch theory must be developed. In Massatt2017, we developed and analyzed a real space scheme that exploits spatial ergodicity and near-sightedness. In the present work, we present an analogous scheme formulated in momentum space, which we prove have significant computational advantages in specific incommensurate systems of physical interest, e.g., bilayers of a specified class of materials with small rotation angles. We use our theoretical analysis to obtain estimates for improved rates of convergence with respect to total CPU time for our momentum space method that are confirmed in computational experiments.