To make the investigation of electronic structure of incommensurate heterostructures computationally tractable, effective alternatives to Bloch theory must be developed. In [Multiscale Model. Simul., 15(2017), pp. 476--499] 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 has 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.

Daniel Massatt

Stephen Carr

Mitchell Luskin

Christoph Ortner

Multiscale Modeling and Simulation

Incommensurate Heterostructures in Momentum Space

This work presents an analogous scheme formulated in momentum space, which it is proved has significant computational advantages in specific incommensurate systems of physical interest, e.g., bilayers of a specified class of materials with small rotation angles.

Category	Quartile
数学	4
数学, 数学跨学科应用	3
数学, 物理数学物理	3

Incommensurate Heterostructures in Momentum Space

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Journal Info

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PHYSICS, MATHEMATICAL	2