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Incommensurate heterostructures in momentum space

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Massatt, D., Carr, S., Luskin, M. and Ortner, Christoph (2018) Incommensurate heterostructures in momentum space. Multiscale Modelling and Simulation : A SIAM Interdisciplinary Journal , 16 (1). pp. 429-451. doi:10.1137/17M1141035

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Official URL: https://doi.org/10.1137/17M1141035

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Abstract

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.

Item Type: Journal Article
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Heterostructures -- Mathematical models
Journal or Publication Title: Multiscale Modelling and Simulation : A SIAM Interdisciplinary Journal
Publisher: SIAM
ISSN: 1540-3459
Official Date: 6 March 2018
Dates:
DateEvent
6 March 2018Published
26 December 2017Accepted
Volume: 16
Number: 1
Page Range: pp. 429-451
DOI: 10.1137/17M1141035
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
OISE-0967140National Science Foundationhttp://dx.doi.org/10.13039/100000001
W911NF-14-1-0247Army Research Officehttp://dx.doi.org/10.13039/100000183
Starting Grant 335120H2020 European Research Councilhttp://dx.doi.org/10.13039/100010663
UNSPECIFIEDMultidisciplinary University Research Initiatives (Organisation)UNSPECIFIED
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