Incommensurate heterostructures in momentum space

Daniel Massatt; Stephen Carr; Mitchell Luskin; Christoph Ortner

doi:10.1137/17M1141035

Incommensurate heterostructures in momentum space

Daniel Massatt, Stephen Carr, Mitchell Luskin, Christoph Ortner

School of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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.

Original language	English (US)
Pages (from-to)	429-451
Number of pages	23
Journal	Multiscale Modeling and Simulation
Volume	16
Issue number	1
DOIs	https://doi.org/10.1137/17M1141035
State	Published - 2018

Bibliographical note

Funding Information:
∗Received by the editors July 27, 2017; accepted for publication (in revised form) December 26, 2017; published electronically March 6, 2018. http://www.siam.org/journals/mms/16-1/M114103.html Funding: The work of the first author was supported by NSF PIRE grant OISE-0967140 and ARO MURI award W911NF-14-1-0247. The work of the second and third authors was supported in part by ARO MURI award W911NF-14-1-0247. The work of the fourth author was supported by ERC starting grant 335120. †School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (massa067@umn.edu, luskin@umn.edu). ‡Department of Physics, Harvard University, Cambridge, MA 02138 (stephencarr@g.harvard.edu). §Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (c.ortner@warwick. ac.uk).

Funding Information:
The work of the first author was supported by NSF PIRE grant OISE-0967140 and ARO MURI award W911NF-14-1-0247. The work of the second and third authors was supported in part by ARO MURI award W911NF-14-1-0247. The work of the fourth author was supported by ERC starting grant 335120.

Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.

Keywords

Density of states
Electronic structure
Heterostructure
Momentum space
Two-dimensional materials

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10.1137/17M1141035

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title = "Incommensurate heterostructures in momentum space",

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.",

keywords = "Density of states, Electronic structure, Heterostructure, Momentum space, Two-dimensional materials",

author = "Daniel Massatt and Stephen Carr and Mitchell Luskin and Christoph Ortner",

note = "Funding Information: ∗Received by the editors July 27, 2017; accepted for publication (in revised form) December 26, 2017; published electronically March 6, 2018. http://www.siam.org/journals/mms/16-1/M114103.html Funding: The work of the first author was supported by NSF PIRE grant OISE-0967140 and ARO MURI award W911NF-14-1-0247. The work of the second and third authors was supported in part by ARO MURI award W911NF-14-1-0247. The work of the fourth author was supported by ERC starting grant 335120. †School of Mathematics, University of Minnesota, Minneapolis, MN 55455 (massa067@umn.edu, luskin@umn.edu). ‡Department of Physics, Harvard University, Cambridge, MA 02138 (stephencarr@g.harvard.edu). §Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK (c.ortner@warwick. ac.uk). Funding Information: The work of the first author was supported by NSF PIRE grant OISE-0967140 and ARO MURI award W911NF-14-1-0247. The work of the second and third authors was supported in part by ARO MURI award W911NF-14-1-0247. The work of the fourth author was supported by ERC starting grant 335120. Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics.",

year = "2018",

doi = "10.1137/17M1141035",

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N2 - 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.

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Incommensurate heterostructures in momentum space

Abstract

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Keywords

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