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Perturbation theory for weakly coupled two-dimensional layers

Published online by Cambridge University Press:  28 March 2016

Georgios A. Tritsaris ,
Sharmila N. Shirodkar ,
Efthimios Kaxiras ,
Paul Cazeaux ,
Mitchell Luskin ,
Petr Plecháč  and
Eric Cancès
Georgios A. Tritsaris
Affiliation:
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Sharmila N. Shirodkar
Affiliation:
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Efthimios Kaxiras*
Affiliation:
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Paul Cazeaux
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
Mitchell Luskin
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
Petr Plecháč
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, USA
Eric Cancès
Affiliation:
Université Paris Est, Ecole des Ponts and INRIA, 77455 Marne-la-Vallée, France
*
a) Address all correspondence to this author. e-mail: kaxiras@physics.harvard.edu
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Abstract

A key issue in two-dimensional structures composed of atom-thick sheets of electronic materials is the dependence of the properties of the combined system on the features of its parts. Here, we introduce a simple framework for the study of the electronic structure of layered assemblies based on perturbation theory. Within this framework, we calculate the band structure of commensurate and twisted bilayers of graphene (Gr) and hexagonal boron nitride (h-BN), and of a Gr/h-BN heterostructure, which we compare with reference full-scale density functional theory calculations. This study presents a general methodology for computationally efficient calculations of two-dimensional materials and also demonstrates that for relatively large twist in the graphene bilayer, the perturbation of electronic states near the Fermi level is negligible.

Keywords

electronic structurenanostructuresimulation
Type
Invited Articles
Information
Journal of Materials Research , Volume 31 , Issue 7: Focus Issue: Two-Dimensional Heterostructure Materials , 14 April 2016 , pp. 959 - 966
Copyright
Copyright © Materials Research Society 2016 

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References

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