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Quantum Hall Conductivity in the Presence of Interactions
Open AccessArticle

Elastic Deformations and Wigner–Weyl Formalism in Graphene

by I.V. Fialkovsky 1,2,† and M.A. Zubkov 1,3,*,†
Physics Department, Ariel University, Ariel 40700, Israel
On Leave of Absence from CMCC-Universidade Federal do ABC, 09210-170 Santo Andre, Brazil
On Leave of Absence from NRC “Kurchatov Institute”-ITEP, B. Cheremushkinskaya 25, Moscow 117259, Russia
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2020, 12(2), 317;
Received: 21 January 2020 / Revised: 12 February 2020 / Accepted: 17 February 2020 / Published: 23 February 2020
We discuss the tight-binding models of solid state physics with the Z 2 sublattice symmetry in the presence of elastic deformations in an important particular case—the tight binding model of graphene. In order to describe the dynamics of electronic quasiparticles, the Wigner–Weyl formalism is explored. It allows the calculation of the two-point Green’s function in the presence of two slowly varying external electromagnetic fields and the inhomogeneous modification of the hopping parameters that result from elastic deformations. The developed formalism allows us to consider the influence of elastic deformations and the variations of magnetic field on the quantum Hall effect. View Full-Text
Keywords: graphene; integer quantum hall effect; Wigner–Weyl calculus graphene; integer quantum hall effect; Wigner–Weyl calculus
MDPI and ACS Style

Fialkovsky, I.; Zubkov, M. Elastic Deformations and Wigner–Weyl Formalism in Graphene. Symmetry 2020, 12, 317.

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