Elastic deformations and Wigner-Weyl formalism in graphene

Understand

We discuss the tight-binding models of solid state physics with the $Z_2$ sublattice symmetry in the presence of elastic deformations, and their important particular case -the tight binding model of graphene.

• In order to describe the dynamics of electronic quasiparticles we explore Wigner-Weyl formalism.
• It allows to calculate the two-point Green's function in the presence of both slowly varying external electromagnetic fields and the inhomogeneous modification of the hopping parameters resulted from the 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.