  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.
