Hall conductivity of strained Z₂crystals

We establish topological nature of Hall conductivity of graphene and other 2 crystals in 2D and 3D in the presence of inhomogeneous perturbations. To this end the lattice Weyl-Wigner formalism is employed. The nonuniform mechanical stress is considered, along with the spatially varying magnetic field. The relation of the obtained topological invariant to level counting is clarified.