Electric field influenced coordinate jump of the guiding centre and magnetotransport

Our studies formulate a classical theory to study the influence of in-plane electric field on electron-impurity scattering process and magnetotransport in a two-dimensional space, in the presence of a strong out-of-plane magnetic field. Our studies connect classical scattering and quantum Landau Level broadening, as will be reviewed in this report. We derived an electric current formula in agreement with the current derived from the Drude theory under a strong magnetic field. Our electric current formula is derived microscopically from the migration of the guiding centres at strong magnetic field regime ωτ>1. The electron-impurity scattering under electromagnetic field not only shifts the guiding centre coordinates X and Y, but also changes cyclotron radius R. The change of cyclotron radius R compensates the change of the electric potential energy during the scattering process. The broadening of cyclotron radius is a classical manifestation of Landau Levels broadening. Our conductivity mnB2τ derived from our current formula in the linear response regime results in the same as the current derived from Kubo current fluctuation theory, providing a special case of the fluctuation-dissipation theorem.