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Electric Field Influenced Coordinate Jump of the Guiding Center and Magnetotransport

We derived an electrical current formula in the presence of a strong out of plane magnetic field and an in plane electric field, and within two dimensional disordered systems. This current is originated from the guiding center coordinate jump. At a strong magnetic field regime, the current can be pictured as the migration of the center coordinates. During the electron impurity scattering, the guiding centers suddenly shift their coordinates. Because of the electric field, the coordinate shift accumulatively contributes to a longitudinal current. During the scattering, the value of cyclotron radius changes, which compensates for the change of the electric potential energy during the coordinate jump. The diversion of cyclotron radius is the classical manifestation of electric field dependent broadening and shifting of the Landau levels.