Single Charged Particle Motion in a Flat Surface with Static Electromagnetic Field and Quantum Hall Effect

Abstract

Taking into account the non separable solution for the quantum problem of the motion of a charged particle in a flat surface of lengths L x and L y with transversal static magnetic field B and longitudinal static electric field E , the quantum current, the transverse (Hall) and longitudinal resistivities are calculated for the state n = 0 and j = 0. We found that the transverse resistivity is proportional to an integer number, due to the quantization of the magnetic flux, and longitudinal resistivity can be zero for times t > > L x B/cE . In addition, using a modified periodicity of the solution, a modified quantization of the magnetic flux is found which allows to have IQHE and FQHE of any filling factor of the form v = k/l , with k, l ∈ Z .