Quantum Hall Effect for a Single Charged Particle in a Flat Surface under an Static Electromagnetic Field

Abstract

While considering 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 estimated for the state n = 0 and j = 0.We noticed 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 \(\gg\) L_xB/cE. Additionally, a modified quantization of the magnetic flux is discovered utilizing a modified periodicity of the eigenfunction, allowing for IQHE and FQHE of any filling factor of the form v = k/l, with k, l \(\in\) \({Z}\).