TITLE:
Single Charged Particle Motion in a Flat Surface with Static Electromagnetic Field and Quantum Hall Effect
AUTHORS:
Gustavo V. López, Jorge A. Lizarraga
KEYWORDS:
Landau’s Gauge, Quantum Hall Effect, Degeneration
JOURNAL NAME:
Journal of Modern Physics,
Vol.13 No.11,
November
4,
2022
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 Lx and Ly 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 >> LxB/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.