Analytic results of the excited electronic states at υ = 1/3 and the Laughlin-Jain microscopic wave function approaches

Abstract

In this work we studied the properties of a two-dimensional electronic gas subjected to a strong magnetic field and cooled at a low temperature. We reported exact analytical results of energies at the ground state. The results are for systems up to N_e = 10 electrons calculated in the integer quantum Hall effect (IQHE) regime at the filling factor υ = 1. To accomplish the calculation we used the complex polar coordinates method. Note that the system of electrons in the quantum Hall regime relied heavily on the disk geometry for finite systems of electrons with arbitrary values of N_e = 2 to 10 particles. The results that we obtained by analytical calculations are in good agreement with those reported by Ciftja [Ciftja O., J. Math. Phys., 2011, 52, 122105], where the representation for certain integrals of products of Bessel functions is obtained. In the end, we have studied the composite fermions energies for the excited states for several systems at υ = 1/3 and the correspondence between the fractional quantum Hall effect (FQHE) and the IQHE.

Keywords

• analytical method
• fractional quantum Hall effect (FQHE)
• integer quantum Hall effect (IQHE)
• Coulomb interaction
• quantum Hall effect
• 2D electron gas