Fermi energy with Landau level broadening: Analytic solution for three- and two-dimensional systems

S. Chaudhuri

Published 2021-06-24Version 1

An analytic solution for the Fermi energy of free electrons subjected to a magnetic field in a three-dimensional metal or doped semiconductor sample including the Landau level broadening is obtained. The solution is in remarkable agreement with the experimental data on the ground state energy of a two-dimensional quantum dot through the entire range of the magnetic field values that had not yet been explained theoretically. In the experiment the ground state energy was measured with respect to the Fermi energy of the n+ electrode which itself depends on the magnetic field thus indirectly providing Fermi energy shift of a three-dimensional electron gas as a function of the magnetic field. Analytic solutions for the Fermi energy and the magnetization including the Landau Level broadening for two-dimensional electron gas are also derived. The theoretical magnetization results are compared with experimental data.