The Quantum Hall Effect in the Non-Isolated Quantum Well Approximation

Abstract

We assume that in modulation doped heterostructures (MDH) the two dimensional electron gas (2 DEG) is a non-isolated system. As a consequence the Fermi level remains constant but both the 2DEG density N and the electrical subbands vary when the magnetic field varies. We performed the calculations for GaAs-GaAlAs hetero junctions (GaAs-H), only one occupied subband, in the triangular well approximation (TWA) taking into account the g factor enhancement and assuming that localized electrons do not participate in the conduction processes. We calculated the components of the conductivity tensor in quantizing magnetic fields and deduced ρ_xx and ρ_xy . The theoretical results have been compared to a large number of experimental ones. For helium or pumped helium temperature experiments (T > 1K), we obtained a good agreement for both ρ_xx and ρ_xv , without any fitting parameter, for a large number of samples with mobility varying between 4×10⁴ and 10⁶ cm² /Vs.