The Quantum Hall Effect in the Non-Isolated Quantum Well Approximation
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 ρxx and ρxy . 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 ρxx and ρxv , without any fitting parameter, for a large number of samples with mobility varying between 4×104 and 106 cm2 /Vs.
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