Theory of magnetoconductivity in a two-dimensional electron-gas system: Self-consistent screening model

Transverse magnetoconductivity ${\sigma }_{\mathrm{xx}}$ is investigated for a two-dimensional electron-gas (2D EG) system in magnetic fields. A scattering model commonly applicable to both Si metal-oxide-semiconductor (MOS) and ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As-GaAs heterostructure field-effect transistors (FET’s) is investigated. Ionized impurities are taken to exert a Coulomb force which is screened by the 2D EG. The screened Coulomb force determines widths of Landau subbands and, hence, the density of states at the Fermi energy in Landau subbands, which specifies the degree of screening. Thus, when calculating the widths, broadening of subbands and static dielectric response (i.e., screening) are considered self-consistently (self-consistent screening model). Both widths and ${\sigma }_{\mathrm{xx}}$ are solved analytically as well as numerically. Calculations are carried out both when impurities exist within the 2D EG and when they are in a remote sheet. Calculated ${\sigma }_{\mathrm{xx}}$ is compared with the experiment by Narita et al. and good agreement, though qualitative, is obtained. The real-space behavior of the screened potential is also discussed. The force range becomes short or remains long, depending on the degree of screening.