Finite-temperature aspects of the quantum Hall effect: A Boltzmann-equation approach

Abstract

A quantum Boltzmann equation developed previously [M. Charbonneau et al., J. Math. Phys. 23, 318 (1982)] is employed to evaluate the dc electrical conductivity in two dimensions in the presence of very strong magnetic fields. The resulting formulas for the conductivity components ${\sigma }_{\mathrm{yx}}$ and ${\sigma }_{\mathrm{xx}}$ are very simple and valid for all temperatures. ${\sigma }_{\mathrm{yx}}$ is independent of any scattering potentials in the first Born approximation; besides, it shows analytically the inadequacy of the independent-electron theory to account for the fractional Hall effect. The quantization becomes obvious whenever the Fermi level lies in an energy gap. For an integer Landau level filling factor ν, good agreement is obtained with the experimental results for the plateau values, for the deviation from the integer plateau values as a function of temperature, magnetic field, effective mass, and position of the Fermi level, and for the temperature dependence of the plateau widths. Besides, we indicate that the formalism can incorporate electron-electron interaction necessary for the fractional Hall effect (ν