Effect of the Landau level broadening on the quantum Hall conductance

Abstract

Summary. --In a previous paper, Kliros et al. presented a model calculation of the Hall conductivity as a function of the Landau level broadening F for finite temperatures. In this paper, the effect of Landau-level broadening on the structure of the Hall conductivity is investigated. The experimental data regarding the Si-MOSFET and GaAs-heterostructure experiments are reproduced including a functional dependence of F on the magnetic field. The influence of the effective g-factor is considered as well.PACS 72.20.My -Galvanomagnetic and other magnetotransport effects. PACS 73.20.Dx -Electron states in low-dimensional structures (including quantum wells, superlattices, layer structures, and intercalation compounds).In a two-dimensional electron system, a magnetic field perpendicular to the plane of electrical confinement leads to full quantization of the electron motion. The energy spectrum consists of Landau levels (LL) separated by the cyclotron energy ho~r In an unperturbed system, the LL are discrete and highly degenerate, with (2~ 10)-1 (10 is the magnetic length) possible states.In a real system the LL are broadened due to scattering by phonons, impurities and other possible mechanisms. In the case of high magnetic fields, where hue >>F, real gaps appear between LL. Current theoretical understanding of the quantum Hall effect (QHE) [1,2] Recently, the author et. a/ [7] presented a model calculation of the Hall conductivity as a function of level broadening assuming a simple form for the density of states. Our purpose in this paper is the investigation of the influence of Landau level broadening on the structure of the Hall conductance as well as the application of a fitting process of our model to the available experimental data. 99

Analytical Fermi energy for broadened Landau levels of 2DEG under a perpendicular strong magnetic field

“…( 7) still remain relevant since most of the interesting effects (e.g. QHE, de Haas-van Alphen effect (dHvA), Shubnikov-de Haas effect (SdH)) happen in the regime of strong magnetic field [7,12,19], where the LL spacing is more prominent than Γ. The derivations herein can also be used for studying the effect of broadening that depends on B as long as the condition for strong magnetic field regime is satisfied.…”