A model for the study of the Shubnikov-de Haas and the integer quantum Hall effects in a two dimensional electronic system

TL;DR

This paper presents an analytical model for the integer quantum Hall effect and Shubnikov-de Haas phenomena in a two-dimensional electron system, emphasizing the role of electron fluctuations and reproducing experimental observations with high precision.

Contribution

The paper introduces a fundamental principles-based analytical approach that highlights electron fluctuations as the cause of IQHE, differing from localized state theories.

Findings

Reproduces Hall plateau widths with 10^-8 to 10^-9 precision

Accurately models minima of diagonal magnetoresistivity

Explains temperature dependence of IQHE and SdH phenomena

Abstract

Up to know all the experimental results concerning the integer and fractional quantum Hall effect are related to semiconductor heterostructures (and more recently with graphene). The common characteristic of all these systems is the presence of a reservoir of electrons, which, in fact, in the initial stage is the source of the electrons, providing the two-dimensional electron gas (2DES). Then, any physical realization of a 2DES is necessarily embedded in a 3D structure, which establishes the Fermi level. Hence, the 2DES appears to be an open system. In this paper we present an analytical approach to the integer quantum Hall effect (IQHE) and the Shubnikov-de Haas (SdH) phenomena in the 2DES, basing us in fundamental principles and showing the secondary role of the localized electron states in both phenomena. In fact, we show that the IQHE is a consequence of the fluctuations of electrons in the 2DES. Once we obtain the density of states of the 2DES under the application of a magnetic field we calculate both magnetoconductivities (diagonal and Hall) deducing them from the Boltzman semiclassical equation. The model proposed reproduces both phenomena, the width of the Hall plateaus (with the precision reached in the experimental measurements, of the order of 10-8-10-9) and the corresponding minima of the diagonal magnetoresistivity, and also the dependence with temperature of the IQHE and SdH.