Reservoir model for two-dimensional electron gases in quantizing magnetic fields: a review

TL;DR

This review discusses how reservoir models explain electron density oscillations in 2D electron gases under magnetic fields, highlighting their role in phenomena like the Quantum Hall Effect and emphasizing the importance of open system approaches.

Contribution

It synthesizes existing research to demonstrate the significance of reservoir models in understanding electron density oscillations and quantum transport in 2D electron gases under magnetic fields.

Findings

Electron density oscillates with magnetic field in quantum wells.

Reservoir models are crucial for explaining IQHE plateaus.

Density oscillations alone do not fully account for IQHE phenomena.

Abstract

We collect and review works which treat two-dimensional electron gases in quantum wells (mostly GaAs/GaAlAs heterostructures) in the presence of quantizing magnetic fields as open systems in contact with outside reservoirs. If a reservoir is sufficiently large, it pins the Fermi level to a certain energy. As a result, in a varying external magnetic field, the thermodynamic equilibrium will force oscillations of the electron density in and out of the quantum well (QW). This leads to a number of physical phenomena in magneto-transport, interband and intraband magneto-optics, magnetization, magneto-plasma dispersion, etc. In particular, as first proposed by Baraff and Tsui, the density oscillations in and out of QW lead to plateaus in the Integer Quantum Hall Effect (IQHE) at values observed in experiments. The gathered evidence, especially from magneto-optical investigations, allows us to conclude that, indeed, in most GaAs/GaAlAs hetrostructures one deals with open systems in which the electron density in QWs oscillates as the magnetic field varies. Relation of the density oscillations to other factors, such as electron localization, and their combined influence on the quantum transport in 2D electron gases, is discussed. In particular, a validity of the classical formula for the Hall resistivity {\rho}xy = B/Nec is considered. It is concluded that the density oscillations are not sufficient to be regarded as the only source of plateaus in IQHE, although such claims have been sometimes made in the past and present. Still, our general conclusion is that the reservoir approach should be included in various descriptions of 2D electron gases in the present of a magnetic field. An attempt has been made to quote all the relevant literature on the subject.