Quantum Hall effects in two-dimensional electron systems: A global approach

TL;DR

This paper presents a unified theoretical approach to quantum Hall effects across various two-dimensional electron systems, including semiconductor heterostructures, graphene, and topological insulators, accounting for both Hall plateaux and SdH oscillations.

Contribution

It introduces a comprehensive model that explains quantum Hall phenomena in diverse 2D systems using a single theoretical framework, incorporating effects of magnetic field and gate voltage.

Findings

Unified explanation for IQHE and FQHE across different materials

Model accounts for Hall plateaux and SdH oscillations simultaneously

FQHE arises from Landau level degeneracy breaking due to electrostatic interactions

Abstract

Up to almost the last two decades all the experimental results concerning the quantum Hall effect (QHE), i.e., the observation of plateaux at integer (IQHE) or fractional (FQHE) values of the constant h/e2, were related to quantum-wells in semiconductor heterostructures (QWs). However, more recently, a renewed interest in revisiting these phenomena has arisen thanks to the observation of entirely similar effects in graphene and topological insulators. In this paper we show an approach encompassing all these QHEs using the same theoretical frame, entailing both Hall effect plateaux and Shubnikov-de Haas (SdH) oscillations. Moreover, the model also enables the analysis of both phenomena as a function not only of the magnetic field but the gate voltage as well. More specifically, in light of the approach, the FQHE in any two-dimensional electron system (2DES) appears to be an effect of the breaking of the degeneration of every Landau level, n, as a result of the electrostatic interaction involved, and being characterized by the set of three integer numbers (n, p, q), where p and q have clear physical meanings too.