Half integer features in the quantum Hall Effect: experiment and theory

TL;DR

This paper introduces an injection model for the quantum Hall effect that enables first-principles calculations of resistivity curves and explains the emergence of half-integer features observed in high-current experiments.

Contribution

The paper presents a novel injection-based theoretical framework that quantitatively explains the shape of Hall plateaus and predicts half-integer features in the quantum Hall effect.

Findings

Resistivity curves are calculable as functions of magnetic field, temperature, and current.

Half-integer features observed in high-current experiments are reproduced by the theory.

Hall plateaus and inflections result from local density of states and electric field gradients at the injection corner.

Abstract

The quantum Hall effect is one of the most important developments in condensed matter physics of the 20th century. The standard explanations of the famous integer quantized Hall plateaus in the transverse resistivity are qualitative, and involve assumptions about disorder, localized states, extended states, edge states, Fermi levels pinned by Landau levels, etc. These standard narratives give plausible reasons for the existence of the plateaus, but provide little in the way of even a qualitative understanding of the shape and width of the Hall plateaus, much less a first principles calculation. The injection model presented in this paper changes that situation. Rather than focusing on the middle of the Hall device, we follow the electrons to their source: one corner of the Hall bar and its steep electric field gradients. We find the entire resistivity curve including the Hall plateaus is calculable as a function of magnetic field, temperature, and current. The new higher current experiments reported here show remarkable half integer features for the first time; these are faithfully reproduced by the injection theory. The Hall plateaus and half integer inflections are shown to result from the local density of states appropriate to the magnetic field and the strong electric field gradient at the injection corner.