Formula for the widths of quantum-Hall-effect plateaus

TL;DR

This paper presents an empirical formula for quantum Hall effect plateau widths that applies across different phenomena and challenges the prevailing disorder-based theory of plateau formation.

Contribution

It introduces a parameter-free empirical formula for plateau widths in the quantum Hall effect, unifying integer, fractional, and Wigner insulator states.

Findings

The formula accurately describes various quantum Hall states.

Plateau widths are not primarily determined by disorder.

The temperature scale matches Wigner crystal melting temperature.

Abstract

We derive an empirical formula for the width of quantum Hall effect plateaus which is free of adjustable parameters. It describes the integer, fractional and $\nu = 0$ (Wigner insulator) quantum Hall effect in single heterojunctions. The temperature scale of the existence of these three phenomena is the same as the melting temperature of a classical Wigner crystal. We conclude that the basic assumption of the current theory of QHE that the plateau width is determined by the disorder is highly improbable.