New universality of metal-insulator transition in integer quantum Hall effect system

TL;DR

This paper uncovers a new universal behavior in the metal-insulator transition within the integer quantum Hall effect, revealing a two-parameter scaling law and a critical point where resistivities are equal, explaining recent experimental observations.

Contribution

It introduces a novel universality class for the IQHE metal-insulator transition based on a lattice model with disorder, highlighting a continuous variation of critical resistivity.

Findings

Discovery of a two-parameter scaling law at the transition boundary.

Identification of a critical point where longitudinal and Hall resistivities are equal.

Explanation of recent experimental results by Song et al.

Abstract

A new universality of metal-insulator transition in integer quantum Hall effect (IQHE) system is studied based on a lattice model, where the IQHE states only exist within a finite range of Fermi energy in the presence of disorders. A two-parameter scaling law is found at the high-energy boundary where direct transitions from high IQHE states to insulator occur. We find $\rho_{xx}= \rho_{xy}$ at the critical point whose value can continuously vary as a single function of the Landau-level filling number $n_{\nu}$. Such a new universality well explains recent experiment by Song et al. (Phys. Rev. Lett. 78, 2200 (1997)).