Phenomenological Understanding of a Transport Regime with Reflection Symmetry in the Quantum Hall System in a Composite Fermion Picture

TL;DR

This paper offers a phenomenological composite fermion theory explanation for a new transport regime with reflection symmetry observed near the quantum Hall to insulator transition, linking experimental findings to underlying symmetries and effective mass calculations.

Contribution

It introduces a phenomenological model based on composite fermion theory that explains the reflection symmetry and transport properties near the quantum Hall transition, including the physical meaning of a key parameter.

Findings

Reflection symmetry in resistivity explained by excitation symmetry

Effective mass derived from parameter α matches known electron masses

Hall resistivity remains nearly invariant across the transition

Abstract

In this paper, we present a phenomenological picture based on the composite fermion theory, in responding to the recent discovery by Shahar et al. of a new transport regime near the transition from a $\nu=1$ quantum Hall liquid to a Hall insulator(ref[8]). In this picture, the seemingly unexpected reflection symmetry in the longitudinal resistivity $\rho_{xx}$ can be understood clearly as due to the symmetry of the gapful excitations which dominate $\sigma_{xx}$ across the transition, and the abrupt change in $\sigma_{xy}$ at the transition. The parameter $\alpha$ in the linear fit of $\nu_0(T)$ in ref[8] is also given a simple physical meaning and the effective mass can be calculated from $\alpha$, which gives a reasonable value of several electron band mass. When taking into account the result of network model, the almost invariant Hall resistivity $\rho_{xy}$ across the transition is also well-understood.