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

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 $ν=1$ quantum Hall liquid to a Hall insulator(ref[8]). In this picture, the seemingly unexpected reflection symmetry in the longitudinal resistivity $ρ_{xx}$ can be understood clearly as due to the symmetry of the gapful excitations which dominate $σ_{xx}$ across the transition, and the abrupt change in $σ_{xy}$ at the transition. The parameter $α$ in the linear fit of $ν_0(T)$ in ref[8] is also given a simple physical meaning and the effective mass can be calculated from $α$, which gives a reasonable value of several electron band mass. When taking into account the result of network model, the almost invariant Hall resistivity $ρ_{xy}$ across the transition is also well-understood.