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

摘要

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