Persistent Hall Voltage and Current in the Fractional Quantum Hall Regime

TL;DR

This paper investigates persistent Hall voltage and current in a fractional quantum Hall system, revealing a universal Hall conductance unaffected by back scattering, with detailed theoretical derivations included.

Contribution

It introduces a theoretical framework for persistent Hall effects in fractional quantum Hall systems, including the effects of constrictions and zero mode dynamics.

Findings

Universal Hall conductance persists despite back scattering.

Persistent Hall voltage and current depend on temperature and magnetic flux.

Detailed bosonization and topological analysis provided.

Abstract

The persistent Hall voltage and current in an isolated annulus in a strong perpendicular magnetic field, at odd inverse filling factor, and in the presence of a weak constriction is obtained as a function of temperature, and flux piercing the annulus. A thermodynamic Hall conductance is found which has a universal value even with back scattering at the constriction. Included are detailed appendices on the bosonization of chiral soliton operators and the derivation of the chiral action, which has an additional topological term originating from the dynamics of the zero modes.