Magnetic Induction Dependence of Hall Resistance in Fractional Quantum Hall Effect

TL;DR

This paper derives a formula for the fractional quantum Hall effect's Hall resistance based on experimental data, incorporating magnetic induction, chemical potential, and temperature, and explaining observed plateaus through phenomenological perturbations.

Contribution

It introduces a new Hall resistance formula that accounts for magnetic induction dependence and phenomenological perturbations in the fractional quantum Hall effect.

Findings

The formula predicts 12 Hall resistance plateaus consistent with experiments.

Perturbation terms can be interpreted as orbital precession or nutation.

The model links single-electron spectra with fractional quantum Hall phenomena.

Abstract

We constructed a Hall resistance formula for the fractional quantum Hall effect by analyzing the experimental data reported in [J. P. Eisenstein and H. L. Stormer, {Science} {\bf 248}, 1510 (1990)]. The formula is given as a function of magnetic induction, chemical potential and temperature. The Hall resistance function contains a single-electron energy spectrum, which has phenomenological perturbation terms with three tunable parameters. The formula yields 12 plateaus that are consistent with the experiment. The perturbations can be interpreted as precession or nutation of a Landau orbital in the three-dimensional space.