Hall resistance in quantum Hall metals due to Pancharatnam phase retardation and energy level spacing

TL;DR

This paper derives a new formula for Hall resistance in quantum Hall metals based on Pancharatnam phase retardation and energy level spacing, explaining both integer and fractional effects.

Contribution

It introduces a novel theoretical approach linking Pancharatnam phase retardation to quantum Hall resistance, providing qualitative explanations for experimental zigzag curves.

Findings

Reproduces the zigzag pattern of Hall resistance for integer and fractional fillings

Links phase retardation to Zeeman splitting and Landau level crossings

Suggests experimental tests to falsify the proposed postulates

Abstract

We derive the trial Hall resistance formula for the quantum Hall metals to address both the integer and fractional quantum Hall effects. Within the degenerate Landau levels, Zeeman splitting and level crossings in the presence of changing magnetic-field strength determine the Pancharatnam phase retardation, including the phase acceleration or deceleration, which are related to the changes in the phase and group momenta of a wavefunction. We discuss the relevant physical postulates with respect to Pancharatnam phase retardation to qualitatively reproduce the measured Hall resistance's zigzag curve for both the integer and the fractional filling factors. Along the way, we give out some hints to falsify our postulates with experiments.