Impurity-induced geometric correlations and fractional quantization in quantum Hall systems

TL;DR

This paper introduces a geometric mechanism involving impurity-induced correlations within Landau levels to explain fractional quantum Hall states, reproducing observed sequences and highlighting impurity geometry's role.

Contribution

It proposes a novel impurity-based geometric framework for fractional quantum Hall states, emphasizing the influence of impurity arrangements on state stability and spectrum.

Findings

Reproduces principal fractional quantum Hall sequences

Predicts impurity geometry affects fractional-state stability

Explains absence of 1/2 Hall plateau via geometric cancellation

Abstract

We propose a geometric mechanism for fractional quantum Hall states based on impurity-induced correlations within a Landau level. A correlated distribution of ionized impurities partially modifies the Landau-level degeneracy through coherent coupling between cyclotron orbits, generating fractional energy sublevels. The odd-denominator hierarchy emerges naturally from the intrinsic guiding-center quantization and the correlated cyclotron motion. The resulting spectrum reproduces the principal experimentally observed fractional sequences and predicts a strong dependence of fractional-state stability on impurity geometry and layer separation. The absence of an incompressible Hall plateau at filling factor 1/2 follows from cancellation of the geometric correlations responsible for odd-denominator states. These results suggest that impurity-induced geometry may constitute an additional organizing principle in quantum Hall systems.