Effects of Zeeman spin splitting on the modular symmetry in the quantum Hall effect

TL;DR

This paper investigates how Zeeman spin splitting affects the modular symmetry in the quantum Hall effect, revealing that particle-hole transformations need modification depending on the relative sizes of Zeeman and cyclotron gaps.

Contribution

It introduces a modified particle-hole transformation to account for Zeeman spin splitting effects in the quantum Hall effect.

Findings

Modifications to particle-hole symmetry depend on Zeeman and cyclotron gap sizes.

Zeeman spin splitting influences the modular symmetry in quantum Hall systems.

The study provides a framework for understanding phase transitions with paired Landau bands.

Abstract

Magnetic-field-induced phase transitions in the integer quantum Hall effect are studied under the formation of paired Landau bands arising from Zeeman spin splitting. By investigating features of modular symmetry, we showed that modifications to the particle-hole transformation should be considered under the coupling between the paired Landau bands. Our study indicates that such a transformation should be modified either when the Zeeman gap is much smaller than the cyclotron gap, or when these two gaps are comparable.