Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets

TL;DR

This paper explores an SU(4) fractional quantum Hall effect in graphene, generalizing Halperin's wave functions to account for spin-valley symmetry, and compares analytical models with numerical studies.

Contribution

It introduces SU(4) generalizations of Halperin's wave functions and analyzes their relevance to the fractional quantum Hall effect in graphene.

Findings

SU(4) wave functions can describe the FQHE in graphene

Comparison with exact diagonalization supports the SU(4) models

Potential realization in bilayer quantum Hall systems

Abstract

Inspired by the four-fold spin-valley symmetry of relativistic electrons in graphene, we investigate a possible SU(4) fractional quantum Hall effect, which may also arise in bilayer semiconductor quantum Hall systems with small Zeeman gap. SU(4) generalizations of Halperin's wave functions [Helv. Phys. Acta 56, 75 (1983)], which may break differently the original SU(4) symmetry, are studied analytically and compared, at nu=2/3, to exact-diagonalization studies.