Fermionic Chern-Simons Theory of SU(4) Fractional Quantum Hall Effect

TL;DR

This paper develops a Fermionic Chern-Simons theory tailored for the SU(4) symmetry in monolayer graphene, predicting possible fractional quantum Hall states considering spin and valley degrees of freedom.

Contribution

It introduces a novel SU(4) symmetric Chern-Simons framework for graphene's fractional quantum Hall effect, including new wavefunctions and state classifications.

Findings

List of potential fractional quantum Hall states in graphene

Proposed wavefunctions for these states

Applicability to bilayer quantum Hall systems

Abstract

We develop a Fermionic Chern-Simons (CS) theory for the fractional quantum Hall effect in monolayer graphene with SU(4) symmetry, arising from the spin and the valley degrees of freedom, which involves four distinct CS gauge fields. We choose the corresponding elements of the CS coupling matrix such that an even number of spin and valley quantum number dependent flux quanta is attached to all electrons and that any electron with a given spin and valley quantum number sees an integer number of flux attached to other electrons with different (spin and valley) quantum numbers. Using this CS matrix, we obtain a list of possible fractional quantum Hall states that might occur in graphene and propose wavefunctions for those states. Our analysis also applies to fractional quantum Hall states of both bilayer quantum Hall systems without spin polarization and bilayer spin polarized graphene.