Fermionic Chern-Simons theory of SU(4) fractional quantum Hall effect

We develop a Fermionic Chern-Simons (CS) theory for the fractional quantum Hall effect in monolayer graphene with SU(4) symmetry. We construct a general CS coupling matrix such that an even number of spin- and valley-dependent flux quanta is attached to all electrons and that any electron sees an integer number of flux attached to other electrons with different spin and valley quantum numbers. Using this matrix, we obtain a list of possible fractional quantum Hall states (FQHS) in graphene and propose wave functions for them. Our analysis unifies previously studied FQHS with different symmetries, predicts several states whose presence may be tested experimentally, and also applies to FQHS of bilayer spin polarized graphene and conventional bilayer quantum Hall systems. We thus provide a systematic way of charting FQHS in these systems and also reproduce earlier results as special cases.