CHERN-SIMONS EFFECTIVE THEORY AND THE FRACTIONAL QUANTUM HALL EFFECTS IN GRAPHENE

Graphene has emerged as an important two dimensional electron system with novel physical properties due to its relativistic-like linear energy-momentum dispersion relation at low energy. Alongside two dimensional electron systems in semiconductor heterostructures, it has a rich set of integer and fractional quantum Hall states. Significant progresses have been made recently, but a full understanding of these states is still lacking. The prevailing approach for fractional quantum Hall effects in graphene has been the numerical exact diagonalization. In this work, we develop a fermionic Chern-Simons effective theory for Dirac fermions as a complement to the existing theories, and to bring new insights in our understanding of the phenomena. In particular, we study the possibility for quantum Hall plateaus at even-denominator filling factors. We first construct a unitary Chern-Simons transformation to attach even number of flux quanta to Dirac fermions. To deal with the four-fold spin-valley degeneracy, a set of K-matrices is introduced. At even-denominator filling factors in the zeroth Landau level, the fictitious magnetic field of the Chern-Simons field cancels the external magnetic fiel