Chiral symmetry breaking and integer and fractional quantum Hall effects in monolayer graphene

Integer quantization of Hall conductivity near the Dirac points in graphene is unique in the sense that only electron-electron interactions can resolve the four fold valley and spin degeneracy, which in turn gives rise to Hall plateaus at filling $\nu=0, \pm 1$. In this work, we will argue that generation of chiral symmetry breaking orderings such as anti-ferromagnetic and charge-density-wave orders, provides an excellent variational description of the Hall states at $\nu=0,\pm 1$. For realistic strength of the sub-critical short-ranged Coulomb interactions, the solutions of the self-consistent gap equations are in very good agreement with the recently observed scaling of the interaction induced gap at $\nu =0, \pm 1$ with magnetic field as measured with a variety of different techniques. Although Zeeman coupling changes the nature of the broken symmetry phases, it otherwise leads to better agreement with experimental results. A possible explanation of recently observed hierarchy of fractional Hall states within the framework of chiral symmetry breaking ordering inside the zeroth Landau level in graphene will also be highlighted.