Incompressible states of dirac fermions in graphene with anisotropic interactions

•• We present a general approach to fractional quantum Hall effect in graphene.• We considered anisotropic interactions.• We determined the consequences of anisotropy in the system.

We report on the properties of incompressible states of Dirac fermions in graphene in the presence of an anisotropic Hamiltonian and a quantizing magnetic field. We introduce the necessary formalism to incorporate the unimodular spatial metric to deal with the anisotropy in the system. The incompressible state in graphene is found to survive the anisotropy up to a critical value of the anisotropy parameter. The anisotropy also introduces two branches in the collective excitations of the corresponding Laughlin state. It strongly influences the short-range behavior of the pair-correlation functions in the incompressible ground state.