Fractional quantum Hall effect in graphene

The electrons in most of the conductors can be described by non-relativistic quantum mechanics but the electrons in graphene behave as massless relativistic particles, called Dirac fermions, though their speed is given by the Fermi velocity. The relativistic nature of the energy dispersion relation of electrons in graphene modifies the inter electron interactions. This results in the observation of a number of peculiar properties e.g. anomalous quantum Hall effect. We study the fractional quantum Hall effect (FQHE) in graphene. The quantized Hall conductivity in graphene in FQHE is shown to be: sigma(xy) = +/- 2n + 1/nm(2n+1) + 1 2e(2)/h, where n = 0, 1, 2, 3 ... This fascinating result shows that the FQHE in graphene has a sequence of states which is different from the sequence found in the 2D electron gas.