Effective Action and Mean Fermion Number Density of Graphene in Constant Magnetic Field at Finite Temperature and Density

The effective action and the mean fermion number density of graphene in constant external magnetic field at finite temperature and density are calculated. Closed expressions for these are given and their variation with temperature are studied. It is found that the mean fermion number density peaks around a particular temperature, depending on the chemical potential at low temperatures. This feature is interpreted as 'condensation of fermions ${\bar{\psi}}{\psi}$' in graphene. In future, it is interesting to extend and explore this calculation and the work of the reference [20] for the case of Graphyne [23].