Conductance of graphene superlattices with correlated disorder in velocity profiles

The propagation of massless Dirac fermion waves through a graphene system is studied in the presence of a long-range correlated disorder. The system consists of a graphene layer in which the Dirac fermions velocity is position-dependent. The velocity profile is multiform and assumed to be long-range correlated. The effect of disorder in the transmission probability through the system with different sizes is also studied. In addition, we show that the conductance of the system increases with increasing the correlation exponent values giving rise to a metallic phase. We obtain a phase transition diagram in which the critical correlation exponent depends strongly on disorder strength. We demonstrate that in the limit of large system size, the conductance fluctuations become independent of the correlation exponent and tend to a constant value.