Graphene in an arbitrary potential

Graphene has attracted a lot of attention recently. One of the first observations made by Novoselov et al is the anomalous electric field effect in graphene [1, 2, 3]. In this experiment the Electrical conductivity has been found to increase linearly with increasing gate voltage Vg for both polarities. The minimal conductivity at 0≈gVhas been reported to be close to in the vast majority of different samples [4]. In this article we find the transmission coefficient and conductivity in graphene for an arbitrary potential using the small-rectangles approximation