On the interpretation of single and bilayer graphene minimal conductivity

Abstract

Within the Boltzmann kinetic theory minimal dc conductivity of single and bilayer graphene is studied. It is shown that the uncertainty principle plays a key role in graphene band structure. In the paper a new alternative interpretation for minimal universal conductivity of single and bilayer graphene is proposed. Minimal conductivity is determined by degenerate electrons and holes of the overlap range of electron and hole bands.  It is established that the minimal conductivity of single and bilayer graphene can be explained in the framework of one definite physical approach based on the uncertainty relations. Within the proposed theoretical approach minimal conductivity of both single-layer and bilayer graphene equals 4e²/h. It is found that in crystals with parabolic dispersion quantum expansion of an energy level  E is asymmetric with respect to E; in a crystal with linear dispersion an energy level quantum expansion is symmetric.