Chemical potential of inhomogeneous single-layer graphene

In this paper, we present measurements of the chemical potential of single-layer graphene as a function of carrier density and temperature, including near the Dirac point. Far from the charge neutrality point, the graphene is homogenous with a single carrier type. However, as the Dirac point is approached, puddles form, and electrons and holes coexist. Hall effect analyses based on two charge carriers are not adequate in this regime. Hence, a new methodology is introduced, and by using the chemical potential and the transport data self-consistently, we were able to extract the density of each carrier. We obtained very good agreement with a recent theory that assumes a Gaussian distribution of the electrostatic disorder potential. Surprisingly, the temperature dependence of the minimum conductivity of graphene was primarily attributed to the temperature dependence of the disorder potential itself through the carrier charge densities, and not to the temperature dependence of the carrier's mobility.