Continuous-distribution puddle model for conduction in trilayer graphene

An insulator-to-metal transition is observed in trilayer graphene based on the temperature dependence of the resistance under different applied gate voltages. At small gate voltages the resistance decreases with increasing temperature due to the increase in carrier concentration resulting from thermal excitation of electron-hole pairs. At large gate voltages excitation of electron-hole pairs is suppressed, and the resistance increases with increasing temperature because of the enhanced electron-phonon scattering. We find that the simple model with overlapping conduction and valence bands, each with quadratic dispersion relations, is unsatisfactory. Instead, we conclude that impurities in the substrate that create local puddles of higher electron or hole densities are responsible for the residual conductivity at low temperatures. The best fit is obtained using a continuous distribution of puddles. From the fit the average of the electron and hole effective masses can be determined.