Theory of graphene transport properties

Abstract

Graphene is of great fundamental interest and has potential applications in disruptive novel technologies. In order to study the novel phenomena in graphene, it is essential to understand its electron transport properties and in particular the main factors limiting its transport mobility. In this dissertation, we study the transport properties of graphene in the presence of electron-hole puddles induced by charged impurities which are invariably present in the graphene environment. We calculate the graphene conductivity by taking into account the non-mean-field two-component nature of transport in the highly inhomogeneous density and potential landscape, where activated transport across the potential fluctuations in the puddle regimes coexists with regular metallic diffusive transport. Our theoretical calculation explains the non-monotonic feature of the temperature dependent transport, which is experimentally generically observed in low mobility graphene samples. Our theory also predicts the existence of an intriguing "disorder by order" phenomenon in graphene transport where higher-quality (and thus more ordered) samples, while having higher mobility at high carrier density, will manifest more strongly insulating (and thus effectively more disordered) behavior as the carrier density is lowered compared with lower quality samples (with higher disorder), which exhibit an approximate resistivity saturation phenomenon at low carrier density near the Dirac point. This predicted behavior, simulating a metal-insulator transition, arises from the suppression of Coulomb disorder induced inhomogeneous puddles near the charge neutrality point in high quality graphene samples. We then study carrier transport through graphene on SrTiO₃ substrates by considering the relative contributions of Coulomb and resonant impurity scattering to graphene resistivity. We establish that the nonuniversal high-density behavior of &sigma(n) in different graphene samples on various substrates arises from the competition among different scattering mechanisms, and it is entirely possible for graphene transport to be dominated by qualitatively different scattering mechanisms at high and low carrier densities. Finally, we calculate the graphene conductivity as a function of carrier density, taking into account possible correlations in the spatial distribution of the Coulomb impurity disorder in the environment. We find that the conductivity could increase with increasing impurity density if there is sufficient inter-impurity correlation present in the system.