Theory of graphene transport properties

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

Theory of 2D transport in graphene for correlated disorder

We theoretically revisit graphene transport properties 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 charged impurity correlations give rise to a density dependent graphene conductivity, which agrees well qualitatively with the existing experimental data. We also find, quite unexpectedly, that the conductivity could increase with increasing impurity density if there is sufficient inter-impurity correlation present in the system. In particular, the linearity (sublinearity) of graphene conductivity at lower (higher) gate voltage is naturally explained as arising solely from impurity correlation effects in the Coulomb disorder.Comment: 5 pages, 3 figure

Anisotropic surface transport in topological insulators in proximity to a helical spin density wave

We study the effects of spatially localized breakdown of time reversal symmetry on the surface of a topological insulator (TI) due to proximity to a helical spin density wave (HSDW). The HSDW acts like an externally applied one-dimensional periodic(magnetic) potential for the spins on the surface of the TI, rendering the Dirac cone on the TI surface highly anisotropic. The decrease of group velocity along the direction $\hat{x}$ of the applied spin potential is twice as much as that perpendicular to $\hat{x}$. At the Brillouin zone boundaries (BZB) it also gives rise to new semi-Dirac points which have linear dispersion along $\hat{x}$ but quadratic dispersion perpendicular to $\hat{x}$. The group velocity of electrons at these new semi-Dirac points is also shown to be highly anisotropic. Experiments using TI systems on multiferroic substrates should realize our predictions. We further discuss the effects of other forms of spin density wave on the surface transport property of topological insulator.Comment: 8 pages, 8 figure