Charge transport and inhomogeneity near the minimum conductivity point in graphene

Abstract

The magnetic-field-dependent longitudinal and Hall components of the resistivity ${\rho }_{\mathrm{xx}}\left(H\right)$ and ${\rho }_{\mathrm{xy}}\left(H\right)$ are measured in graphene on silicon dioxide substrates at temperatures $1.6\mathrm{K}\le T\le 300\mathrm{K}$. At charge densities near the minimum conductivity point ${\rho }_{\mathrm{xx}}\left(H\right)$ is strongly enhanced and ${\rho }_{\mathrm{xy}}\left(H\right)$ is suppressed, indicating nearly equal electron and hole contributions to the current. The data are inconsistent with the standard two-fluid model but consistent with the prediction for inhomogeneously distributed electron and hole regions of equal mobility. At low $T$ and high $H$, ${\rho }_{\mathrm{xx}}\left(H\right)$ saturates to a value $\sim h∕e^2$, with Hall conductivity $\ll e^2∕h$, which may indicate a regime of localized $v=2$ and $v=-2$ quantum Hall puddles.