Charge transport and inhomogeneity near the minimum conductivity point in graphene

Abstract

The magnetic-field-dependent longitudinal and Hall components of the resistivity ${\ensuremath{\rho}}_{\mathrm{xx}}(H)$ and ${\ensuremath{\rho}}_{\mathrm{xy}}(H)$ are measured in graphene on silicon dioxide substrates at temperatures $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}\ensuremath{\le}T\ensuremath{\le}300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. At charge densities near the minimum conductivity point ${\ensuremath{\rho}}_{\mathrm{xx}}(H)$ is strongly enhanced and ${\ensuremath{\rho}}_{\mathrm{xy}}(H)$ 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 $H$, ${\ensuremath{\rho}}_{\mathrm{xx}}(H)$ saturates to a value $\ensuremath{\sim}h∕{e}^{2}$, with Hall conductivity $\ensuremath{\ll}{e}^{2}∕h$, which may indicate a regime of localized $v=2$ and $v=\ensuremath{-}2$ quantum Hall puddles.