Insulator-quantum Hall transition and Dirac fermion heating in low-carrier-density monolayer epitaxial graphene

We present magneto-transport measurements on ungated, low-carrier-density epitaxial graphene Hall devices at low temperatures $T$. At $T=$4.25 K the carrier density and mobility of one device are 1.38x10$^{11}$ cm$^{-2}$ and 6500 cm$^{2}$V$^{-1}$s$^{-1}$, respectively. At low magnetic fields $B$, this device shows insulating behavior in the sense that the measured resistivity $\rho_{\mathrm{xx}}$ increases with decreasing $T$. A highly developed quantum Hall (QH) resistivity plateau $\rho _{\mathrm{xy}}\approx \frac{h}{2e^{2}}$ corresponding to a Landau-level filling factor $\nu =$2 in monolayer graphene can be observed at magnetic fields $B\ge $ 1.5 T. Between the low-field insulator regime and the $\nu =$2 QH state we observe a $T$-independent point in $\rho _{\mathrm{xx}}$ which corresponds to the insulator-quantum Hall (I-QH) transition. This transition, like those in semiconductor-based two-dimensional (2D) systems, can be also observed by increasing the driving current $I$ at fixed ambient temperature. However, the measured $\rho _{\mathrm{xx}}$ at the I-QH transition is close to $\frac{h}{4e^{2}}$, rather than $\frac{h}{2e^{2}}$as expected by conventional I-QH theory. Furthermore, $\rho_{\mathrm{xx}}$ is substantially higher than $\rho _{\mathrm{xy}}$ at the crossing point. By using the zero-field resistivity and weak localization effect as two independent thermometers to determine effective Dirac fermion temperature ($T_{DF})$ at various $I$, we find that $T_{DF}$ $\sim$ $I^{0.5}$, consistent with those obtained in various 2D systems.