Tuning the Fermi Level in the Topological Insulator Bi$_{2}$Se$_{3}$ by Gate Voltage

We have fabricated field-effect devices using cleaved, few-monolayer Bi$_{2}$Se$_{3}$ for electrical transport measurements. By varying the applied gate potential $V_{G}$, we can shift the chemical potential $\mu$ through the bulk electronic bands. In as-grown crystals $\mu$ is pinned to the bulk conduction band due to carriers donated by Se vacancies. In these crystals the density of electrons can be varied continuously with $V_{G}$ and mobilities ~ 2000 cm$^{2}$ / Vs realized. In crystals chemically doped with Ca to suppress the density from the remnant bulk electron pocket, we can tune $\mu$ below the conduction band edge. From the behavior of the resistance and Hall resistivity vs. $V_{G}$, we show that we can access states inside the energy gap. A finite conductance is observed for all $V_{G}$ consistent with conducting surface states or impurity bands in the bulk band gap. Transport measurements are performed down to $T$ = 0.3 K and up to magnetic field $H$ = 14 T. We measure the Hall resistivity to extract the carrier density $n_{Hall}$ and observe suppression of conductance $\sigma_{xx}$ in large $H$.