Surface state conduction observed in voltage-tuned crystals of the topological insulator Bi$_2$Se$_3$

We report transport experiments obtained by applying a gate voltage to very thin crystals of Bi$_{2}$Se$_{3}$ to tune the chemical potential $\mu$ over a large energy interval. We show that the surface states have a metallic resistance profile. Measuring their conductance fluctuations and field suppression of weak anti-localization, we show that the surface states retain their integrity when $\mu$ lies deep in the conduction band. In addition we tune the charge carrier density from electron to hole like carriers and find the two-dimensional character of the transport is strongest near charge neutrality and that the Hall response is suppressed in the surface states.