Control and characterization of the metallic surface state of bulk insulating Bi$_2$Se$_3$*

Bi$_2$Se$_3$ is a three dimensional strong topological insulator with a conducting two-dimensional surface state whose existence is guaranteed by topology. The bulk Bi$_2$Se$_3$ has a 300 meV bandgap, but is often a degenerately \textit{n}-doped metal in as-grown material. I will discuss our efforts to remove this doping in thin crystals and films to achieve surface-dominated conduction. Electrochemical gating (using PEO+LiClO4 electrolyte) or molecular doping (using F4-TCNQ) is shown to effectively bring the Fermi energy of thin (3-20 nm) exfoliated Bi$_2$Se$_3$ crystals to the conduction band edge, where it can be further modulated at low temperature using field-effect gating. These techniques allowed us to reveal the gapless ambipolar transport in the topological surface, and measure the minimum conductivity,\footnote{D. Kim et al., \textit{Nature Physics} \textbf{8}, 460 (2012)} electron-acoustic phonon scattering,\footnote{D. Kim et al., \textit{Phys. Rev. Lett.} \textbf{109}, 166801 (2012)} thermopower,\footnote{D. Kim et al., \textit{Nano Lett.} \textbf{14}, 1701 (2014)} and inter-surface coupling of the topological surfaces.\footnote{S. Cho et al., \textit{Nano Letters} \textbf{11}, 1925 (2011); S. Cho et al., \textit{Nano Letters} \textbf{12}, 469 (2012); D. Kim et al., \textit{Nature Comm.} \textbf{4}, 2040 (2013)} Recently we have developed techniques to measure the transport properties of Bi$_2$Se$_3$ in situ during growth in ultra-high vacuum, enabling better understanding of the doping mechanisms.\footnote{J. Hellerstedt et al., \textit{APL} \textbf{105}, 173506 (2014)} We have also studied vacuum-deposited MoO$_3$ as a highly effective acceptor dopant which remains stable on air exposure for time scales of days.\footnote{M.T. Edmonds et al., \textit{ACS Nano} \textbf{8}, 6400 (2014)}