Surface conduction of topological Dirac electrons in bulk insulating Bi$_{2}$Se$_{3}$

The three dimensional strong topological insulator (STI) is a new phase of electronic matter which is distinct from ordinary insulators in that it supports on its surface a conducting two-dimensional surface state whose existence is guaranteed by topology. I will discuss experiments on the STI material Bi$_{2}$Se$_{3}$, which has a bulk bandgap of 300 meV, much greater than room temperature, and a single topological surface state with a massless Dirac dispersion. Field effect transistors consisting of thin (3-20 nm) Bi$_{2}$Se$_{3}$ are fabricated from mechanically exfoliated from single crystals, and electrochemical and/or chemical gating methods are used to move the Fermi energy into the bulk bandgap, revealing the ambipolar gapless nature of transport in the Bi$_{2}$Se$_{3}$ surface states. The minimum conductivity of the topological surface state is understood within the self-consistent theory of Dirac electrons in the presence of charged impurities. The intrinsic finite-temperature resistivity of the topological surface state due to electron-acoustic phonon scattering is measured to be $\sim$60 times larger than that of graphene largely due to the smaller Fermi and sound velocities in Bi$_{2}$Se$_{3}$, which will have implications for topological electronic devices operating at room temperature.~As samples are made thinner, coherent coupling of the top and bottom topological surfaces is observed through the magnitude of the weak anti-localization correction to the conductivity, and, in the thinnest Bi$_{2}$Se$_{3}$ samples ($\sim$ 3 nm), in thermally-activated conductivity reflecting the opening of a bandgap.