Tuning Quantum Oscillations of Dirac Surface States on the Topological Insulator Bi$_2$Te$_2$Se by Ionic Liquid Gating*

An \emph{in-situ} method to tune the chemical potential near the Dirac Point (DP) of a topological insulator (TI) would greatly facilitate several key experiments. However, in as-grown crystals of Bi-based TIs, the chemical potential $\mu$ lies high above the DP. Using liquid gating on 50-$\mu$m thick crystals of Bi$_2$Te$_2$Se, we demonstrate that $\mu$ can be tuned by a factor of 6 by observing changes to the Shubnikov-de Haas (SdH) period. A surprise is that the SdH amplitudes increase sharply with gating. Liquid gating allows the n=1 Landau level to be accessed, and the $\pi$-Berry phase to be determined with improved accuracy. We will discuss reversibility of liquid gating, and how we may distinguish the purely gating action from chemical reaction.