Doping effects in Bi$_{2}$Se$_{3}$ and Bi$_{2}$Te$_{3}$ topological insulators*

Topological insulators are found to have a bulk electronic gap and a gapless surface state. The surface state has been observed in Bi$_{2}$Se$_{3}$ and Bi$_{2}$Te$_{3}$ by ARPES and STM, but is still considered a challenging problem for transport measurements due to the dominant bulk conductance. By chemical doping, the Fermi level can be tuned to fall inside the band gap\footnote{Hor \textit{et al.} PRB \textbf{79} 195208 (09)} and therefore suppress the bulk conductivity. Non-metallic conducting Bi$_{2}$Se$_{3}$ crystals are obtained. Previously unobserved $p$-type behavior has been induced\footnote{Ibid.} and a novel magnetofingerprint signal\footnote{Checkelsky \textit{et al.} arXiv:0909.1840} is seen through low level Ca-doping in Bi$_{2}$Se$_{3}$. Bi$_{2}$Se$_{3}$ can also be tuned to a bulk superconductor, with $T_{c}\sim $3.8 K, by Cu-intercalation in the van der Waals gaps.\footnote{Hor \textit{et al}. arXiv:0909.2890.} This shows that Cooper pairing is possible in Bi$_{2}$Se$_{3}$ with implications for Majorana fermion physics study and potential quantum computing devices. Mn-doped Bi$_{2}$Te$_{3}$ has ferromagnetic transition at $\sim $15 K, suggesting a possible magnetic topological insulator.