A study on the effect of Sn concentration on the transport properties of epitaxial Bi$_{\mathrm{2-\delta }}$Sn$_{\mathrm{\delta }}$Te$_{\mathrm{3}}$ thin films

We have performed a systematic study on the transport properties of epitaxial Bi$_{\mathrm{2-\delta }}$Sn$_{\mathrm{\delta }}$Te$_{\mathrm{3}}$ thin films with varying $\delta $ from the underdoped to the overdoped region. By compensating unintentional carriers doped by defects in Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$, the bulk conductivity has been found to be highly suppressed with a very small amount of Sn resulting in the insulating behavior of resistivity at high temperatures. Furthermore, from the temperature- and magnetic field-dependence of the longitudinal resistance and the Hall resistance, we have separately characterized the surface state showing that the phase-relaxation length of the surface state of Sn-doped Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$ films increases up to \textasciitilde 250 nm at 1.8 K, about three times of that of the undoped Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$ film. And, finally, the magnetoresistance ratio (MR) of the Sn-doped Bi$_{\mathrm{2}}$Te$_{\mathrm{3}}$ films has been found to have a peak at a certain temperature, which is attributed to the carrier compensation similar to the semimetals.