Quantum oscillations in metallic Sb$_{\mathrm{\mathbf{2}}}$\textbf{Te}$_{\mathrm{\mathbf{2}}}$\textbf{Se topological insulator}

We have studied the magnetotransport properties of the metallic, $p$-type Sb$_{\mathrm{2}}$Te$_{\mathrm{2}}$Se which is a topological insulator. Magnetoresistance shows Shubnikov de Haas oscillations in fields above B$=$15 T. The maxima/minima positions of oscillations measured at different tilt angles with respect to the B direction align with the normal component of field Bcos$\theta $, implying the existence of a 2D Fermi surface in Sb$_{\mathrm{2}}$Te$_{\mathrm{2}}$Se. The value of the Berry phase $\beta =$0.43, determined from a Landau level fan diagram, further suggests that the oscillations result from topological surface states. From Lifshitz-Kosevich analyses, the position of the Fermi level is found to be E$_{\mathrm{F}}=$250 meV, above the Dirac point. This value of E$_{\mathrm{F}}$ is almost 3 times as large as that in our previous study on the Bi$_{\mathrm{2}}$Se$_{\mathrm{2.1}}$Te$_{\mathrm{0.9}}$ topological insulator; however, it still touches the tip of the bulk valence band. This explains the metallic behavior and hole-like bulk charge carriers in the Sb$_{\mathrm{2}}$Te$_{\mathrm{2}}$Se compound.