Converting topological insulators into topological metals within the tetradymite family

We report the electronic band structures and concomitant Fermi surfaces for a family of exfoliable tetradymite compounds with the formula $T_2$$Ch_2$$Pn$, obtained as a modification to the well-known topological insulator binaries Bi$_2$(Se,Te)$_3$ by replacing one chalcogen ($Ch$) with a pnictogen ($Pn$) and Bi with the tetravalent transition metals $T$ $=$ Ti, Zr, or Hf. This imbalances the electron count and results in layered metals characterized by relatively high carrier mobilities and bulk two-dimensional Fermi surfaces whose topography is well-described by first principles calculations. Intriguingly, slab electronic structure calculations predict Dirac-like surface states. In contrast to Bi$_2$Se$_3$, where the surface Dirac bands are at the $\Gamma-$point, for (Zr,Hf)$_2$Te$_2$(P,As) there are Dirac cones of strong topological character around both the $\bar {\Gamma}$- and $\bar {M}$-points which are above and below the Fermi energy, respectively. For Ti$_2$Te$_2$P the surface state is predicted to exist only around the $\bar {M}$-point. In agreement with these predictions, the surface states that are located below the Fermi energy are observed by angle resolved photoemission spectroscopy measurements, revealing that they coexist with the bulk metallic state. Thus, this family of materials provides a foundation upon which to develop novel phenomena that exploit both the bulk and surface states (e.g., topological superconductivity).