Topological electronic structure and Weyl semimetal in the TlBiSe ₂ class of semiconductors

We present an analysis of bulk and surface electronic structures of thallium-based ternary III-V-VI ₂ series of compounds TlMQ ₂, where M=Bi or Sb and Q=S, Se, or Te, using the ab initio density functional theory framework. Based on parity analysis and (111) surface electronic structure, we predict TlSbSe ₂, TlSbTe ₂, TlBiSe ₂, and TlBiTe ₂ to be nontrivial topological insulators with a single Dirac cone at the Γ point and TlSbS ₂ and TlBiS ₂ to be trivial band insulators. Our predicted topological phases agree well with available angle-resolved photoemission spectroscopy measurements, in particular, the topological phase changes between TlBiSe ₂ and TlBiS ₂. Moreover, we propose that Weyl semimetal can be realized at the topological critical point in TlBi(S _1-xSe _x) ₂ and TlBi(S _1-xTe _x) ₂ alloys by breaking the inversion symmetry in the layer-by-layer growth in the order Tl-Se(Te)-Bi-S, yielding six Dirac cones centered along the Γ-L directions in the bulk band structure.