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We present an analysis of bulk and surface electronic structures of thallium based ternary III-V-VI2 series of compounds TlMQ2, 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 TlSbSe2, TlSbTe2, TlBiSe2 and TlBiTe2 to be non-trivial topological insulators with a single Dirac cone at the Γ-point, and TlSbS2 and TlBiS2 to be trivial band insulators. Our predicted topological phases agree well with available angle-resolved photoemission spectroscopy (ARPES) measurements, in particular the topological phase changes between TlBiSe2 and TlBiS2. Moreover, we propose that Weyl semimetal can be realized at the topological critical point in TlBi(S1−xSex)2 and TlBi(S1−xTex)2 alloys by breaking the inversion symmetry in the layer by layer growth in the order of Tl-Se(Te)-Bi-S, yielding six Dirac cones centered along the Γ − L directions in the bulk band structure.

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We demonstrate room temperature ferroelectricity in the epitaxial thin films of magnetoelectric