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We predict a new class of three dimensional topological insulators in thallium-based III-V-VI2 ternary chalcogenides, including TlBiQ2 and TlSbQ2 (Q = Te, Se and S). These topological insulators have robust and simple surface states consisting of a single Dirac cone at the Γ point. The mechanism for topological insulating behavior is elucidated using both first principle calculations and effective field theory models. Remarkably, one topological insulator in this class, TlBiTe2 is also a superconductor when doped with p-type carriers. We discuss the possibility that this material could be a topological superconductor. Another material TlSbS2 is on the border between topological insulator and trivial insulator phases, in which a topological phase transition can be driven by pressure. PACS numbers:Topological insulators have attracted great attention in condensed matter physics 1 . Since the first theoretical prediction 2 and the subsequent experimental observation 3 in HgTe quantum wells, several other topological insulators in three dimensional (3D) bulk materials have been theoretically predicted and experimentally observed 4-8 . In particular, tetradymite semiconductors Bi 2 Te 3 , Bi 2 Se 3 , and Sb 2 Te 3 are predicted to be topological insulators with a large bulk band gap whose surface state consists of a single Dirac cone 6 . The mechanism for the topological insulating behavior in these 3D materials is the band inversion at the Γ point caused by large spin-orbit coupling, similar to the mechanism first discovered in HgTe quantum wells 2 . The tetradymite semiconductors have a layered structure consisting of stacking quintuple layers, making surface preparation particularly simple.In this work we predict a new class of 3D topological insulators in the thallium-based III-V-VI 2 ternary chalcogenides. These inversion symmetric topological insulators have a bulk energy gap and topologically protected surface states consisting of a single Dirac cone. Unlike the tetradymite semiconductors, these materials are intrinsically 3D, and do not have a weakly coupled layer structure. Nonetheless, effective field theory model describing the band electrons close to the Fermi energy takes the same form as the model proposed earlier for the tetradymite semiconductors 6 , and the mechanism for topological insulating behavior can be understood in a similar way.The discovery of topological insulators also inspired the intense search for topological superconductors 9-13 . Time reversal invariant topological superconductors have a full pairing gap in the bulk and topologically protected surface states consisting of Majorana fermions, see Fig 1 of Ref. 9 . Wheareas Dirac fermions have both particle and hole types, Majorana fermions are their own antiparticles. 14 In the simplest version, the surface state of a 3D topological superconductor consists of a single Majorana cone, thus containing half the degree of freedom of the Dirac surface states of a simple 3D topological insulator. This fractionalization of the degree of freedo...

One of the most exciting subjects in solid state physics is a single layer of graphite which exhibits a variety of unconventional novel properties. The key feature of its electronic structure are linear dispersive bands which cross in a single point at the Fermi energy. This so-called Dirac cone is closely related to the surface states of the recently discovered topological insulators. The ternary compounds, such as LiAuSe and KHgSb with a honeycomb structure of their Au-Se and Hg-Sb layers feature band inversion very similar to HgTe which is a strong precondition for existence of the topological surface states. In contrast to graphene with two Dirac cones at K and K ′ points, these materials exhibit the surface states formed by only a single Dirac cone at the Γ point together with the small direct band gap opened by a strong spin-orbit coupling (SOC) in the bulk. These materials are centro-symmetric, therefore, it is possible to determine the parity of their wave functions, and hence, their topological character. Surprisingly, the compound KHgSb with the strong SOC is topologically trivial, whereas LiAuSe is found to be a topological non-trivial insulator. The search for new materials with inverted band structure provides the basis for the Quantum Spin Hall effect (QSH) [1][2][3][4][5][6][7][8][9][10][11][12][13]. This new exciting field started with the prediction and experimental observation of the QSH in quantum wells in two-dimensional topological insulator of the binary semiconductor HgTe [1, 2]. In a series of single crystals, such as Bi 2 Se 3 , three-dimensional topological insulting behavior was observed in topological surface states appearing as Dirac cones [7][8][9]. Later on, the manifold of Heusler semiconductors with 18 valence electrons and a similar band inversion was proposed [10,11]. Since this proposed class of materials is extremely rich, it provides much wider flexibility in design by tuning the band gap size and the spin-orbit coupling (SOC) magnitude. In addition, the multi-functionality allows the incorporation of new properties such as superconductivity or magnetism [10].The structure of the XYZ Heusler compounds can be simply viewed as "stuffed" YZ-zinc-blende. Depending on the stuffing element X Heuslers are semiconducting or semi-metallic [14]. Materials like ScPtBi are topologically similar to HgTe: the inversion of the conduction and valence bands occurs due to small electronegativity differences. Since HgTe and ScPtBi are both 2D topological insulators, the QSH is also expected in the corresponding quantum wells, as e. g. ScPtSb/ScPtBi, in full analogy to CdTe/HgTe. We emphasize that the check of parity at the time reversal points, as a sufficient condition for their topological character, is not possible here because of the absence of inversion symmetry [3].