Existence of dual topological phases in Sn-based ternary chalcogenides

It is quite intriguing to investigate the transition from a topological insulator (TI) phase to topological crystalline insulator (TCI) phase in a material as the latter has an advantage over the former in controlled device applications. This work investigates the existence of this dual topological behavior in Sn-based ternary chalcogenides family PbSnX2 (X=S, Se, Te) under the hydrostatic pressure using first-principles approach. These materials are dynamically sTABLE at ambient and elevated pressure conditions up to which the topological phase transitions (TPTs) are studied. This family have a topologically trivial ground state with direct band gap values 0.338 eV, 0.183 eV and 0.217 eV for PbSnS2, PbSnSe2 and PbSnTe2, respectively. The first TPT i.e., TI phase for these materials is observed, under the effect of external pressure of 5 GPa, 2.5 GPa and 3.5 GPa, with a single band inversion at F-point in the bulk band structure and an odd number of Dirac cones along the (111) surface. A further increase in pressure to 5.5 GPa, 3 GPa and 4 GPa results in another band inversion at {\Gamma}-point and an even number of Dirac cones along the (111) plane. These even number of band inversions suggest that (\(\bar{1}2\bar{1}\)) surface has mirror symmetry around (\(\bar{1}0\bar{1}\)) plane and hence, the TCI phase is obtained. This TCI phase is further corroborated with even value of mirror Chern number calculated using winding of Wannier charge centers.