Exploring strong and weak topological states on isostructural substitutions in TlBiSe$$_2$$

Abstract Topological Insulators (TIs) are unique materials where insulating bulk hosts linearly dispersing surface states protected by the Time-Reversal Symmetry. These states lead to dissipationless current flow, which makes this class of materials highly promising for spintronic applications. Here, we predict TIs by employing state-of-the-art first-principles based methodologies, viz., density functional theory and many-body perturbation theory (G $$_0$$ 0 W $$_0$$ 0 ) combined with spin-orbit coupling effects. For this, we take a well-known 3D TI, TlBiSe $$_2$$ 2 and perform complete substitution with suitable materials at different sites to check if the obtained isostructural materials exhibit topological properties. Subsequently, we scan these materials based on SOC-induced parity inversion at Time-Reversal Invariant Momenta. Later, to confirm the topological nature of selected materials, we plot their surface states along with calculation of Z $$_2$$ 2 invariants. Our results show that GaBiSe $$_2$$ 2 is a strong Topological Insulator, besides, we report six weak Topological Insulators, viz., PbBiSe $$_2$$ 2 , SnBiSe $$_2$$ 2 , SbBiSe $$_2$$ 2 , Bi $$_2$$ 2 Se $$_2$$ 2 , TlSnSe $$_2$$ 2 and PbSbSe $$_2$$ 2 . We have further verified that all the reported TIs are dynamically stable, showing all real phonon modes of vibration.