The discovery of topological insulators with boundary states protected by time-reversal symmetry opened up a new area of research in condensed matter physics. However, it was shown that gapped topological phases could also be protected by crystalline point group symmetries, which are known as topological crystalline insulators (TCIs). Antiperovskite Sr₃PbO was identified as a TCI candidate with nontrivial surface states protected by mirror symmetry. Using the first-principles calculations and different numerical methods based on the tight-binding approach, we reveal their topological electronic structure in their bulk and thin-film systems. We prove that the odd-atomic-layer thin film with Sr₂-O terminated surfaces is the stablest 2D phase. Moreover, we show the topological phase transi...[ Read more ]

The discovery of topological insulators with boundary states protected by time-reversal symmetry opened up a new area of research in condensed matter physics. However, it was shown that gapped topological phases could also be protected by crystalline point group symmetries, which are known as topological crystalline insulators (TCIs). Antiperovskite Sr₃PbO was identified as a TCI candidate with nontrivial surface states protected by mirror symmetry. Using the first-principles calculations and different numerical methods based on the tight-binding approach, we reveal their topological electronic structure in their bulk and thin-film systems. We prove that the odd-atomic-layer thin film with Sr₂-O terminated surfaces is the stablest 2D phase. Moreover, we show the topological phase transition between quantum spin Hall and the normal insulating phase occurred as we increase the thickness of the thin film. This behavior can also be obtained using a low-energy effective model with infinite potential well boundary conditions. The notion of topology can be generalized to the gapless system. We study a nitride anti-perovskite class material with a non-collinear AFM structure. It hosts a number of Weyl-point pairs around the Fermi level, which contribute a large amount of Berry curvature. The magnetization of the unit-cell increase with the strength of the applied strain. This is the source of a large anomalous Nernst signal observed in the experiment. We provid numerical evidence for this phenomenon.