Designing topological states by pressure, strain, and functionalization

Various examples of the design of topological states by means of first-principles calculations are discussed. The presentation focusses on the design parameters (1) pressure, (2) strain, and (3) functionalization. TiTe$_2$ is found to be unusually accessible to strain effects and the first compound that under hydrostatic pressure (up to experimentally reasonable 30 GPa) is subject to a series of four topological phase transitions, which are related to band inversions at different points of the Brillouin zone. Therefore, TiTe$_2$ enables experimental access to all these transitions in a single compound. Phase transitions in TlBiS$_2$ and TlSbS$_2$ are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS$_2$ and TlSbS$_2$ when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the ${\rm \overline{M}}$ points are anisotropic with large out-of-plane component. TlBiS$_2$ shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator. While monolayer arsenic and arsenic antimonide are semiconductors (direct band gap at the $\Gamma$ point), fluorination results for both compounds in Dirac cones at the K points. Fluorinated monolayer arsenic shows a band gap of 0.16 eV due to spin-orbit coupling and fluorinated arsenic antimonide a larger band gap of 0.37 eV due to inversion symmetry breaking. Spin-orbit coupling induces spin splitting similar to monolayer MoS$_2$. Phonon calculations confirm that both materials are dynamically stable. Calculations of the edge states of nanoribbons by the tight-binding method demonstrate that fluorinated arsenic is topologically nontrivial in contrast to fluorinated arsenic antimonide.