Series of topological phase transitions in TiTe${}_2$ under strain

First-principles calculations are performed to investigate the topological properties of TiTe${}_2$ under hydrostatic pressure, uniaxial strain, and biaxial strain. It is found that the system is 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.

Figure 1

(a) Unit cell of TiTe${}_2$ and (b) corresponding Brillouin zone.

Figure 2

Band structures of TiTe${}_2$ without (a) and with (b) 3 GPa, (c) 8 GPa, and (d) 15 GPa hydrostatic pressure.

Figure 3

Energy difference between states around the Fermi level: variation with the lattice parameter.

Figure 4

Band structures of TiTe${}_2$ under (a) uniaxial compressive ($-5\%$), (b) uniaxial tensile ($+5\%$), (c) biaxial compressive ($-2\%$), and (d) biaxial tensile ($+2\%$) strain.

Figure 5

Evolution curves of the WFC in the (a) $k_3=0$ plane, (b) $k_3=\pi$ plane without strain, (c) $k_3=\pi$ plane with 3 GPa pressure, and (d) $k_3=\pi$ plane with 8 GPa pressure.

Figure 6

Evolution curves of the WFC in the $k_3=\pi$ plane with (a) uniaxial compressive ($-5\%$), (b) uniaxial tensile ($+5\%$), (c) biaxial compressive ($-2\%$), and (d) biaxial tensile ($+2\%$) strain.