First Principles Electronic and Lattice Dynamics Calculations of TiSe₂and TiTe₂

TiSe2 bulk and monolayer both undergo a charge density wave (CDW) instability,^1,2 whereas only monolayer TiTe2 undergoes a CDW transition.³ We performed electronic structure and lattice dynamics calculations (Phonopy code)⁴ for both of these Ti(IV) dichalcogenides using hybrid (HSE06)⁵ density functional theory. We also mapped the potential energy surfaces⁶ spanned by the imaginary mode eigenvectors to estimate the barrier associated with the transition and to track the route to the CDW phase. Our results successfully show that though TiTe₂ bulk has no lattice instability, its monolayer has an instability similar to, but much weaker than that seen in TiSe₂, highlighting the origin of a weak coupling CDW distortion brought about by a lattice instability. These results could have impact in understanding of CDW instabilities in other systems, particularly the methodology of following imaginary modes to track the transitions between phases.

¹Di Salvo et al., Phys. Rev. B, 1976, 14, 4321
²Chen et al., Nat. Commun., 2015, 6, 8943
³Chen et al., Nat. Commun., 2017, 8, 516
⁴Togo et al., Scr. Mater., 2015, 108, 1-5
⁵Heyd et al., J. Chem. Phys., 2003, 118, 8207
⁶Skelton et al., Phys. Rev. Lett., 2016, 117, 075502