Origin of robust out-of-plane ferroelectricity in d1T-MoS₂ monolayer

The d1T-MoS₂, distorted-1T group-VIB transition metal dichalcogenides monolayer, is considered as promising atomically thin out-of-plane ferroelectric materials. We study the origin of the ferroelectricity in d1T-MoS₂ monolayer using first-principles calculations and the Landau theory of phase transition. In contrast to conventional improper ferroelectrics, we find that the polarization has dependence on both primary and secondary modes. It turns out that the charge imbalance between chalcogen atoms at different symmetry sites is the source for the out-of-plane polarization without any out-of-plane displacement in the primary mode. The secondary mode following the primary mode cancels partially the polarization and secures it against the depolarization field. We show that the polarization of d1T-MoS₂ is robust to external electric fields and can be manipulated by the uniaxial strain.