Ferroelectric phase transition in a 1T monolayer of MoTe2 : A first-principles study

A ferroelectric distorted (d) 1T (d1T)-phase characterized by out-of-plane (OOP) polarization was previously predicted in monolayer transition-metal dichalcogenides, such as ${\mathrm{MoS}}_{2}$. A phenomenological model was proposed to explain the centrosymmetric 1T (c1T)-to-d1T transition; however, this model fails to account for polarization reversal. In this work, we reassess the underlying physical origin of spontaneous OOP polarization in the 1T-phase of monolayer ${\mathrm{MoTe}}_{2}$. Through first-principles calculations and the incorporation of a phenomenological model approach utilizing an alternative set of basis states, we confirm that OOP polarization emerges due to its interaction with twofold degenerate, nonpolar primary order parameters. Additionally, we investigate the unique coupling between the polar mode and the primary mode. Notably, employing our newly defined basis sets, we clarify the hybrid improper ferroelectric mechanism, the coupling behavior of lattice modes, phase transitions, and polarization switching within a proposed subspace. Furthermore, our findings highlight that the ferroelectric phase transition can occur even in the absence of unstable phonon modes within the highly symmetric c1T-phase, attributed to the higher order coupling between lattice modes.