  We developed a Landau type theory for the description of polar phenomena in
low-dimensional transition metal dichalcogenides (TMDs), specifically exploring
flexoelectric origin of the polarization induced by a spontaneous bending and
by inversion symmetry breaking due to the interactions with substrate. We
consider the appearance of the spontaneous out-of-plane polarization due to the
flexoelectric coupling with the strain gradient of the spontaneous surface
rippling and surface-induced piezoelectricity. Performed calculations proved
that the out-of-plane spontaneous polarization, originated from flexoelectric
effect in a rippled TMD, is bistable and reversible by a non-uniform electric
field. In contrast, the spontaneous polarization induced by a misfit strain and
symmetry-sensitive surface-induced piezoelectric coupling, cannot be reversed
by an external electric field. The special attention is paid to the spectral
analysis of the linear dielectric susceptibility and gain factor, which
enhancement is critically important for the observation of the polar phenomena
in low-dimensional TMDs by the surface-enhanced vibrational spectroscopy.
