  The symmetry breaking induced by the ferroelectric transition often triggers
the emergence of topological electronic states such as Weyl fermions in
ferroelectric-like metals/semimetals. Such strong coupling between the lattice
deformation and electronic states is therefore essentially important for the
control of novel topological phases. Here, we study the terahertz lattice and
charge dynamics in ferroelectric semiconductor SnxPb1-xTe thin films hosting
versatile topological phases by means of the terahertz time-domain
spectroscopy. With lowering the temperature, the resonant frequency of
transverse optical phonon shows the significant softening and upturn. This
temperature anomaly of lattice dynamics directly indicates the displacive-type
ferroelectric transition. The resulting phase diagram suggests the enhancement
of ferroelectricity in the films due to compressive strain compared with the
bulk crystals. The soft phonon induces the large DC and terahertz dielectric
constant even in metallic state. Furthermore, we find that the Born effective
charge of soft phonon mode is enhanced at around the compositions showing the
band gap closing associated with the topological transition.
