Spectroscopic signatures of Kohn anomaly in a topological crystalline insulator
Topological crystalline insulators extend the concept of topological insulators by hosting surface states protected by crystallographic symmetry. Their topological phase transitions arise from spin-orbit-driven band inversion in the bulk electronic structure, reshaping the low-energy electronic environment and its coupling to lattice excitations. While the electronic aspects of band topology are well established, the corresponding dynamics of lattice and electron-phonon interactions remain largely unexplored. Here, we report a pronounced softening of a low-energy surface phonon mode across the topological phase transition in Pb$_{0.77}$Sn$_{0.23}$Se, revealed by temperature-dependent time-domain terahertz spectroscopy. Unlike the well-known phonon softening in ferroelectrics, this effect does not signal a structural instability but instead reflects electronic reconstruction. We attribute the softening to the spectroscopic manifestations of a Kohn anomaly, indicating a strong coupling between lattice vibrations and Dirac-like surface electrons in the topological phase. Consistently, the phonon linewidth deviates from the standard anharmonic temperature dependence, further evidencing enhanced electron-phonon coupling. The observed changes in phonon frequency and linewidth at around 120 K are consistent with the reported topological phase transition temperature in this material. Our results thus provide a spectroscopic route for the distinct identification of the onset of a topological phase.