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Phonon softening near topological phase transitions

Topological phase transitions occur when the electronic bands change their topological properties, typically featuring the closing of the bandgap. While the influence of topological phase transitions on electronic and optical properties has been extensively studied, its implication on phononic properties and thermal transport remains unexplored. In this work, we use first-principles simulations to show that certain phonon modes are significantly softened near topological phase transitions, leading to increased phonon-phonon scattering and reduced lattice thermal conductivity. We demonstrate this effect using two model systems: pressure-induced topological phase transition in $\rm ZrTe_5$ and chemical composition induced topological phase transition in $\rm{Hg_{1-x}Cd_{x}Te}$. We attribute the phonon softening to emergent Kohn anomalies associated with the closing of the bandgap. Our study reveals the strong connection between electronic band structures and lattice instabilities and opens up a potential direction towards controlling heat conduction in solids.