Electronic Tuning of the Soft-Phonon Transport Anomaly in Ta_{2}Ni(S_{x}Se_{1-x})_{5}

Ta_{2}NiSe_{5} continues to be investigated for its phase transition at T_{c}=326  K, where it develops both an electronic gap and a distortion of its Ta/Ni chains. One intriguing feature at T_{c} seen in thermal transport is the giant anisotropic scattering of phonons moving perpendicular to the chains, which is apparently associated with the softening of a transverse acoustic phonon, but whose microscopic origin and significance demand clarification. By tuning the normal-state band overlap or gap with S substitution, we uncover a close connection between this soft-phonon transport anomaly and underlying electronic instabilities: when Ta_{2}Ni(S_{x}Se_{1-x})_{5} approaches a band insulator at high x, and signatures of the electronic transition are suppressed, the soft-phonon transport anomaly concomitantly vanishes. Our results establish the following picture for the Ta_{2}Ni(S_{x}Se_{1-x})_{5} family: near the S end, a sole lattice instability gives rise to a weak structural transition with T_{c} approaching 130 K. Near the Se end, additional electronic instabilities boost T_{c} up to 326 K and amplify experimental signatures of the transition. The strong interaction between electrons, holes, and the lattice is manifested as a soft-phonon transport anomaly accompanied by electronic fluctuations, which include excitonic and hybridization-gap fluctuations.