Unusual phonon density of states and response to the superconducting transition in the In-doped topological crystalline insulator Pb0.5Sn0.5Te

We present inelastic neutron scattering results of phonons in (Pb0.5Sn0.5)1-xInxTe powders, with x=0 and 0.3. The x=0 sample is a topological crystalline insulator, and the x=0.3 sample is a superconductor with a bulk superconducting transition temperature Tc of 4.7 K. In both samples, we observe unexpected van Hove singularities in the phonon density of states at energies of 1-2.5 meV, suggestive of local modes. On cooling the superconducting sample through Tc, there is an enhancement of these features for energies below twice the superconducting-gap energy. We further note that the superconductivity in (Pb0.5Sn0.5)1-xInxTe occurs in samples with normal-state resistivities of order 10 mΩcm, indicative of bad-metal behavior. Calculations based on density functional theory suggest that the superconductivity is easily explainable in terms of electron-phonon coupling; however, they completely miss the low-frequency modes and do not explain the large resistivity. While the bulk superconducting state of (Pb0.5Sn0.5)0.7In0.3Te appears to be driven by phonons, a proper understanding will require ideas beyond simple BCS theory.