Electron-phonon coupling and superconductivity in the doped topological crystalline insulator (Pb0.5Sn0.5)1-xInxTe

We present a neutron-scattering study of phonons in single crystals of (Pb0.5Sn0.5)1-xInxTe with x=0 (metallic, but nonsuperconducting) and x=0.2 (nonmetallic normal state, but superconducting). We map the phonon dispersions (more completely for x=0) and find general consistency with theoretical calculations, except for the transverse and longitudinal optical (LO) modes at the Brillouin-zone center. At low temperature, both modes are strongly damped but sit at a finite energy (≈4meV in both samples), shifting to higher energy at room temperature. These modes are soft due to a proximate structural instability driven by the sensitivity of Pb-Te and Sn-Te p-orbital hybridization to off-center displacements of the metal atoms. The impact of the soft optical modes on the low-energy acoustic modes is inferred from the low thermal conductivity, especially at low temperature. Given that the strongest electron-phonon coupling is predicted for the LO mode, which should be similar for both studied compositions, it is intriguing that only the In-doped crystal is superconducting. In addition, we observe elastic diffuse (Huang) scattering that is qualitatively explained by the difference in Pb-Te and Sn-Te bond lengths within the lattice of randomly distributed Pb and Sn sites. We also confirm the presence of anomalous diffuse low-energy atomic vibrations that we speculatively attribute to local fluctuations of individual Pb atoms between off-center sites.