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We present a neutron scattering study of phonons in single crystals of (Pb$_{0.5}$Sn$_{0.5}$)$_{1-x}$In$_x$Te 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 (TO and LO) modes at the Brillouin zone center. At low temperature, both modes are strongly damped but sit at a finite energy ($sim4$ meV 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.
Indium substitution turns the topological crystalline insulator (TCI) Pb$_{0.5}$Sn$_{0.5}$Te into a possible topological superconductor. To investigate the effect of the indium concentration on the crystal structure and superconducting properties of
We present inelastic neutron scattering results of phonons in (Pb$_{0.5}$Sn$_{0.5}$)$_{1-x}$In$_x$Te 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 supercon
Pb$_{1-x}$Sn$_x$Te has been shown to be an interesting tunable topological crystalline insulator system. We present a magneto-terahertz spectroscopic study of thin films of Pb$_{0.5}$Sn$_{0.5}$Te. The complex Faraday rotation angle and optical conduc
The temperature dependence of the London penetration depth $Deltalambda(T)$ in the superconducting doped topological crystalline insulator Sn$_{1-x}$In$_x$Te was measured down to 450 mK for two different doping levels, x $approx$ 0.45 (optimally dope
The ratio of the Zeeman splitting to the cyclotron energy ($M=Delta E_Z / hbar omega_c$), which characterizes the relative strength of the spin-orbit interaction in crystals, is examined for the narrow gap IV-VI semiconductors PbTe, SnTe, and their a