Electron-phonon coupling and superconductivity in the doped topological-crystalline insulator (Pb$_{0.5}$Sn$_{0.5}$)$_{1-x}$In$_x$Te

TL;DR

This neutron scattering study investigates phonon behavior in doped topological-crystalline insulator (Pb,Sn)Te, revealing soft optical modes and their relation to superconductivity, with findings on phonon damping, diffuse scattering, and local atomic fluctuations.

Contribution

The study provides detailed phonon dispersion data and insights into electron-phonon interactions in doped (Pb,Sn)Te, highlighting differences between superconducting and non-superconducting samples.

Findings

Soft optical phonon modes are strongly damped but finite at low temperature.

In-doped (Pb,Sn)Te exhibits superconductivity despite similar phonon features to non-superconducting samples.

Diffuse scattering indicates local atomic fluctuations and bond length variations.

Abstract

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.