Unusual phonon density of states and response to the superconducting transition in the In-doped topological crystalline insulator Pb$_{0.5}$Sn$_{0.5}$Te

TL;DR

This study investigates phonon behavior in In-doped PbSnTe, revealing unusual low-energy modes and their enhancement below the superconducting transition, suggesting complex electron-phonon interactions beyond standard BCS theory.

Contribution

It provides experimental inelastic neutron scattering data on phonons in In-doped PbSnTe and discusses the limitations of density functional theory in explaining observed phenomena.

Findings

Unusual van Hove singularities in phonon density of states at 1-2.5 meV

Enhancement of low-energy phonon features below T_c in superconducting sample

Superconductivity occurs in a bad-metal regime with high resistivity

Abstract

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 superconducting transition temperature $T_c$ 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 $T_c$, there is an enhancement of these features for energies below twice the superconducting-gap energy. We further note that the superconductivity in (Pb$_{0.5}$Sn$_{0.5}$)$_{1-x}$In$_x$Te occurs in samples with normal-state resistivities of order 10 m$\Omega$~cm, 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 (Pb$_{0.5}$Sn$_{0.5}$)$_{0.7}$In$_{0.3}$Te appears to be driven by phonons, a proper understanding will require ideas beyond simple BCS theory.