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

Abstract

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 mΩ 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 (Pb0.5Sn0.5)0.7In0.3Te appears to be driven by phonons, a proper understanding will require ideas beyond simple BCS theory.Topological insulators (TIs) represent an exotic state of matter in which the bulk is insulating but the surface is metallic 1,2 . The topological state is protected by the time-reversal symmetry 1 . By including a certain crystal point group symmetry instead of time reversal, topological crystalline insulators (TCIs), a state analogous to TIs, was also proposed 3,4 . In particular, it was predicted that compounds such as SnTe might be TCIs 5 , and the key features, including the inverted character of bands near the chemical potential 6,7 and surface states within the band gap that are protected from back-scattering 8,9 , were soon verified.These developments have also spurred renewed interest in topological superconductors, as such materials may exhibit gapless surface states that could be beneficial for quantum computing 1-3 . A common aspect of TCIs is strong spin-orbit coupling in the atomic states contributing to the valence and conduction bands, and this is a useful ingredient for obtaining the unusual pairing symmetry expected for a topological superconductor. Hence, there is interest in seeing whether doping TCIs can induce superconductivity with a topological nature. Indeed, one can make SnTe superconducting by introducing In, and a point-contact study found evidence of surface Andreev bound states 10 , though thermodynamic studies suggest a fully gapped superconducting state [11][12][13] .SnTe is a compound that has the rocksalt structure despite the fact that the component elements do not all form closed-shell ions. A consequence is a strong intrinsic electron-phonon coupling 14,15 , which leads to a ferro-electric phase transition in SnTe 16,17 . One way to suppress the ferroelectric transition is to substitute Pb for Sn, and it has been estimated that the transition should hit 0 K for Pb y Sn 1−y Te with y ≈ 0.5 18 . At this Pb concentration the system becomes a TCI 19 . Also, s...

Reinvestigation of crystal symmetry and fluctuations in La$_2$CuO$_4$

“…Besides the case of LSCO x = 0.07 [36], we have seen related entropic modes in systems such as superconducting (Pb 1−x Sn x ) 1−y In y Te [73,74] and in both superconducting and non-superconducting Fe 1+y Te 1−x Se x [75].…”

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

“…With a more complete set of measurements on the x = 0 crystal, we find that its normal modes are reasonably consistent with the phonons calculated by density-functional perturbation theory. 12 An interesting difference is that, while the calculation was done for an insulating compound which can have a large LO-TO splitting, our sample is weakly metallic (probably due to vacancies), so that the LO and TO energies must be equal at Γ. We find this energy is ∼ 4 meV and that the modes are strongly damped.…”

“…7 Furthermore, partial substitution of indium induces superconductivity, with a transition temperature, T c , as high as 4.7 K, 8,9 while the normal state, from which the superconductivity develops, is nonmetallic, with a large resistivity. 10 Calculations of phonons and electron-phonon coupling using density-functional perturbation theory 11 yield an electron-phonon coupling constant that is large and sufficient to explain the superconducting transition temperature, T c , in In-doped Pb 1−y Sn y Te 12 and SnTe, 13 assuming that the assumptions behind the Allen-Dynes modification of the McMillan formula 14 are satisfied. There are reasons to question that for In-doped Pb 1−y Sn y Te: 1) the strongest electron-phonon coupling involves the LO mode, which has the potential to be relatively soft at the zone center; 2) the non-metallic normal state 10,12 is inconsistent with the assumption of a Fermi liquid; 3) the value of 1.4 calculated for the electron-phonon coupling constant is near the limit of validity of Migdal-Eliashberg theory.…”

“…10 Calculations of phonons and electron-phonon coupling using density-functional perturbation theory 11 yield an electron-phonon coupling constant that is large and sufficient to explain the superconducting transition temperature, T c , in In-doped Pb 1−y Sn y Te 12 and SnTe, 13 assuming that the assumptions behind the Allen-Dynes modification of the McMillan formula 14 are satisfied. There are reasons to question that for In-doped Pb 1−y Sn y Te: 1) the strongest electron-phonon coupling involves the LO mode, which has the potential to be relatively soft at the zone center; 2) the non-metallic normal state 10,12 is inconsistent with the assumption of a Fermi liquid; 3) the value of 1.4 calculated for the electron-phonon coupling constant is near the limit of validity of Migdal-Eliashberg theory. 15,16 Indeed, while the calculated phonon density of states (PDOS) describes most of the experimental features for (Pb 0.5 Sn 0.5 ) 1−x In x Te, the observation of anomalous low-frequency modes 12 provided the motivation for the present investigation.…”

“…There are reasons to question that for In-doped Pb 1−y Sn y Te: 1) the strongest electron-phonon coupling involves the LO mode, which has the potential to be relatively soft at the zone center; 2) the non-metallic normal state 10,12 is inconsistent with the assumption of a Fermi liquid; 3) the value of 1.4 calculated for the electron-phonon coupling constant is near the limit of validity of Migdal-Eliashberg theory. 15,16 Indeed, while the calculated phonon density of states (PDOS) describes most of the experimental features for (Pb 0.5 Sn 0.5 ) 1−x In x Te, the observation of anomalous low-frequency modes 12 provided the motivation for the present investigation.…”