Low-energy phonons and superconductivity in ${\mathrm{Sn}}_{0.8}{\mathrm{In}}_{0.2}\mathrm{Te}$

We present neutron scattering measurements on low-energy phonons from a superconducting $\left(T_c=2.7\mathrm{K}\right)$ ${\mathrm{Sn}}_{0.8}{\mathrm{In}}_{0.2}\mathrm{Te}$ single-crystal sample. The longitudinal acoustic phonon mode and one transverse acoustic branch have been mapped out around the (002) Bragg peak for temperatures of 1.7 and 4.2 K. We observe a substantial energy width of the transverse phonons at energies comparable to twice the superconducting gap; however, there is no change in this width between the superconducting and normal states, and the precise origin of this energy width anomaly is not entirely clear. We also confirm that the compound is well ordered, with no indications of structural instability.

Figure 1

(a) Temperature dependence of ZFC magnetization (blue dashed line, left side) in an applied field of 1 mT; and resistivity (red solid line, right side) data from Ref. [22]. (b) Elastic scans in scattering plane $\left(HHL\right)$ at 1.7 K. The dashed and solid arrows show the longitudinal acoustic phonon (LA) and transverse acoustic phonon (TA) measured around Bragg peak (002), respectively.

Figure 2

Constant-$q$ cuts of phonon spectra along transverse directions near (002) Bragg peak at (a) 1.7 K and (b) 4.2 K and at various $\mathbf{Q}$ positions with $\mathbf{Q}=(q,q,2)$, with $q=0.05$ (red circle), 0.1 (orange square), 0.15 (green diamond), 0.2 (teal up triangle), 0.3 (blue down triangle), 0.4 (purple pentagon), and 0.5 (black hexagon). The data are taken on SPINS. (c), (d) The ${\mathrm{TA}}_1$ phonon dispersions around (002) at (c) 1.7 K and (d) 4.2 K. The phonon energies are obtained from fitting the energy cuts from (a) and (b) as described in the text. The lines are guides to the eye. The errors are obtained from the fitting process.

Figure 3

Phonon intensity plots in energy-momentum space around Bragg peak (002) at (a) 1.7 K and (b) 4.2 K. For each panel, the left half corresponds to longitudinal phonons going along the [001] direction; and the right half corresponds to transverse phonons going along the [110] direction. The white lines are phonon dispersions obtained from fitting of the energy cuts.

Figure 4

Summary of the fitting parameters. The dynamic response ${\chi }^{\prime \prime }$ multiplied by phonon energy $\hslash \omega$ for acoustic phonons measured along (a) transverse [110] direction, and (b) longitudinal [001] direction at various $q$ positions. (c) The energy width $2\Gamma$ for the ${\mathrm{TA}}_1$ phonon mode measured on SPINS. (d) The $q$ width for the LA phonon measured on MACS. In (a) and (b), the errors represent $\pm 1$ standard deviation. In (c) and (d), the errors are obtained from the fitting process.