Soft-phonon-driven superconductivity in CaAlSi as seen by inelastic x-ray scattering

Inelastic x-ray scattering and ab initio calculation are applied to investigate the lattice dynamics and electron-phonon coupling of the ternary silicide superconductor CaAlSi $\left(P\overline{6}m2\right)$. A soft $c$-axis polarized mode is clearly observed along the $\Gamma \text{−}A\text{−}L$ symmetry directions. The soft mode is strongly anharmonically broadened at room temperature, but at $10\mathrm{K}$, its linewidth narrows and comes in good agreement with calculations of linear electron-phonon coupling. This establishes a coherent description of the detailed phonon properties into this system and links them clearly and consistently with the superconductivity.

Figure 1

(Color online) IXS spectra at $10\mathrm{K}$ (blue, circle) and $280\mathrm{K}$ (red, square) in almost longitudinal geometry measured at $\mathbf{Q}=(-1.03-0.034.50)$ corresponding to $A$ point in the hexagonal Brillouin zone. Inset shows the eigenpolarization for the soft phonon mode.

Figure 2

(Color online) IXS spectra at $10\mathrm{K}$ along the $\Gamma \text{−}A\text{−}L$ lines. Panels (a)–(c) are the data collected at $\mathbf{Q}=(-104+\xi )$, while (c)–(e) are along $A\text{−}L$ direction measured at $\mathbf{Q}=(-1+\xi 04.5)$ ($\xi$ is expressed in reciprocal lattice units). The solid line is a fit (see the text).

Figure 3

(Color online) Phonon dispersion obtained by both IXS experiments (open symbols) and ab initio calculation (lines) of $1H\text{−}\mathrm{Ca}\mathrm{Al}\mathrm{Si}$ along the $\Gamma \text{−}M$ and $\Gamma \text{−}A\text{−}L$ lines. The additional points at $\Gamma$ (filled circles and crosses) are data obtained by Raman scattering (Refs. 20, 21).

Figure 4

(Color online) Experimental (at $10\mathrm{K}$, symbols) and calculated (solid line) electron-phonon coupling constant ${\lambda }_{\mathbf{q}\lambda }$ of soft mode and $A_{2\text{low}}^{″}$ modes along the $\Gamma \text{−}A\text{−}L$ lines. Square symbols and dot-dashed line correspond to the measured and calculated data of electronic contribution to the linewidth for the soft mode, respectively. The calculated results correspond to those of bold lines in Fig. 3.