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 ($P/bar{6}m2$). A soft c-axis polarized mode is clearly observed along
the $/Gamma$-$A$-$L$ symmetry directions. The soft mode is strongly anharmonically broadened at room temperature, but, at 10 K, its linewidth narrows and becomes in good agreement with calculations of linear electron-phonon coupling. This establishes a coherent description of the detailed phonon properties in this system and links them clearly and consistently with the superconductivity.
A complex structure of the superconducting order parameter in $Ln_2$C$_3$ ($Ln$ = La, Y) is demonstrated by muon spin relaxation ($mu$SR) measurements in their mixed state. The muon depolarization rate [$sigma_{rm v}(T)$] exhibits a characteristic te
mperature dependence that can be perfectly described by a phenomenological double-gap model for nodeless superconductivity. While the magnitude of two gaps is similar between La$_2$C$_3$ and Y$_2$C$_3$, a significant difference in the interband coupling between those two cases is clearly observed in the behavior of $sigma_{rm v}(T)$.
The full-potential linear augmented plane-wave calculations have been applied to investigate the systematic change of electronic structures in CaAlSi due to different stacking sequences of AlSi layers. The present ab-initio calculations have revealed
that the multistacking, buckling and 60 degrees rotation of AlSi layer affect the electronic band structure in this system. In particular, such a structural perturbation gives rise to the disconnected and cylindrical Fermi surface along the M-L lines of the hexagonal Brillouin zone. This means that multistacked CaAlSi with the buckling AlSi layers increases degree of two-dimensional electronic characters, and it gives us qualitative understanding for the quite different upper critical field anisotropy between specimens with and without superstructure as reported previously.
Local magnetic field distribution B(r) in the mixed state of a boride superconductor, YB6, is studied by muon spin rotation (muSR). A comparative analysis using the modified London model and Ginzburg-Landau (GL) model indicates that the GL model exhi
bits better agreement with muSR data at higher fields, thereby demonstrating the importance of reproducing the field profile near the vortex cores when the intervortex distance becomes closer to the GL coherence length. The temperature and field dependence of magnetic penetration depth ($lambda$) does not show any hint of nonlocal effect nor of low-lying quasiparticle excitation. This suggests that the strong coupling of electrons to the rattling motion of Y ions in the boron cage suggested by bulk measurements gives rise to a conventional superconductivity with isotropic s-wave pairing. Taking account of the present result, a review is provided for probing the anisotropy of superconducting order parameters by the slope of $lambda$ against field.
