Evolution of Anomalous Angular Dependence of $H_{c2}$ in CaAl$_{1-x}$Ga$_{x}$Si

In CaAlSi, the angular dependence of the upper critical field, $H_{c2}(\theta )$, shows an anomalous cusp when the field is applied parallel to the superconducting layer. $H_{c2}(\theta )$ can be reasonably well fitted by the Tinkham model for thin film superconductors. On the other hand, $H_{c2}(\theta )$ in CaGaSi does not show such an anomaly. Concomitant with these features, a lattice modulation along the $c$-axis exists only in CaAlSi. We have grown single crystals of the alloy CaAl$_{1-x}$Ga$_{x}$Si, and studied the evolution of the anomalous angular dependence of $H_{c2}$ and the superstructure. The superstructure.is sustained at least up to x = 0.2, although the period of the modulation changes from $\sim $6$c$ to $\sim $3$c$. On the other hand, the cusp-like feature in $H_{c2}(\theta )$ is strongly suppressed by the Ga substitution, and only evident at low temperatures. We have also investigated the homogeneity of the crystal by inspecting the vortex penetration using magneto-optical technique. We have found an inhomogeneous penetration of vortices along the superconducting plane in the \textit{ac} plane, suggesting the presence of modulation of superconducting parameters. Based on these results, we will discuss the origin of the anomalous $H_{c2}(\theta )$.