Optical Investigation on the Electronic Structures of Multi-band Ca$_{2-x}$Sr$_{x}$RuO$_{4}$

We investigated the polarization dependent optical spectra of the quasi-two-dimensional multi-band Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ (0.0$<$x$\le $2.0) system. Recently, it becomes an important issue to understand how the electronic structure evolves from a multi-band metal Sr$_{2}$RuO$_{4}$ to a Mott-insulator Ca$_{2}$RuO$_{4}$ in the Ca$_{2-x}$Sr$_{x}$RuO$_{4}$ system, especially whether the orbital selective Mott-transition occurs at x=0.5 or not. In the in-plane optical spectra, we observed an intriguing behavior in the electrodynamics, i.e., the decrease of the mass enhancement accompanying the reduction of the plasma frequency. We found that such result could not be attributed to the Mott-gap opening. Instead, with the detailed understanding of the c-axis optical spectra, we suggested that the critical behaviors near x=x$_{c}$ should be closely related with the renormalization of the d$_{xy}$ band, which is strongly affected by the tilting of the RuO$_{6}$ octahedra.