Tunneling Spectroscopy on $c$-axis Y$_{1-x}$Ca$_x$Ba$_2$Cu$_3$O$_{7-\delta}$ Thin Films: Evidence for Multiband Superconductivity

We report scanning tunneling spectroscopy measurements on \{001\} oriented Y$_{1-x}$Ca$_x$Ba$_2$Cu$_3$O$_{7-\delta}$ thin films at \emph{x}= 0, 0.05, 0.15 and 0.20 Ca-doping at 4.2K. The tunneling spectra exhibit main-gap, sub-gap and satellite features which we analyze using a generic multiband tunneling model that accounts for the separate contributions of the plane and chain bands to the tunneling conductance spectrum. Our analysis indicates the sub-gap features could arise from the chain band density of states, while the satellite features could come from the plane band for a $d_{x^2-y^2}+s$ pairing symmetry. The doping dependent evolution indicates that all three spectral features are set by a single parameter $\Delta_0$, which monotonically decreases with Ca-doping, suggesting that superconductivity in Y$_{1-x}$Ca$_x$Ba$_2$Cu$_3$O$_{7-\delta}$ involves multiple bands.