Observation of a Bulk Nodal-Gap in Overdoped Y$_{0.9}$Ca$_{0.1}$Ba$_{2}$Cu$_{3}$O$_{7-\delta }$ Thin Films

Abstract

Complex conductivity of overdoped Y$_{0.9}$Ca$_{0.1}$Ba$_{2}$Cu$_{3}$O$_{7-\delta }$ thin films was measured in Terahertz frequency using frequency and time domain methods. The films were measured in the frequency range of 3–100 cm$^{-1}$ and in the temperature range of 20–300 K. Results show a possible deviation from a pure $d_{x^{2}-y^{2}}$-wave superconductor, indicated by the existence of an energy sub-gap in overdoped Y$_{0.9}$Ca$_{0.1}$Ba$_{2}$Cu$_{3}$O$_{7-\delta }$ films. Evidence for this sub-gap appears as non-monotonic behavior of $\sigma _{1}(\omega ,T)$ as a function of frequency followed by a sharp decrease at low frequencies, and a dip in the imaginary part of the optical conductivity multiplied by frequency, $\omega {{\sigma }_{2}}(\omega ,T)$. The mentioned features were observed at energy of about 1.2 meV in 10 % Ca-doped YBCO thin films. Our complex conductivity spectra are in agreement with the theoretical prediction obtained by using a mixed symmetry order parameter within the Born limit, shown by Schürrer et al. We suggest that these observations are direct evidence for a nodal gap obtained in a $d_{x^{2}-y^{2}}$-wave superconductor and can be theoretically clarified by adding an imaginary component as $is$ or $i{{d}_{xy}}$ to the main $d_{x^{2}-y^{2}}$-wave order parameter.