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