Evidence of two-gap s-wave superconductivity in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ from microwave surface impedance measurements

Epitaxial thin films of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ with low cation and oxygen disorder exhibit two features in the temperature dependence of the microwave surface impedence which are consistent with a weak s-wave superconducting state associated with the CuO chains. First, both the microwave surface resistance and the magnetic field penetration depth exhibit a weak exponential temperature dependence below 30 K corresponding to an energy gap of about 6 meV. Second, the penetration depth exhibits a small bump at about 60 K, which is consistent with a two-band BCS calculation using 6 meV for the smaller gap.