Energy gap, penetration depth, and surface resistance of MgB2 thin films determined by microwave resonator measurements

We have measured the temperature dependence of the microwave surface impedance Zs5Rs1ivm0l of two c-axis oriented MgB2 films employing dielectric resonator techniques. The temperature dependence of the magnetic-field penetration depth l determined by a sapphire dielectric resonator at 17.9 GHz can be well fitted from 5 K close to Tc by the standard BCS integral expression assuming the reduced energy gap D(0)/kTc to be as low as 1.13 and 1.03 for the two samples. For the penetration depth at zero temperatures, values of 102 and 107 nm were determined from the fit. Our results clearly indicate the s-wave character of the order parameter. A similar fit of the penetration depth data was obtained with an anisotropic s-wave BCS model. Within this model we had to assume a prolate order parameter, having a large gap value in the c-axis direction and a small gap within the ab plane. This is in contrast to recent fits of the anisotropic s-wave model to upper critical-field data, where an oblate order parameter had to be used, and raises interesting questions about the nature of the superconducting state in MgB2 . A rutile dielectric resonator was employed to obtain the temperature dependence of Rs with high accuracy. Below about Tc/2, Rs(T)2Rs(5 K) exhibits an exponential temperature dependence with a reduced energy gap consistent with that determined from the penetration depth data. The Rs value at 4.2 K was found to be as low as 19 mV at 7.2 GHz, which is comparable with a high-temperature superconducting copper oxide thin film.