Determination of the doping dependence of the penetration depth using YBCO microstrip ring resonators

We present a method to determine the temperature dependent London penetration depth measured by a microstrip ring resonator for YBCO thin films with various oxygen contents. It allows us to get the following important results of the superconducting properties in the underdoped cuprate superconductors. With increasing δ (e.g. δ = 0.05, 0.2, and 0.4), the superfluid density, λ²(5K)/λ²(T), is linear in the low temperature range (T < T_c/3), and the slope changes with increasing oxygen deficiency. After the temperature normalization with respect to the critical temperature, the temperature dependence of the superfluid density is shown to be independent of doping concentration. Moreover the maximum energy gap can be estimated from the model of the d-wave pairing. We found that the ratio Δ/T_c is nearly fixed value, 3.0 ± 0.4.