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Temperature and Frequency Dependence of Complex Conductance of Ultrathin YBa2Cu3O7-x Films: A Study of Vortex-Antivortex Pair Unbinding

We have studied the temperature dependencies of the complex sheet conductance of 1-3 unit cell (UC) thick YBa2Cu3O7-x films sandwiched between semiconducting Pr0.6Y0.4Ba2Cu3O7-x layers at high frequencies. Experiments have been carried out in a frequency range between: 2 - 30 MHz with one-spiral coil technique, 100 MHz - 1 GHz frequency range with a new technique using the spiral coil cavity and at 30 GHz by aid of a resonant cavity technique. The real and imaginary parts of the mutual-inductance between a coil and a film were measured and converted to complex conductivity by aid of the inversion procedure. We have found a quadratic temperature dependence of the kinetic inductance, L_k^-1(T), at low temperatures independent of frequency, with a break in slope at T^dc_BKT, the maximum of real part of conductance and a large shift of the break temperature and the maximum position to higher temperatures with increasing frequency. We obtain from these data the universal ratio T^dc_BKT/L_k^-1(T^dc_BKT) = 25, 25, and 17 nHK for 1-, 2- and 3UC films, respectively in close agreement with theoretical prediction of 12 nHK for vortex-antivortex unbinding transition. The activated temperature dependence of the vortex diffusion constant was observed and discussed in the framework of vortex-antivortex pair pinning. PACS numbers: 74.80.Dm, 74.25.Nf, 74.72.Bk, 74.76.Bz