Temperature and frequency dependence of complex conductance of ultrathin YBa2Cu3O7-x films:: Observation of vortex-antivortex pair unbinding

We have studied the temperature dependencies of the complex sheet conductance, sigma(omega, T), 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, in 100 MHz - 1 GHz frequency range with a new technique using a single spiral coil cavity, and at 30 GHz by aid of a resonant cavity technique. The real, ReM( T), and imaginary parts of the mutual-inductance M( T, omega), between a coil and a film, were measured and converted to complex conductivity by aid of the inversion procedure. We have found quadratic temperature dependence of the kinetic inductance, L-k(-1)(T), at low temperatures independent of frequency, with a break in slope at T-BKT(dc), the maximum of real part of conductance and large shift of the onset temperature and the maximum omega sigma(1)(T) position to higher temperatures with increasing frequency omega. We obtain from these data the universal ratio T-BKT(dc)/L-k(-1)(T-BKT(dc)) = 25, 25, and 17 nHK for 1, 2 and 3-UC films, respectively in close relation 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.