  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

Superconductivity;Mesoscale and Nanoscale Physics