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, σ(ω, T), of 1–3 unit cell (UC) thick YBa₂Cu₃O_7−x films sandwiched between semiconducting Pr_0.6Y₀.4Ba₂Cu₃O_7−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, Re M(T), and imaginary parts of the mutual-inductance M(T, ω), 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^dc_BKT, the maximum of real part of conductance and large shift of the onset temperature and the maximum ωσ₁(T) position to higher temperatures with increasing frequency ω. We obtain from these data the universal ratio T^dc_BKT/L⁻¹_k (T^dc_BKT) = 25, 25 and 17, nH K for 1, 2 and 3-UC films, respectively in close relation with theoretical prediction of 12 nH K 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. [ABSTRACT FROM AUTHOR]