Effect of Thermal Phase Fluctuations on the Inductances of Josephson Junctions, Arrays of Junctions, and Superconducting Films

Abstract

We calculate the factor by which thermal phase fluctuations, as distinct from phase-slip fluctuations, increase the inductance, LJ, of a resistively-shunted Josephson junction (JJ) above its mean-field value, L0. We find that quantum mechanics suppresses fluctuations when T drops below a temperature, TQ = h/kBGL0, where G is the shunt conductance. Examination of the calculated sheet inductance, LA(T)/L0(T), of arrays of JJ's reveals that 2-D interconnections halve fluctuation effects, while reducing phase-slip effects by a much larger factor. Guided by these results, we calculate the sheet inductance, LF(T)/L0(T), of 2-D films by treating each plasma oscillation mode as an overdamped JJ. In disordered s-wave superconductors, quantum suppression is important for LF(0)/LF(T) > 0.14, (or, T/TC0 < 0.94). In optimally doped YBCO and BSCCO quantum suppression is important for l2(0)/l2(T) > 0.25, where l is the penetration depth.