Effect of thermal phase fluctuations on the inductances of Josephson junctions, arrays of junctions, and superconducting films

We calculate the factor by which thermal phase fluctuations, as distinct from phase-slip fluctuations, increase the inductance L-J of a resistively shunted Josephson junction (JJ) above its mean-field value L-0. We find that quantum mechanics suppresses fluctuations when T drops below a temperature, T-Q = h/k(B)GL(0), where G is the shunt conductance. Examination of the calculated sheet inductance L-A(T)/L-0(T) of arrays of JJ's reveals that two-dimensional (2D) interconnections halve fluctuation effects, while reducing phase-slip effects by a much larger factor. Guided by these results, we calculate the sheet inductance L-F(T)/L-0(T) of 2D films by treating each plasma oscillation mode as an overdamped JJ. In disordered s-wave superconductors, quantum suppression is important for L-F(0)/L-F(T)>0.14 (or T/T-C0<0.94). In optimally doped YBCO and BSCCO quantum suppression is important for lambda(2)(0)/lambda(2)(T)>0.25, where lambda is the penetration depth.