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 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, TQ5\/kBGL0 , where G is the shunt conductance. Examination of the calculated sheet inductance LA(T)/L0(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 LF(T)/L0(T) of 2D 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 l(0)/l(T).0.25, where l is the penetration depth.