Fluctuations, dissipation, and nonuniversal superfluid jumps in two-dimensional superconductors

We report a comprehensive study of the complex ac conductivity of thin effectively two-dimensional amorphous superconducting InO_x films at zero applied field. Below a temperature scale T_c0 where the superconducting order parameter amplitude becomes well defined, there is a temperature where both the generalized superfluid stiffness acquires a frequency dependence and the dc magnetoresistance becomes linear in field. We associate this with a transition of the Kosterlitz-Thouless-Berezinskii (KTB) type. At our measurement frequencies the superfluid stiffness at T_KTB is found to be larger than the universal value. Although this may be understood with a vortex dielectric constant of ϵ_v≈1.9 within the usual KTB theory, this is a relatively large value and indicates that such a system may be out of the domain of applicability of the low-fugacity (low-vortex-density) KTB treatment. This opens up the possibility that at least some of the discrepancy from a nonuniversal magnitude is intrinsic. Our finite-frequency measurements allow us access to a number of other phenomena concerning the charge dynamics in superconducting thin films, including an enhanced conductivity near the amplitude fluctuation temperature T_c0 and a finite dissipation at low temperature which appears to be a universal aspect of highly disordered superconducting films.