Dynamic impedance of two-dimensional superconducting films near the superconducting transition

The sheet impedances, Z(omega ,T), of several superconducting n-Mo77Ge23 films and one In/InOx film have been measured in zero field using a two-coil mutual inductance technique at frequencies from 100 Hz to 100 kHz. Z(omega ,T) is found to have three contributions: the inductive superfluid, renormalized by nonvortex phase fluctuations; conventional vortex-antivortex pairs, whose contribution turns on very rapidly just below the Kosterlitz-Thouless-Berezinskii (KTB) unbinding temperature; and an anomalous contribution. The latter is predominantly resistive, persists well below the KTB temperature, and is weakly dependent on frequency down to remarkably low frequencies, at least 100 Hz. It increases with T as e(-U'(T)/kBT), where the activation energy, U'(T), is about half the energy to create a vortex-antivortex pair, indicating that the frequency dependence is that of individual excitations, rather than critical behavior.