Superconducting Order-Parameter Fluctuations belowTc

Abstract

Measurements of the frequency-and wave-vector-dependent pair-field susceptibility have been carried out below the transition temperature of a superconductor using a tunneling technique. The results suggest that the dynamical equation of the order parameter below T c is something other than a diffusive time-dependent Ginzburg-Landau equation.In this Letter we report the first measurements of the frequency-and wave-vector-dependent pair-field susceptibility 1 ' 2 of a superconductor below its transition temperature. Previous measurements 3 have been confined to the case where the average pair field of one superconductor with transition temperature T c > was used to determine the pair-field susceptibility of a second metal with transition temperature T c in the temperature range T C <T<T C >. The two metals formed the electrodes of a thin-film tunnel junction, with an excess current in the dc I-V characteristic due to pair tunneling giving a direct measure of the imaginary part of the frequency-and wave-vector-dependent pair-field susceptibility of the normal electrode. The frequency and wave-vector dependence of this susceptibility were determined by measuring the voltage and magnetic-fie Id dependence of the excess current.When both metals are superconducting, the phases of the order parameters of the two electrodes are coupled by the tunneling interaction. The physical manifestations of this coupling are the usual ac and dc Josephson effects. A new effect is observed as the temperature is lowered below T c in the presence of a magnetic field applied in the plane of the junction, sufficient in magnitude to uncouple the order parameters and destroy the Josephson effect, but not greater than the critical field of either metal. Under these conditions, a contribution to the excess current-voltage characteristic is observed to develop in a continuous manner from features observed above T c which have been previously interpreted as the pair-field susceptibility. 2 ' 3 We interpret these low-temperature features of excess current as pair currents arising from the coupling between the order parameter in the electrode with transition temperature T c f and the fluctuating order parameter in the electrode with transition temperature T c . In analogy with the situation occurring above T c , we would expect the excess tunneling current to be a measure of the susceptibility of the low-transition-temperature electrode.In superconductors above T c fluctuations of the order parameter are governed by a diffusive time-dependent Ginzburg-Landau equation, 4 ' 5 which has been studied in previous measurements of the pair-field susceptibility. 3 These order-parameter fluctuations are also responsible for the precursive behavior in the electrical conductivity, 6 magnetic susceptibility, 7 and single-particle density of states 8 which have also been studied extensively in recent years. Below T c there have been few measurements which have quantitatively probed the dynamical behavior of the order parameter. 9 Knowledge of the dynamics is i...

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