Negative Self-Inductance in Superconducting Thin Wires and Weak Links

One of the most promising implications of the phenomenological Ginzburg-Landau (GL) theory of superconductivity is the possible existence of current-carrying metastable states with a negative effective self-inductance. Microscopically this phenomenon can be explained as a result of the depairing mechanism which, when the center-of-mass velocity v(s) of the Cooper pairs is sufficiently large, can be so strong that a further increase of v(s) will lead to a decrease of the total current. Using a one-dimensional formulation of the GL theory we investigate the thermodynamic stability of these states for different external constraints and obtain the result that a negative self-inductance can only be stable if the length of the system in the direction of the current is smaller than a critical value comparable to the GL coherence length lambda/kappa. It is an experimental fact that states of negative self-inductance are realized in Josephson junctions and other types of superconducting weak links because the dc supercurrent can be a decreasing function of the phase variable phi. The thermodynamic stability theory can therefore explain why weak links have to be short, and it also provides us with a unifying point of view by treating the phase phi and the current as a pair of thermodynamically conjugate variables for arbitrary one-dimensional systems. An important point is the operational phase definition as a thermodynamic parameter that can be controlled by the experimentalist. This requirement is essential for the general validity of the ac Josephson equation and it implies that phi must depend on the magnetic self-inductance of the system. By applying the GL theory to weak links we can delimit the validity of the usual dc Josephson equation I proportional to sin phi and see that deviations from this functional form are most likely to be found in thin-film bridges of the Anderson-Dayem (AD) type. When the current I is the controlled variable the conjugate phase variable phi will fluctuate and the magnitude of these fluctuations depends strongly on the functional form I(phi). The phase fluctuations for constant I lead to a reduction of the critical current which will be absent when phi is the controlled variable. The observed microwave enhancement of the critical current in AD bridges, the so-called Dayem effect, can be explained as a result of a switch from current control to phase control, and the fluctuation formulae explain why the effect is negligible in structures exhibiting the classical Josephson sine law for the current-phase relation.