Negative self-inductance in superconducting thin wires and weak links

• DOI: 10.1007/bf00628738
• Publication Date: 2004-11-26T07:15:09Z
• Authors: P. V. Christiansen; E. B. Hansen; C. J. Sj�str�m
• Keywords: Supercurrent; Ginzburg–Landau theory; Metastability; Cooper pair

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 velocityvs of the Cooper pairs is sufficiently large, can be so strong that a further increase ofvs 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 λ/κ. 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 φ. 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 φ 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 φ 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 equationI ∝ sin φ 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 currentI is the controlled variable the conjugate phase variable φ will fluctuate and the magnitude of these fluctuations depends strongly on the functional formI(φ). The phase fluctuations for constantI lead to a reduction of the critical current which will be absent when φ 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.