Exact Solution of a New Superconducting State

Abstract

An exact solution of a new superconducting state is obtained which exists for DC currents larger than the critical current in thin wires. The order-parameter is zero at all times at certain points in the whisker, thereby permitting the phase to slip at a constant rate, a consequence of which is a dc potential difference between the separate singly-connected superconducting regions. These solutions are periodic in space and lead to voltage steps in the do voltage-current characteristic. It is proven in the limit when the zeros of the orderparameter are far apart that these solutions are stable.Eine exakte Losung eines neuen supraleitenden Zustands wird berechnet, der in diinnen Drahten bei Gleichstromen, die grol3er sind als der kritische Strom, vorhanden ist. Der Ordnungsparameter hat zeitunabhkngige Nullstellen an gewissen Punkten innerhal b des Drahts, deshalb tritt eine Phasenverschiebung mit konstanter Rate auf, deren Wirkung einen elektrostatischen Potentialunterschied zwischen den getrennten, einfach-verbundenen supraleitenden Gebieten zur Folge hat. Diese Losungen sind raumlich periodisch und fiihren zu Spannungsstufen in den Gleichstrom-Spannungscharakteristiken dunner Drahte. Es wird fur den Grenzfall, wo die Nullstellen weit voneinander entfernt sind, bewiesen, daB die Losungen stabil sind. TntroductionWhen a dc transport current I , flows in a superconductor, the fully superconducting state is destroyed at the critical current I , and the metal goes over into the normal state by a series of voltsage steps [l to 41 which are particularly pronounced in whiskers [2] whose length L is large compared to the coherence length E( T ) and whose radius is much smaller than 6 and smaller than or approximately equal to the temperature-dependent penetration depth A( T). The latter structure is one-dimensional in the sense of the Ginzburg-Landau theory. It is the purpose of this work to report exact solutions of the time-dependent Ginzburg-Landau (TDGL) equations for I , > I,, to derive general time-dependent fluctuation equations, and to use t,hese to test the stability of the above solutions.Experiments [l to 41 show that between the fully superconducting and fully normal state there is a range of currents for which the metal is partially normal and superconducting, and that the relative mixture of normal and superconducting properties is a function of the external dc transport current. Although the measured currents and voltages are strictly dc, we have suggested a model [5] which is based in a limited sense on the TDGL equations [6]. This is so because a dc voltage difference in a superconductor is proportional to the time rate of change of the superconducting phase difference between two points in the superconductor.