Static properties of two- and three-dimensional superconducting constrictions

Journal Article · Fri Dec 01 04:00:00 EST 1978 · J. Low Temp. Phys.; (United States)

DOI:https://doi.org/10.1007/BF00115575· OSTI ID:6441244

Mooij, J E; Dekker, P

Calculations have been performed on superconducting constrictions with hyperbolic geometry. Stationary Ginzburg--Landau equations are used, neglecting magnetic fields. Emphasis is placed on the difference between two- and three-dimensional constrictions, which is related to the difference between uniform-thickness (UT) and variable-thickness (VT) superconducting microbridges. The width of the constriction w, normalized to the coherence length xi, is indicated by the parameter A (approx. =w/2xi). It is found that small (A<0.1), three-dimensional constrictions and VT bridges have a sinusoidal current--phase relation, linear temperature dependence of the critical current I/sub c/, and an I/sub c/R product (R is the normal state resistance) equal to the Ambegaokar--Baratoff expression for Josephson junctions near T/sub c/. Two-dimensional constrictions behave as if they consist of an inner core with junction properties, in series with the films on both sides. The core shows a sinusoidal current--phase relation and I/sub c/R according to Ambegaokar and Baratoff. For the whole constriction neither the phase difference nor R is finite. Two-dimensional constrictions have linear temperature dependence only when they are extremely narrow (A<0.001). In two-dimensional bridges the order parameter is depressed over a distance of approximately the coherence length; in small three-dimensional constrictions this distance is approximately equal to the width. In narrow constrictions (and short microbridges) the current is not homogeneously distributed over the cross section. The effect has been investigated that occurs when in three-dimensional constrictions the width w is not much larger than l/sub o/, the electron mean free path in the basic material. The critical current is decreased, but the I/sub c/R product remains constant. The results of the calculations are compared with experiment.

• Research Organization: Department of Applied Physics, Delft University of Technology, Delft, The Netherlands
• OSTI ID: 6441244
• Journal Information: J. Low Temp. Phys.; (United States), Journal Name: J. Low Temp. Phys.; (United States) Vol. 33:5; ISSN JLTPA
• Country of Publication: United States
• Language: English

Related Subjects

656101* -- Solid State Physics-- Superconductivity-- General Theory-- (-1987)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
BOUNDARY CONDITIONS
COHERENCE LENGTH
CRITICAL CURRENT
CURRENTS
ELECTRIC BRIDGES
ELECTRIC CURRENTS
ELECTRICAL EQUIPMENT
EQUIPMENT
GINZBURG-LANDAU THEORY
TEMPERATURE DEPENDENCE
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS