Superconducting micronets: The Wheatstone bridge

Using the Ginzburg-Landau theory, a particular superconducting (sc) micronet, called the Wheatstone bridge, is studied. This planar micronet is made of two nodes connected by three thin sc wires. A magnetic field is applied perpendicularly to its plane. The sc-normal second-order phase transition is characterized by only two configurations of the order parameter: cphiA=cphiB and cphiA=-cphiB, where cphiA and cphiB are the order parameters at the nodes. For temperatures near Tc, we show that only the cphiA=cphiB configuration is admissible for fluxes near {Φ}=nΦ₀, where n is an integer and Φ₀ is the flux quantum. Finally, the exact solution of the nonlinear Ginzburg-Landau equations for one-dimensional systems is numerically fitted to the boundary conditions of the Wheatstone bridge for the two configurations cphiA=cphiB and cphiA=-φB. Graphs of the Gibbs energy and of the spontaneous supercurrent, which for these two configurations is always a screening supercurrent, are given as functions of the total flux. A discontinuous transition between configurations occurs as a function of the flux.