Superconducting micronets: A state-variable approach

A state-variable formulation of the nonlinear Ginzburg-Landau equations for superconducting micronets is introduced. The state variables are the Cooper-pair density N, kinetic energy E, and the imaginary part I of the Cooper-pair momentum density scrP. Purely algebraic relations among the state variables are derived, and several fundamental properties of micronets are proven. The current density J=RescrP is given by ${\mathit{J}}^2$=NE-${\mathit{I}}^2$, where I=ImscrP. For the limit N≪1, a quasilinear theory yields the superfluid velocity Q as the only relevant transport parameter at the phase-transition boundary. Applying the full nonlinear theory, the maximum supercurrent that can be injected into a microladder is calculated as a function of normalized nodal spacing scrL/ξ(T) and magnetic flux φ for low magnetic fields, where ξ(T) is the temperature-dependent coherence length. The critical current ${\mathit{J}}_{\mathit{c}}$ approaches zero at a new temperature-critical flux boundary, ${\mathrm{\phi }}_{\mathit{c}1}$(T), which is first order and distinct from the second-order phase-transition boundary, ${\mathrm{\phi }}_{\mathit{c}2}$(T).