Superconducting micronets: A state-variable approach.

Abstract

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\ensuremath{\ll}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/\ensuremath{\xi}(T) and magnetic flux \ensuremath{\varphi} for low magnetic fields, where \ensuremath{\xi}(T) is the temperature-dependent coherence length. The critical current ${\mathit{J}}_{\mathit{c}}$ approaches zero at a new temperature-critical flux boundary, ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}1}$(T), which is first order and distinct from the second-order phase-transition boundary, ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}2}$(T).