Inhomogeneous Current States in a Gauged Two-Component Ginzburg–Landau Model

We consider the energy bounds of inhomogeneous current states in doped antiferromagnetic insulators in the framework of the two-component Ginzburg–Landau model. Using the formulation of this model in terms of the gauge-invariant order parameters (the unit vector $\bold n$, spin stiffness field $\rho^{2}$, and particle momentum $\bold c$), we show that this strongly correlated electron system involves a geometric small parameter that determines the degree of packing in the knots of filament manifolds of the order parameter distributions for the spin and charge degrees of freedom. We find that as the doping degree decreases, the filament density increases, resulting in a transition to an inhomogeneous current state with a free energy gain.