Minimal geometric correction to vortex interactions in GL

We introduce a minimal, gauge-invariant geometric correction within the Ginzburg–Landau (GL) framework that modifies intervortex interactions without introducing additional dynamical fields. The correction is encoded as a weak, smooth modulation of an effective GL length scale, providing a compact parameterization of geometry-induced mesoscopic effects beyond the homogeneous GL limit. In the London regime, we derive the leading-order correction to the intervortex potential and obtain an analytic criterion that delineates a crossover between bulk-like and mesoscopic interaction regimes. Two simple model profiles are discussed, illustrating how the approach reproduces qualitative macroscopic–mesoscopic transitions reported in time-dependent GL simulations. The microscopic origin of the effective modulation is intentionally left open, establishing a controlled and GL-consistent entry point for future theoretical and numerical investigations.