Fluxoid quantization in geometrically coupled superconducting loops

Superconducting networks composed of coupled loops with different areas exhibit a rich spectrum of macroscopic fluxoid quantum states. We analyze networks consisting of two types of loops and show that the ratio, R , of their areas, expressed as a reduced rational fraction, governs the system’s periodic response, the fluxoid occupation of both large and small loops, and the number of distinct fluxoid states within a single period. Furthermore, we identify a condition on the fraction R under which the coupled loops exchange fluxoids at a specific magnetic field. Numerical simulations, based on the “J 2 ” model, corroborate these results and reveal how geometrical coupling can produce complex fluxoid configurations, offering potential applications in multistate superconducting memory and flux-based devices.