Pearson correlation coefficient as a tool to identify the composite vortex states in a two-band superconducting slab

In this study, we employed the Pearson product-moment correlation coefficient ([Formula: see text]) to identify non-composite vortex states in a two-band superconducting slab. The fractional vortices were simulated using the two-component Ginzburg–Landau equations TDGL, with the link variable method and the healing coupling between the superconducting bands. The coefficient [Formula: see text] was calculated based on the square modulus of the order parameters of the two condensates, providing insight into the correlation between the two bands. Statistically, [Formula: see text] ranges from [Formula: see text]1 to 1, where values approaching 1 indicate composite vortices, while values nearing 0 suggest non-composite vortices. In this context, negative values of [Formula: see text] are irrelevant. The use of this tool enabled us to assess the degree of decoupling (coincidence of the position of the vortex centers in the superconducting bands) within the vortex lattice, allowing for the identification of specific fields and currents associated with the uncoupled vortex states in the superconducting slab. Such findings are crucial for managing energy dissipation in multi-band superconducting materials and manipulation of the vortices state in multi-band superconducting system.