Fluxoid (${\Phi }_{\mathrm{f}}=\Phi +{\mu }_0{\lambda }^2{\oint }_C\mathbf{j}\cdot d\mathbf{l}$)

For uniform superconducting carrier density, the displayed combination of enclosed magnetic flux and the circulating supercurrent is quantized on a closed contour where the order parameter does not vanish. It follows by integrating the gauge-invariant phase gradient. Magnetic flux alone is quantized only when the current contribution on that contour is negligible.