This phase effect is responsible for the quantized-flux requirement and the Little–Parks effect in superconducting loops and empty cylinders. The quantization occurs because the superconducting wave function must be single valued in a loop or an empty superconducting cylinder: its phase difference Δ φ around a closed loop must be an integer multiple of 2π, with the charge q = 2 e for the BCS electronic superconducting pairs.