Supercurrents and Flux Quantization

The moving supercondensate, which is made up of $\pm$ pairons all condensed at a finite momentum $\mathbf{p}$, generates a supercurrent. Flux quantization is the first quantization effect manifested on a macroscopic scale. The phase of a macro-wavefunction depends on the pairon circulation and the magnetic field, leading to London’s equation. The penetration depth $\lambda$ based on the pairon flow model is given by $\lambda = (c/e)(p/4\pi k_{0}n_{0}|v_{F}^{(2)}+v_{F}^{(1)}|)^{1/2}$. The quasi-wavefunction $\Psi_{\sigma}(\mathbf{r})$ representing the super current can be expressed in terms of the pairon density operator n as $\Psi_{\sigma}(\mathbf{r})\equiv \left< \mathbf{r}|n|\sigma \right>$,