supercurrent density

The supercurrent density \mathbf{J}_s in a superconductor can be expressed as:

\begin{equation} \mathbf{J}_s = n_s q \mathbf{v}_s \end{equation}

where n_s is the density of superconducting carriers, q is the charge of the carriers, and \mathbf{v}_s is the velocity of the superfluid. The supercurrent density can also be related to the electromagnetic field through the London equations:

\begin{equation} \mathbf{J}_s = -\frac{n_s e^2}{m} \mathbf{A} \end{equation}

where \mathbf{A} is the vector potential, e is the elementary charge, and m is the effective mass of the superconducting carriers.