= Fluxoid and flux quantization in a superconductor
{title2=$\oint_C\left(A+\frac{m}{q^2n_s}j\right)\cdot dl=\frac hqN$}
For a nonvanishing superconducting <order parameter> $\psi=\sqrt{n_s}e^{i\theta}$, $j=(qn_s/m)(\hbar\nabla\theta-qA)$. Single-valuedness gives phase winding $2\pi N$ around a closed curve, hence the <fluxoid and flux quantization in a superconductor> identity above. Magnetic flux alone is $Nh/q$ when the current integral vanishes. If the entire spanning surface is in a region where $D\psi=0$, the field vanishes there and the winding is zero; nonzero quantized flux requires a hole or a vortex core where that condition does not hold.
Back to article page
