7. Superconductivity - University of Liverpool

∫
∆φ = m
∫L v.dl + q A.dl.
L
The phase change ∆φ is zero or a multiple of 2π, because the
wavefunction returns to the same value after one loop.
The integral over A gives the magnetic flux Φ.
The velocity v is related to the current density J by
J = ρqv,
where ρ is the number density of the electrons. The above
equation then becomes
∆φ = m ρq
∫
L
J.dl + qΦ.
Superconductivity 20