QED3 Theory of High Temperature Superconductors • What is the ...

How Does a Superconductor Become Normal?
In superconductors electrons form Cooper pairs: 〈c † ↑(r)c † ↓(r)〉 ∼
∆(r). The order parameter ∆(r) is a complex wave function with
amplitude |∆| and phase exp(iϕ(r)). In the superconducting state
Cooper pairs are “Bose condensed” and 〈∆〉 ≠ 0.
Superconducting vortex is a topological
defect in ϕ (see arrows).
If one goes around the vortex,
ϕ winds by 2π (−2π around
antivortex). The amplitude is
uniform except in the core where
|∆| → 0.
If vortices proliferate, through thermal or quantum fluctuations,
it is this strong phase winding that ultimately destroys superconducting
order: lim |r|→∞ 〈∆(r)∆ ∗ (0)〉 → 0 , 〈∆〉 = 0