coherence length
/ koh-HEER-uns length /
Think of dancers in a chorus line who must stay in step. There is a natural span over which the line can shift its rhythm — you cannot make two dancers a hair apart move totally differently, but neither does a change at one end instantly reach the other. The superconducting state has a similar built-in span over which it cannot change too sharply.
The coherence length is the shortest distance over which the strength of the superconducting state — loosely, the density of Cooper pairs — can vary appreciably. It is roughly the size of a single Cooper pair: try to suppress superconductivity at a point, and it cannot recover any faster than this distance allows. Equivalently, the two electrons of a pair stay correlated over about this span, which can range from a few atomic spacings in cuprates to hundreds of nanometres in simple metals.
This matters because the coherence length, compared against how deeply magnetic field penetrates, decides whether a material is type-I or type-II, and it sets how tightly vortices can be packed. A common confusion is to picture a Cooper pair as a tight little dumbbell; in classic superconductors the coherence length is enormous on the atomic scale, meaning the two partners are actually far apart and many pairs overlap. Where the coherence length is very short, vortex cores are tiny and superconductivity is more robust against disorder.
In aluminium the coherence length is over a thousand nanometres, so a single Cooper pair sprawls across thousands of atoms; in a copper-oxide superconductor it can be barely one or two nanometres, making the pairs almost compact by comparison.
Coherence length varies hugely — from over a micron in aluminium to about a nanometre in cuprates.
Superconductors actually have two characteristic lengths: the coherence length and the penetration depth, the distance a magnetic field reaches into the surface. Their ratio is the single number that determines type-I versus type-II behaviour.