Representation of the mixed state. A magnetic field is applied (in black). Superconducting currents (in red) develop on the surface in order to make a screen against this field; those are the currents responsible for the Meissner effect. Other superconducting currents develop (in green) creating vortices (like non superconducting “tunnels”). These vortices allow a quantum of magnetic flux to go through them and thus enable part of the applied magnetic field to go through the superconducting sample.
Because of these vortices, the superconductor becomes a sieve which enables part of the applied magnetic field to pass through. Actually, the superconductor properties are improved. The part of its volume which stops being superconducting (inside the vortices) is lost, but in return, it only has to expel a fraction of the external magnetic field, since the rest of the magnetic field goes through the vortex. The superconductor can then bear much higher magnetic fields.
This state is called the mixed state. Abrikosov came up with the idea of this vortex compromise in 1952, but initially, it was considered merely a theoretical speculation. Since then, experiments have quickly proved that the vortices do exist, and today, many techniques enable researchers to observe them. When the magnetic field is raised or lowered, vortices can be observed getting in or out the sample in a strange leapfrog motion. [http://www.fys.uio.no/super/results/sv/index.html#svmovies]
The Abrikosov theory shows that the magnetic flux going through the vortex is unvarying. This flux quantum has a value of Φ0= h/2e = 2.07 10-15 T m2. This quantization is the result of the existence of the condensate combined with the formation of collective Cooper pairs. The exact value of Φ0 is the experimental proof that electrons are paired in a superconductor.
Vortices can also be observed in superfluids or in Bose-Einstein condensates, which are two similar forms of superconductivity for liquids and gases.
In the mixed state, even if the magnetic field is no longer expelled and diamagnetism does not exist, the electric resistance remains equal to zero. Indeed, the electric current can flow in the parts that remained superconducting and can go through the sample unimpeded simply by avoiding the vortices. There is only one exception: in some cases (for instance, cuprates at a high temperature), the vortices move and behave as a liquid and a resistance due to this movement appears.
