To understand this definition in the context of the Dirac flux quantum one shall consider that the effective quasiparticles active in a superconductors are Cooper pairs with an effective charge of 2 electrons q = 2e.
The phenomenon of flux quantization was first discovered in superconductors experimentally by B. S. Deaver and W. M. Fairbank[6] and, independently, by R. Doll and M. Näbauer,[7] in 1961.
The quantization of magnetic flux is closely related to the Little–Parks effect,[8] but was predicted earlier by Fritz London in 1948 using a phenomenological model.
[9][10] The inverse of the flux quantum, 1/Φ0, is called the Josephson constant, and is denoted KJ.
The Josephson effect is very widely used to provide a standard for high-precision measurements of potential difference, which (from 1990 to 2019) were related to a fixed, conventional value of the Josephson constant, denoted KJ-90.
With the 2019 revision of the SI, the Josephson constant has an exact value of KJ = 483597.84841698... GHz⋅V−1.
If this is so, then one has n magnetic flux quanta trapped in the hole/loop,[10] as shown below: Per minimal coupling, the current density of Cooper pairs in the superconductor is:
Now, because the order parameter must return to the same value when the integral goes back to the same point, we have:[12]
Due to the Meissner effect, the magnetic induction B inside the superconductor is zero.
More exactly, magnetic field H penetrates into a superconductor over a small distance called London's magnetic field penetration depth (denoted λL and usually ≈ 100 nm).
The screening currents also flow in this λL-layer near the surface, creating magnetization M inside the superconductor, which perfectly compensates the applied field H, thus resulting in B = 0 inside the superconductor.
However, the value of the flux quantum is equal to Φ0 only when the path/trajectory around the hole described above can be chosen so that it lays in the superconducting region without screening currents, i.e. several λL away from the surface.
There are geometries where this condition cannot be satisfied, e.g. a loop made of very thin (≤ λL) superconducting wire or the cylinder with the similar wall thickness.
The flux quantization is a key idea behind a SQUID, which is one of the most sensitive magnetometers available.
Flux quantization also plays an important role in the physics of type II superconductors.
The Abrikosov vortex consists of a normal core – a cylinder of the normal (non-superconducting) phase with a diameter on the order of the ξ, the superconducting coherence length.
The normal core plays a role of a hole in the superconducting phase.
The magnetic field lines pass along this normal core through the whole sample.
In total, each such Abrikosov vortex carries one quantum of magnetic flux Φ0.
Prior to the 2019 revision of the SI, the magnetic flux quantum was measured with great precision by exploiting the Josephson effect.
This may be counterintuitive, since h is generally associated with the behaviour of microscopically small systems, whereas the quantization of magnetic flux in a superconductor and the quantum Hall effect are both emergent phenomena associated with thermodynamically large numbers of particles.
Therefore, both the Josephson constant KJ = 2e/h and the von Klitzing constant RK = h/e2 have fixed values, and the Josephson effect along with the von Klitzing quantum Hall effect becomes the primary mise en pratique[15] for the definition of the ampere and other electric units in the SI.