Magnetic flux quantum

The magnetic flux, represented by the symbol Φ, threading some contour or loop is defined as the magnetic field B multiplied by the loop area S, i.e. Φ = B ⋅ S. Both B and S can be arbitrary, meaning Φ can be as well. However, if one deals with the superconducting loop or a hole in a bulk superconductor, the magnetic flux threading such a hole/loop is quantized. The (superconducting) magnetic flux quantum Φ0 = h/(2e) ≈ is a combination of fundamental physical constants: the Planck constant h and the electron charge e. Its value is, therefore, the same for any superconductor. The phenomenon of flux quantization was discovered experimentally by B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Näbauer, in 1961. The quantization of magnetic flux is closely related to the Little–Parks effect, but was predicted earlier by Fritz London in 1948 using a phenomenological model. The inverse of the flux quantum, 1/Φ0, is called the Josephson constant, and is denoted KJ. It is the constant of proportionality of the Josephson effect, relating the potential difference across a Josephson junction to the frequency of the irradiation. 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 redefinition of SI base units, the Josephson constant has an exact value of KJ = 483597.84841698GHz⋅V^−1, which replaces the conventional value KJ-90. The following physical equations use SI units. In CGS units, a factor of c would appear. The superconducting properties in each point of the superconductor are described by the complex quantum mechanical wave function Ψ(r,t) — the superconducting order parameter. As any complex function Ψ can be written as Ψ = Ψ0eiθ, where Ψ0 is the amplitude and θ is the phase. Changing the phase θ by 2πn will not change Ψ and, correspondingly, will not change any physical properties.