Magnetic flux quantum
|2010 CODATA values||Units|
The magnetic flux quantum Φ0 is the quantum of magnetic flux passing through a superconducting loop. The phenomenon of flux quantization was discovered by B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Nabauer, 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 (since 1990) have been related to a fixed, "conventional" value of the Josephson constant, denoted KJ–90.
It is a property of a supercurrent (superconducting electrical current) that the magnetic flux passing through any area bounded by such a current is quantized. The quantum of magnetic flux is a physical constant, as it is independent of the underlying material as long as it is a superconductor. Its value is Φ0 = h/(2e) = 2.067833758(46)×10−15 Wb. Here, h is Planck's constant and e is the elementary charge.
If the area under consideration consists entirely of superconducting material, the magnetic flux through it will be zero, for supercurrents always flow in such a way as to expel magnetic fields from the interior of a superconductor, a phenomenon known as the Meissner effect. A non-zero magnetic flux may be obtained by embedding a ring of superconducting material in a normal (non-superconducting) medium. There are no supercurrents present at the center of the ring, so magnetic fields can pass through. However, the supercurrents at the boundary will arrange themselves so that the total magnetic flux through the ring is quantized in units of Φ0. This is the idea behind SQUIDs, which are the most accurate type of magnetometer available.
A similar effect occurs when a type II superconductor is placed in a magnetic field. At sufficiently high field strengths, some of the magnetic field may penetrate the superconductor in the form of thin threads of material that have turned normal. These threads, which are sometimes called fluxons because they carry magnetic flux, are in fact the central regions ("cores") of vortices in the supercurrent. Each fluxon carries an integer number of magnetic flux quanta.
Measuring the magnetic flux 
The magnetic flux quantum may be measured with great precision by exploiting the Josephson effect. In fact, when coupled with the measurement of the von Klitzing constant RK = h/e2, this provides the most precise values of Planck's constant h obtained to date. This is remarkable since h is generally associated with the behavior of microscopically small systems, whereas the quantization of magnetic flux in a superconductor and the quantum Hall effect are both collective phenomena associated with thermodynamically large numbers of particles.
See also 
- Macroscopic quantum phenomena
- Committee on Data for Science and Technology
- Brian D. Josephson
- Dirac flux quantum
- von Klitzing constant
- "Josephson constant KJ". 2010 CODATA recommended values. Retrieved 10 January 2012.
- B. S. Deaver and W. M. Fairbank, Bascom; Fairbank, William (1961). "Experimental Evidence for Quantized Flux in Superconducting Cylinders". Phys. Rev. Lett. 7 (2): 43. Bibcode:1961PhRvL...7...43D. doi:10.1103/PhysRevLett.7.43.
- R. Doll and M. Nabauer, R.; Näbauer, M. (1961). "Experimental Proof of Magnetic Flux Quantization in a Superconducting Ring". Phys. Rev. Lett. 7 (2): 51. Bibcode:1961PhRvL...7...51D. doi:10.1103/PhysRevLett.7.51.
- "magnetic flux quantum Φ0". 2010 CODATA recommended values. Retrieved 10 January 2012.