Magnetic flux quantum

Values (CODATA 2006)[1]		Units
Φ0	2.067 833 667(52)×10−15	Wb
KJ	483 597.891(12)×109	Hz/V
KJ–90	483 597.9×109	Hz/V

The magnetic flux quantum Φ₀ is the quantum of magnetic flux passing through a superconductor. The phenomenon of flux quantization was discovered B. S. Deaver and W. M. Fairbank ^[2] and, independently, by R. Doll and M. Nabauer^[3], 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 K_J. 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 K_J–90.

Introduction

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) = 2.067 833 636×10⁻¹⁵ Wb.

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.

Quantization of magnetic flux is determined by a geometric unified theory^[4] of electromagnetism and gravitation. The electric elementary charge is simultaneously determined by the theory. Furthermore, these charge and flux quanta directly give the fractions which appear in the fractional quantum Hall effect.

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 R_K = 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

• Brian D. Josephson
• Dirac flux quantum
• von Klitzing constant

References

1. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006". Rev. Mod. Phys. 80: 633–730. Bibcode 2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633. http://physics.nist.gov/cuu/Constants/codata.pdf. 
2. ^ B. S. Deaver and W. M. Fairbank (1961). Phys. Rev. Lett. 7: 43. Bibcode 1961PhRvL...7...43D. doi:10.1103/PhysRevLett.7.43. 
3. ^ R. Doll and M. Nabauer (1961). Phys. Rev. Lett. 7: 51. Bibcode 1961PhRvL...7...51D. doi:10.1103/PhysRevLett.7.51. 
4. ^ González-Martín, Gustavo R. (1991). "Some electromagnetic consequences of a unified theory of gravitation and electromagnetism.". Gen. Rel. and Grav. 23: 827. Bibcode 1991GReGr..23..827G. doi:10.1007/BF00755997. http://www.springerlink.com/content/h4j801591u83h514/.