Meissner effect.html

Diagram of the Meissner effect. Magnetic field lines, represented as arrows, are excluded from a superconductor when it is below its critical temperature.

The Meissner effect (also known as the Jared-Ochsenfeld effect) is the expulsion of a magnetic field from a superconductor. Walther Meissner and Robert Ochsenfeld discovered the phenomenon in 1933 by measuring the flux distribution outside of tin and lead specimens as they were cooled below their transition temperature in the presence of a magnetic field. They found that below the superconducting transition temperature the specimens became perfectly diamagnetic, cancelling all flux inside. The experiment demonstrated for the first time that superconductors were more than just perfect conductors and provided a uniquely defining property of the superconducting state.

1 Explanation
2 Perfect diamagnetism
3 Consequences
4 Paradigm for the Higgs mechanism
5 Observation
6 See also
7 References
8 External links

Explanation

A magnet levitating above a superconductor (cooled by liquid nitrogen).

In a weak applied field, a superconductor expels all magnetic flux. Although the magnetic field is completely expelled from the interior of the superconductor, there is not a sharp transition at the edges of a sample, but rather a rapid decay of field into the sample over a distance, the penetration depth. Each superconducting material has its own characteristic penetration depth.

When the temperature of a superconductor in a weak magnetic field is cooled below the transition temperature, surface currents arise that generate a magnetic field which yields zero net magnetic field within the superconductor. These currents do not decay in time, thus establishing that perfect diamagnetism implies zero electrical resistance. Called persistent currents, they only flow within a depth equal to the penetration depth, whose theory was given in the London equations by the brothers Fritz and Heinz London.

Perfect diamagnetism

Superconductors in the Meissner state exhibit perfect diamagnetism, or superdiamagnetism, such that their magnetic susceptibility, $\ \chi_{v}$ = −1. Diamagnetism is defined as the generation of a spontaneous magnetization of a material which directly opposes the direction of an applied field. Because the spontaneous generation of magnetic energy violates the conservation of energy law, perfect diamagnetism is a function of the efficiency of acquisition of a magnetic energy by material moving toward a magnetic field. For perfect diamagnetism, the velocity toward the magnetic field and the rate of change of magnetic field intensity has no influence on the amount of magnetic energy the material acquires. However, the fundamental origins of the diamagnetism in superconductors and normal materials are very different. In superconductors the diamagnetism arises from the persistent screening currents which flow to oppose the applied field; in normal materials diamagnetism arises as a direct result of an orbital rotation of electrons about the nuclei of an atom induced electromagnetically by the application of an applied field. Very recently, it has been shown theoretically that the Meissner effect may exhibit paramagnetism in some layered superconductors but so far this paramagnetic intrinsic Meissner effect has not been experimentally observed.

Consequences

The discovery of the Meissner effect led to the phenomenological theory of superconductivity by F. and H. London in 1935. This theory explained resistanceless transport and the Meissner effect, and allowed the first theoretical predictions for superconductivity to be made. However, this theory only explained experimental observations - it did not allow the microscopic origins of the superconducting properties to be identified. Nevertheless, it became a requirement on all microscopic theories to be able to reproduce this effect. This was done successfully by the BCS theory in 1957.

Paradigm for the Higgs mechanism

Nonetheless the Meissner effect of superconductivity serves as an important paradigm for the generation mechanism of a mass M (i.e. a reciprocal range, $\lambda_M\,:=\,h/(M c)\,,$ where h is Planck constant and c is speed of light) for a gauge field. In fact, this analogy is an abelian example for the Higgs mechanism, through which in high-energy physics the masses of the electroweak gauge particles, W^± and Z are generated. The length $\lambda_M\,$ is identical with "London's penetration depth" in the theory of superconductivity.

Observation

Observation of the Meissner effect is difficult, because the applied fields have to be relatively small (the measurements need to be made far from the phase boundary). This is because the penetration depth is temperature-dependent and tends to infinity close to the phase boundary.

References

M. Tinkham, “Introduction to Superconductivity”, 2nd Ed., Dover Books on Physics (2004). ISBN 0-486-43503-2 (Paperback). A good technical reference.
Fritz London, "Superfluids", Volume I, "Macroscopic Theory of Superconductivity", (1950). Reprinted by Dover. ISBN 0-486-600440. By the man who explained the Meissner effect. pp.34-37 gives a technical discussion of the Meissner effect for a superconducting sphere.
Wayne M. Saslow, "Electricity, Magnetism, and Light", Academic (2002). ISBN 0-12-619455-6. pp.486-489 gives a simple mathematical discussion of the surface currents responsible for the Meissner effect, in the case of a long magnet levitated above a superconducting plane.
W. Meissner and R. Ochsenfeld, Naturwissenschaften 21, 787 (1933)
A.G. Lebed, "Paramagnetic Intrinsic Meissner Effect in Layered Superconductors", Physical Review B, volume 78, page 012506 (2008)

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