Meissner effect

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 is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state. The German physicists Walther Meissner and Robert Ochsenfeld discovered this phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin and lead samples.^[1] The samples, in the presence of an applied magnetic field, were cooled below their superconducting transition temperature. Below the transition temperature the samples cancelled nearly all interior magnetic fields. They detected this effect only indirectly because the magnetic flux is conserved by a superconductor: when the interior field decreases, the exterior field increases. The experiment demonstrated for the first time that superconductors were more than just perfect conductors and provided a uniquely defining property of the superconductor state.

A superconductor with little or no magnetic field within it is said to be in the Meissner state. The Meissner state breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value H_c. Depending on the geometry of the sample, one may obtain an intermediate state^[2] consisting of a baroque pattern^[3] of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value H_c1 leads to a mixed state (also known as the vortex state) in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electric current as long as the current is not too large. At a second critical field strength H_c2, superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called fluxons because the flux carried by these vortices is quantized. Most pure elemental superconductors, except niobium and carbon nanotubes, are Type I, while almost all impure and compound superconductors are Type II.

Explanation

The Meissner effect was given a phenomenological explanation by the brothers Fritz and Heinz London, who showed that the electromagnetic free energy in a superconductor is minimized provided

$\nabla^2\mathbf{H} = \lambda^{-2} \mathbf{H}\,$

where H is the magnetic field and λ is the London penetration depth.

This equation, which is known as the London equation, predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface.

A magnet levitating above a superconductor cooled by liquid nitrogen.

In a weak applied field, a superconductor "expels" nearly all magnetic flux. It does this by setting up electric currents near its surface. The magnetic field of these surface currents cancels the applied magnetic field within the bulk of the superconductor. As the field expulsion, or cancellation, does not change with time, the currents producing this effect (called persistent currents) do not decay with time. Therefore, the conductivity can be thought of as infinite: a superconductor.

Near the surface, within the London penetration depth, the magnetic field is not completely cancelled. Each superconducting material has its own characteristic penetration depth.

Any perfect conductor will prevent any change to magnetic flux passing through its surface due to ordinary electromagnetic induction at zero resistance. The Meissner effect is distinct from this: when an ordinary conductor is cooled so that it makes the transition to a superconducting state in the presence of a constant applied magnetic field, the magnetic flux is expelled during the transition. This effect cannot be explained by infinite conductivity alone. Its explanation is more complex and was first given in the London equations by the brothers Fritz and Heinz London. It should thus be noted that the placement and subsequent levitation of a magnet above an already superconducting material does not demonstrate the Meissner effect, while an initially stationary magnet later being repelled by a superconductor as it is cooled through its critical temperature does.

Perfect diamagnetism

Superconductors in the Meissner state exhibit perfect diamagnetism, or superdiamagnetism, meaning that the total magnetic field is very close to zero deep inside them (many penetration depths from the surface). This means that their magnetic susceptibility, $\chi_{v}$ = −1. Diamagnetics are defined by the generation of a spontaneous magnetization of a material which directly opposes the direction of an applied field. However, the fundamental origins of diamagnetism in superconductors and normal materials are very different. In normal materials diamagnetism arises as a direct result of the orbital spin of electrons about the nuclei of an atom induced electromagnetically by the application of an applied field. In superconductors the illusion of perfect diamagnetism arises from persistent screening currents which flow to oppose the applied field (the Meissner effect); not solely the orbital spin.

Consequences

The discovery of the Meissner effect led to the phenomenological theory of superconductivity by Fritz and Heinz 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. This was done successfully by the BCS theory in 1957, from which the penetration depth and the Meissner effect result.^[4] However, some physicists argue that BCS theory does not explain the Meissner effect.^[5]

• 

  A tin cylinder—in a Dewar flask filled with liquid helium—has been placed between the poles of an electromagnet. The magnetic field is about 8 millitesla (80 G).

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  T=4.2 K, B=8 mT (80 G). Tin is in the normally conducting state. The compass needles indicate that magnetic flux permeates the cylinder.

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  The cylinder has been cooled from 4.2 K to 1.6 K. The current in the electromagnet has been kept constant, but the tin became superconducting at about 3 K. Magnetic flux has been expelled from the cylinder (the Meissner effect).

Paradigm for the Higgs mechanism

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,^[6] 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 the London penetration depth in the theory of superconductivity.^[7][8]

See also

• Superfluid
• Type-I superconductor
• Type-II superconductor
• Flux pinning

References

1. Meissner, W.; R. Ochsenfeld (1933). "Ein neuer Effekt bei Eintritt der Supraleitfähigkeit". Naturwissenschaften 21 (44): 787–788. Bibcode:1933NW.....21..787M. doi:10.1007/BF01504252.
2. Lev D. Landau; Evgeny M. Lifschitz (1984). Electrodynamics of Continuous Media. Course of Theoretical Physics 8. Oxford: Butterworth-Heinemann. ISBN 0-7506-2634-8.
3. David J. E. Callaway (1990). "On the remarkable structure of the superconducting intermediate state". Nuclear Physics B 344 (3): 627–645. Bibcode:1990NuPhB.344..627C. doi:10.1016/0550-3213(90)90672-Z.
4. J. Bardeen; L. N. Cooper; J. R. Schrieffer (1957). "Theory of superconductivity" (PDF). Physical Review B 106 (1175): 162–164. Bibcode:1957PhRv..106..162B. doi:10.1103/physrev.106.162.
5. J.E Hirsch (2012). "The origin of the Meissner effect in new and old superconductors". Physica Scripta 85: 035704. Bibcode:2012PhyS...85a5704P. doi:10.1088/0031-8949/85/01/015704.
6. P. W. Higgs (1966). "Spontaneous Symmetry Breakdown without Massless Bosons". Phys. Rev. 145 (4): 1156. arXiv:cond-mat/0305542. Bibcode:2003PhLA..315..474H. doi:10.1103/PhysRev.145.1156.
7. Wilczek, F. (2000). "The recent excitement in high-density QCD". Nuclear Physics A 663: 257–271. arXiv:hep-ph/9908480. Bibcode:2000NuPhA.663..257W. doi:10.1016/S0375-9474(99)00601-6.
8. Weinberg, S. (1986). "Superconductivity for particular theorists". Prog. Theor. Phys. Supplement 86: 43–53. Bibcode:1986PThPS..86...43W. doi:10.1143/PTPS.86.43.

Further reading

• Albert Einstein (1922). "Theoretical remark on the superconductivity of metals". arXiv:physics/0510251v2. Bibcode:2005physics..10251E.
• Fritz Wolfgang London (1950). "Macroscopic Theory of Superconductivity". Superfluids. Structure of matter series 1. OCLC 257588418.. Revised 2nd edition, Dover (1960) ISBN 978-0-486-60044-4. 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 (2002). Electricity, Magnetism, and Light. Academic. ISBN 978-0-12-619455-5. OCLC 51032778.. 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.
• Michael Tinkham (2004). Introduction to Superconductivity. Dover Books on Physics (2nd ed.). ISBN 978-0-486-43503-9.. A good technical reference.

External links

• Maglev Trains Audio slideshow from the National High Magnetic Field Laboratory discusses magnetic levitation, the Meissner Effect, magnetic flux trapping and superconductivity.
• Meissner Effect (Science from scratch) Short video from Imperial College London about the Meissner effect and levitating trains of the future.
• Introduction to superconductivity Video about Type 1 Superconductors: R=0/Transition temperatures/B is a state variable/Meissner effect/Energy gap (Giaever)/BCS model.
• Meissner Effect (Hyperphysics)
• Historical Background of the Meissner Effect