Meissner effect
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The Meissner effect (or Meißner–Ochsenfeld effect) is the expulsion of a
The German physicists Walther Meißner (anglicized Meissner) and Robert Ochsenfeld[1] discovered this phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin and lead samples.[2] The samples, in the presence of an applied magnetic field, were cooled below their superconducting transition temperature, whereupon 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. The ability for the expulsion effect is determined by the nature of equilibrium formed by the neutralization within the unit cell of a superconductor.
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 strong. 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 Hc. Depending on the geometry of the sample, one may obtain an intermediate state[3] consisting of a baroque pattern[4] 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 Hc1 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 electric current as long as the current is not too large. Some type-II superconductors exhibit a small but finite resistance in the mixed state due to motion of the flux vortices induced by the Lorentz forces from the current. As the cores of the vortices are normal electrons, their motion will have dissipation. At a second critical field strength Hc2, superconductivity is destroyed. The mixed state is 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
where H is the magnetic field and λ is the London penetration depth.
This equation, known as the
In a weak applied field (less than the critical field that breaks down the superconducting phase), a superconductor expels nearly all magnetic flux by setting up electric currents near its surface, as the magnetic field H induces magnetization M within the London penetration depth from the surface. These surface currents shield the internal bulk of the superconductor from the external applied field. As the field expulsion, or cancellation, does not change with time, the currents producing this effect (called persistent currents or screening currents) do not decay with time.
Near the surface, within the London penetration depth, the magnetic field is not completely canceled. 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. However, 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, but only by the London equation. 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 below its critical temperature does.
The persisting currents that exist in the superconductor to expel the magnetic field is commonly misconceived as a result of
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 volume magnetic susceptibility is = −1.
Consequences
The discovery of the Meissner effect led to the
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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 8millitesla (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 superconductivity effect serves as an important paradigm for the generation mechanism of a mass M (i.e., a reciprocal range, where h is the
See also
- Flux pinning
- Silsbee effect
- Superfluid
References
- ^ "Meissner effect | physics". Encyclopedia Britannica. Retrieved 22 April 2017.
- ^
Meissner, W.; Ochsenfeld, R. (1933). "Ein neuer Effekt bei Eintritt der Supraleitfähigkeit". S2CID 37842752.
- ^
Landau, L. D.; Lifschitz, E. M. (1984). Electrodynamics of Continuous Media. ISBN 0-7506-2634-8.
- ^ Callaway, D. J. E. (1990). "On the remarkable structure of the superconducting intermediate state". .
- .
- .
- ^
Wilczek, F. (2000). "The recent excitement in high-density QCD". S2CID 119354272.
- ^ Weinberg, S. (1986). "Superconductivity for particular theorists". .
Further reading
- arXiv:physics/0510251.
- 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.
- Saslow, W. M. (2002). Electricity, Magnetism, and Light. Academic. ISBN 978-0-12-619455-5. 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.
- Tinkham, M. (2004). Introduction to Superconductivity. Dover Books on Physics (2nd ed.). Dover. ISBN 978-0-486-43503-9. A good technical reference.
External links
- The Meissner effect - The Feynman Lectures on Physics
- 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