Meissner effect

The Meissner effect (or Meißner–Ochsenfeld effect) is the

expulsion of a magnetic field from a superconductor during its
transition to the superconducting state when it is cooled below the
critical temperature. This expulsion will repel a nearby magnet.

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 Diagram of the Meissner effect.
interior field decreases, the exterior field increases. The experiment Magnetic field lines, represented as
demonstrated for the first time that superconductors were more than arrows, are excluded from a
just perfect conductors and provided a uniquely defining property superconductor when it is below its
of the superconductor state. The ability for the expulsion effect is critical temperature.
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 London equation, predicts that the magnetic field in a superconductor decays
exponentially from whatever value it possesses at the surface. This exclusion of magnetic field is a
manifestation of the superdiamagnetism emerged during the phase transition from conductor to
superconductor, for example by reducing the temperature below critical temperature.

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 do 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 Lenz's Law or Faraday's Law. A reason this is not the case is that no change in
flux was made to induce the current. Another explanation is that since the superconductor experiences zero
resistance, there cannot be an induced emf in the superconductor. The persisting current therefore is not a
result of Faraday's Law.

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. 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.[5] However, some physicists argue that BCS theory does not explain the
Meissner effect.[6]

A tin cylinder—in a Dewar flask T = 4.2 K, B = 8 mT (80 G). Tin is

filled with liquid helium—has been in the normally conducting state.
placed between the poles of an The compass needles indicate that
electromagnet. The magnetic field magnetic flux permeates the
is about 8 millitesla (80 G). cylinder.

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 Planck constant and c is the speed of
light) for a gauge field. In fact, this analogy is an abelian example for the Higgs mechanism,[7] which
±
generates the masses of the electroweak W and Z gauge particles in high-energy physics. The length
is identical with the London penetration depth in the theory of superconductivity.[8][9]

See also
Physics portal

Science portal

Flux pinning
Silsbee effect
Superfluid

References
1. "Meissner effect | physics" (https://www.britannica.com/science/Meissner-effect).
Encyclopedia Britannica. Retrieved 22 April 2017.
2. Meissner, W.; Ochsenfeld, R. (1933). "Ein neuer Effekt bei Eintritt der Supraleitfähigkeit".
Naturwissenschaften. 21 (44): 787–788. Bibcode:1933NW.....21..787M (https://ui.adsabs.har
vard.edu/abs/1933NW.....21..787M). doi:10.1007/BF01504252 (https://doi.org/10.1007%2FB
F01504252). S2CID 37842752 (https://api.semanticscholar.org/CorpusID:37842752).
3. Landau, L. D.; Lifschitz, E. M. (1984). Electrodynamics of Continuous Media. Course of
Theoretical Physics. Vol. 8 (2nd ed.). Butterworth-Heinemann. ISBN 0-7506-2634-8.
4. Callaway, D. J. E. (1990). "On the remarkable structure of the superconducting intermediate
state". Nuclear Physics B. 344 (3): 627–645. Bibcode:1990NuPhB.344..627C (https://ui.ads
abs.harvard.edu/abs/1990NuPhB.344..627C). doi:10.1016/0550-3213(90)90672-Z (https://d
oi.org/10.1016%2F0550-3213%2890%2990672-Z).
5. Bardeen, J.; Cooper, L. N.; Schrieffer, J. R. (1957). "Theory of superconductivity" (https://doi.
org/10.1103%2Fphysrev.106.162). Physical Review. 106 (1175): 162–164.
Bibcode:1957PhRv..106..162B (https://ui.adsabs.harvard.edu/abs/1957PhRv..106..162B).
doi:10.1103/physrev.106.162 (https://doi.org/10.1103%2Fphysrev.106.162).
6. Hirsch, J. E. (2012). "The origin of the Meissner effect in new and old superconductors".
Physica Scripta. 85 (3): 035704. arXiv:1201.0139 (https://arxiv.org/abs/1201.0139).
Bibcode:2012PhyS...85c5704H (https://ui.adsabs.harvard.edu/abs/2012PhyS...85c5704H).
doi:10.1088/0031-8949/85/03/035704 (https://doi.org/10.1088%2F0031-8949%2F85%2F0
3%2F035704). S2CID 118418121 (https://api.semanticscholar.org/CorpusID:118418121).
7. Higgs, P. W. (1966). "Spontaneous symmetry breakdown without massless bosons" (https://d
oi.org/10.1103%2FPhysRev.145.1156). Physical Review. 145 (4): 1156–1163.
Bibcode:1966PhRv..145.1156H (https://ui.adsabs.harvard.edu/abs/1966PhRv..145.1156H).
doi:10.1103/PhysRev.145.1156 (https://doi.org/10.1103%2FPhysRev.145.1156).
8. Wilczek, F. (2000). "The recent excitement in high-density QCD". Nuclear Physics A. 663:
257–271. arXiv:hep-ph/9908480 (https://arxiv.org/abs/hep-ph/9908480).
Bibcode:2000NuPhA.663..257W (https://ui.adsabs.harvard.edu/abs/2000NuPhA.663..257
W). doi:10.1016/S0375-9474(99)00601-6 (https://doi.org/10.1016%2FS0375-9474%2899%2
900601-6). S2CID 119354272 (https://api.semanticscholar.org/CorpusID:119354272).
 9. Weinberg, S. (1986). "Superconductivity for particular theorists" (https://doi.org/10.1143%2F
PTPS.86.43). Progress of Theoretical Physics Supplement. 86: 43–53.
Bibcode:1986PThPS..86...43W (https://ui.adsabs.harvard.edu/abs/1986PThPS..86...43W).
doi:10.1143/PTPS.86.43 (https://doi.org/10.1143%2FPTPS.86.43).

Further reading
Einstein, A. (1922). "Theoretical remark on the superconductivity of metals".
arXiv:physics/0510251 (https://arxiv.org/abs/physics/0510251).
London, F. W. (1960). "Macroscopic Theory of Superconductivity". Superfluids. Structure of
matter series. Vol. 1 (Revised 2nd ed.). Dover. 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 (https://www.feynmanlectures.calte
ch.edu/III_21.html#Ch21-S6)
Meissner Effect (Science from scratch) (https://www.youtube.com/watch?v=44mVZdnR6Yc)
Short video from Imperial College London about the Meissner effect and levitating trains of
the future.
Introduction to superconductivity (https://web.archive.org/web/20160125175255/http://alfredl
eitner.com/superconductors.html) Video about Type 1 Superconductors: R = 0/Transition
temperatures/B is a state variable/Meissner effect/Energy gap (Giaever)/BCS model.
Meissner Effect (Hyperphysics) (http://hyperphysics.phy-astr.gsu.edu/hbase/solids/meis.htm
l)
Historical Background of the Meissner Effect (https://web.archive.org/web/20140828152921/
http://web.ornl.gov/info/reports/m/ornlm3063r1/pt2.html)

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