Meissner–Ochsenfeld Effect
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In
condensed-matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases, that arise from electromagnetic forces between atoms and electrons. More gen ...
, the Meissner effect (or Meißner–Ochsenfeld effect) is the expulsion of a
magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
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 A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, ...
. The German physicists Walther Meißner (anglicized ''Meissner'') and Robert Ochsenfeld discovered this phenomenon in 1933 by measuring the magnetic field distribution outside superconducting tin and lead samples. 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 In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the we ...
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 In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector In mathematics, a unit vector i ...
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 superconductor The interior of a bulk superconductor cannot be penetrated by a weak magnetic field, a phenomenon known as the Meissner effect. When the applied magnetic field becomes too large, superconductivity breaks down. Superconductors can be divided into ...
s, 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 consisting of a baroque pattern of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. *In
type-II superconductor In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the ...
s, raising the applied field past a critical value ''H''''c''1 leads to a mixed state (also known as the vortex state) in which an increasing amount of
magnetic flux In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the we ...
penetrates the material, but there remains no resistance to the
electric current An electric current is a flow of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is defined as the net rate of flow of electric charge through a surface. The moving particles are called charge c ...
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 ''H''''c''2, 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 An elemental is a mythic supernatural being that is described in occult and alchemy, alchemical works from around the time of the European Renaissance, and particularly elaborated in the 16th century works of Paracelsus. According to Paracelsu ...
superconductors, except
niobium Niobium is a chemical element; it has chemical symbol, symbol Nb (formerly columbium, Cb) and atomic number 41. It is a light grey, crystalline, and Ductility, ductile transition metal. Pure niobium has a Mohs scale of mineral hardness, Mohs h ...
and
carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometre range ( nanoscale). They are one of the allotropes of carbon. Two broad classes of carbon nanotubes are recognized: * ''Single-walled carbon nanotubes'' (''S ...
s, 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 Fritz is a common German language, German male name. The name originated as a German diminutive of Friedrich (given name), Friedrich or Frederick (given name), Frederick (''Der Alte Fritz'', and ''Stary Fryc'' were common nicknames for King Fred ...
and
Heinz London Heinz London (Bonn, Germany 7 November 1907 – 3 August 1970) was a German-British physicist. Together with his brother Fritz London he was a pioneer in the field of superconductivity. Biography London was born in Bonn in a liberal Jewish-Ger ...
, who showed that the electromagnetic free energy in a superconductor is minimized provided : \nabla^2\mathbf = \lambda^ \mathbf\, where H is the magnetic field and λ is the
London penetration depth In superconductors, the London penetration depth (usually denoted as \lambda or \lambda_L) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to e^ times that of the magnetic field at the surface ...
. This equation, known as the
London equation The London equations, developed by brothers Fritz and Heinz London in 1935, are constitutive relations for a superconductor relating its superconducting current to electromagnetic fields in and around it. Whereas Ohm's law is the simplest con ...
, 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 Superdiamagnetism (or perfect diamagnetism) is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of magnetic permeability (i.e. a volume magnetic susceptibility \chi_ = −1) and the exclusio ...
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 In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the we ...
by setting up electric currents near its surface, as the magnetic field H induces
magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Accordingly, physicists and engineers usually define magnetization as the quanti ...
M within the London penetration depth from the surface. These surface currents
shield A shield is a piece of personal armour held in the hand, which may or may not be strapped to the wrist or forearm. Shields are used to intercept specific attacks, whether from close-ranged weaponry like spears or long ranged projectiles suc ...
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 In superconductors, the London penetration depth (usually denoted as \lambda or \lambda_L) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to e^ times that of the magnetic field at the surface ...
, 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 Electromagnetic or magnetic induction is the production of an electromotive force, electromotive force (emf) across an electrical conductor in a changing magnetic field. Michael Faraday is generally credited with the discovery of induction in 1 ...
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 Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
does. The persisting currents that exist in the superconductor to expel the magnetic field is commonly misconceived as a result of
Lenz's Law Lenz's law states that the direction of the electric current Electromagnetic induction, induced in a Electrical conductor, conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes changes in t ...
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 Superdiamagnetism (or perfect diamagnetism) is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of magnetic permeability (i.e. a volume magnetic susceptibility \chi_ = −1) and the exclusio ...
, 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 In electromagnetism, the magnetic susceptibility (; denoted , chi) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the applied magnet ...
is \chi_ = −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 Fritz is a common German language, German male name. The name originated as a German diminutive of Friedrich (given name), Friedrich or Frederick (given name), Frederick (''Der Alte Fritz'', and ''Stary Fryc'' were common nicknames for King Fred ...
and
Heinz London Heinz London (Bonn, Germany 7 November 1907 – 3 August 1970) was a German-British physicist. Together with his brother Fritz London he was a pioneer in the field of superconductivity. Biography London was born in Bonn in a liberal Jewish-Ger ...
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 physics, the Bardeen–Cooper–Schrieffer (BCS) theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory descr ...
in 1957, from which the penetration depth and the Meissner effect result. However, some physicists argue that BCS theory does not explain the Meissner effect. Image:Tin_4.2K_Electromagnet.jpg, 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). Image:Tin_80gauss_4.2K.jpg, ''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. Image:Tin_80gauss_1.6K.jpg, 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'', \lambda_M: = h/(M c) where ''h'' is the
Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...
and ''c'' is the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...
) for a
gauge field In physics, a gauge theory is a type of field theory in which the Lagrangian, and hence the dynamics of the system itself, does not change under local transformations according to certain smooth families of operations (Lie groups). Formally, t ...
. In fact, this analogy is an abelian example for the
Higgs mechanism In the Standard Model of particle physics, the Higgs mechanism is essential to explain the Mass generation, generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles ...
, which generates the masses of the
electroweak In particle physics, the electroweak interaction or electroweak force is the unified description of two of the fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two forc ...
and gauge particles in
high-energy physics Particle physics or high-energy physics is the study of fundamental particles and forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the scale of protons and neutrons, while the stu ...
. The length \lambda_M is identical with the
London penetration depth In superconductors, the London penetration depth (usually denoted as \lambda or \lambda_L) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to e^ times that of the magnetic field at the surface ...
in the theory of
superconductivity Superconductivity is a set of physical properties observed in superconductors: materials where Electrical resistance and conductance, electrical resistance vanishes and Magnetic field, magnetic fields are expelled from the material. Unlike an ord ...
.


See also

*
Flux pinning Flux pinning is a phenomenon that occurs when flux quantum vortex, vortices in a type-II superconductor are prevented from moving within the bulk of the superconductor, so that the magnetic field lines are "pinned" to those locations. The supercon ...
* Silsbee effect *
Superfluid Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortex, vortices that continue to rotate indefinitely. Superfluidity occurs ...


References


Further reading

* * By the man who explained the Meissner effect. pp. 34–37 gives a technical discussion of the Meissner effect for a superconducting sphere. * 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. * A good technical reference.


External links


The Meissner effect - The Feynman Lectures on PhysicsMeissner Effect (Science from scratch)
Short video from Imperial College London about the Meissner effect and levitating trains of the future.

Video about Type 1 Superconductors: ''R'' = 0/Transition temperatures/B is a state variable/Meissner effect/Energy gap (Giaever)/BCS model.

{{DEFAULTSORT:Meissner Effect Magnetic levitation Quantum magnetism Superconductivity