Editing Superconductivity (section)

=== Meissner effect ===
{{Main|Meissner effect}}
[[File:Meissner_effect.ogv|thumb|Meissner effect in a high-temperature superconductor (black pellet) with a NdFeB magnet (metallic)]]
When a superconductor is placed in a weak external magnetic field ''H'', and cooled below its transition temperature, the magnetic field is ejected. The Meissner effect does not cause the field to be completely ejected but instead, the field penetrates the superconductor but only to a very small distance, characterized by a parameter&nbsp;''λ'', called the [[London penetration depth]], decaying exponentially to zero within the bulk of the material. The Meissner effect is a defining characteristic of superconductivity. For most superconductors, the London penetration depth is on the order of 100&nbsp;nm.

The Meissner effect is sometimes confused with the kind of [[diamagnetism]] one would expect in a perfect electrical conductor: according to [[Lenz's law]], when a ''changing'' magnetic field is applied to a conductor, it will induce an electric current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field.

The Meissner effect is distinct from this{{snd}}it is the spontaneous expulsion that occurs during transition to superconductivity. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law.

The Meissner effect was given a phenomenological explanation by the brothers [[Fritz London|Fritz]] and [[Heinz London]], who showed that the electromagnetic [[Thermodynamic free energy|free energy]] in a superconductor is minimized provided <math display="block"> \nabla^2\mathbf{H} = \lambda^{-2} \mathbf{H}\, </math> 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 [[Exponential decay|decays exponentially]] from whatever value it possesses at the surface.

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''<sub>c</sub>. Depending on the geometry of the sample, one may obtain an intermediate state<ref>{{cite book |author=Landau |first1=Lev D. |title=Electrodynamics of Continuous Media |last2=Lifschitz |first2=Evgeny M. |date=1984 |publisher=Butterworth-Heinemann |isbn=978-0-7506-2634-7 |series=[[Course of Theoretical Physics]] |volume=8 |location=Oxford, England |language=en-uk}}</ref> consisting of a baroque pattern<ref>{{cite journal |author=Callaway |first=David J. E. |date=1990 |title=On the remarkable structure of the superconducting intermediate state |journal=[[Nuclear Physics B]] |volume=344 |issue=3 |pages=627–645 |bibcode=1990NuPhB.344..627C |doi=10.1016/0550-3213(90)90672-Z}}</ref> 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''<sub>c1</sub> 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''<sub>c2</sub>, superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called [[Fluxon|fluxons]] because the flux carried by these [[Abrikosov vortex|vortices]] is [[Quantum|quantized]]. Most pure [[Chemical element|elemental]] superconductors, except [[niobium]] and [[Carbon nanotube|carbon nanotubes]], are Type I, while almost all impure and compound superconductors are Type&nbsp;II.