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In Meissner effect we say that below critical temperature there is an expulsion of external field lines or field lines do not penetrate inside the specimen. But here is what I am not able to understand, if the sample creates a mystical force which do not allow field line to pass then it can be imagined as if there is an field due to specimen which cancels its effect. I know experimentally field lines are expelled, but why they are expelled I want to know the reason like who are the one that causes no fields to penetrate inside it.

Somewhere I have read that a persistent current rises in such a way that it creates a field which cancels the external field. Now how is that possible that a superconductor inside in it already has a field?

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Superconductivity is closely related to magnetic properties. Suppose one has a sample which begins in a normal state (not superconducting) with an applied magnetic field penetrating the sample. If such a sample is cooled through the superconducting transition, then during the phase transition (and associated with it) a surface current is produced. This surface current has just the right size, at each place on the surface, to produce a magnetic field inside the superconductor which is exactly opposite to the externally applied field. So the result is zero net field inside the superconductor.

So this surface current (a persistent current) is the source of the counter-field. But the process whereby the surface current arises with exactly the right amount during the phase transition is quite tricky to understand. A thermodynamic argument gives a valid insight (the state overall minimises the Gibbs free energy) but if you want the microscopic details then you have to look at your full theory of superconductivity. And that is beyond the scope of this answer; sorry!

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  • $\begingroup$ can you elaborate on the thermodynamic argument will be helpful. Thanks $\endgroup$ Commented Jun 7, 2023 at 10:11
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Yes, as you said the external magnetic field is exactly canceled out by another magnetic field which is produced by a persistent current flowing along the edge of the specimen. This current is localized in a shell of length $\lambda$ at the edge, where $\lambda$ is the London penetration depth. The nature of the persistent current is really deep, as it is a purely quantum phenomenon called "sponaneous symmetry breaking". The idea is that at such low temperatures, all the electrons are in a coherent state, i.e. a state where they can not be described as many individual particles, but rather as a unique wave characterized by a phase.

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