# A "Classical" Explanation of The Meissner Effect?

I know that the Meissner Effect is fundamentally quantum, but can a similar logic to the one used for normal conductors be applied to superconductors? I am referring to the idea that in normal conductors, charges move so smoothly such that when there is an external electric field, all the negative charges get pulled towards the field, while the positive charges get repelled, so that the combined effect creates a contending electric field inside, cancelling out the external field. If I then gave a similar analogy to someone for superconductors, namely that the moving charges in them get pulled by the external magnetic field, such that they create a contending magnetic field that cancels out the external field, would this be a good enough "classical" approximation?

Just to give an example, when a conducting spherical shell is placed in an otherwise uniform magnetic field in the z-direction, I would explain that the charges start moving in circular motion, which is why this creates a current in the azimuthal direction, and thus creating a contending magnetic field that cancels out the external one.

I recognize that this is only a "story" that we tell ourselves, but I think it would help students accept the fact better. I only ask, is there any immediate flaw to this logic? For reference, I'm only hoping for an approximation as good as Griffiths' explanation of diamagnetism. Speaking of which, my main solace for this theory lies on the fact that Griffiths mentioned that the effect is entirely due to free currents, not from bound ones (i.e. not due to electron spin, I presume). On the other hand, it would make sense why superconductivity would be affected by temperature, though I don't see how it would explain why superconductivity is lost above a certain temperature, and not below.

• What you're describing is a perfect diamagnet, not a superconductor. In a perfect diamagnet, changing the external magnetic field will always set up screening currents, to keep the internal magnetic field the same. A superconductor is different: it keeps the internal magnetic field zero. For example, if you put a non-superconducting object in a magnetic field, so it has some internal field, then cool it to become superconducting, then it will create screening currents which change the internal field to zero. Commented Mar 21 at 3:29
• I don't quite understand the difference—so there's no guarantee that the screening current from a perfect diamagnet cancels out the external magnetic field, unlike perfect conductors under external electric fields? But a perfect diamagnet can still have internal magnetic field of zero? Commented Mar 21 at 3:54
• Yes to both questions. But the thing that makes a superconductor distinctive is that if you make something start superconducting when it already has a nonzero internal field, then it will produce currents that expel that internal field. That's the property you can't explain classically. Commented Mar 21 at 4:37
• Ah, I guess the problem with comparing it to normal perfect conductors and electric fields with superconductors and magnetic fields is that you can't turn a non-conducting object into a conducting one. I see. Thanks! Commented Mar 21 at 7:34
• Actually, that’s not the problem either: if you make something normally conducting it will redistribute charges to expel the internal electric field. The difference is that electric fields affect charges at rest, but magnetic fields don’t, so there’s no way for a newly formed superconductor to classically “know” it has a constant internal magnetic field. Commented Mar 21 at 16:16

Topic: Cohomology of multiply connected 2d-manifolds, plus energy flatness of the conduction band at the Fermi energy with respect to the pseudo meomentum vector $$\vec k$$, plus the fact, that in the superconducting thermal equilibrium state, the inner energy is dominated by the spin energy in the magnetic field, that is minimized by B=0.