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I am a high school student doing a science project in superconductivity so my physics knowledge is limitated but I have read a lot about the topic so I understand quite a bit. :)

I understand that the magnetic field lines from a magnet wrap around the superconductor, so the superconductor is neither repelled nor attracted to the magnet. It just stays there, trapped in that position and this is due to the Meissner effect. No magnetic flux can penetrate the superconductor.

My question is: Why does the Meissner effect happen? What is the "driving force" behind the Meissner effect? Why can't a magnetic flux penetrate the superconductor ?

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    $\begingroup$ > so the superconductor is neither repelled nor attracted to the magnet. Where did you read this? I don't think it is correct. $\endgroup$
    – Ján Lalinský
    Commented Oct 20, 2021 at 23:38
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    $\begingroup$ It was an answer I received in this physic forum but Yeah Now I realised it was wrong. Now I know that the meissner effect indeed repells the magnet from the superconductor . but if you pull the magnet from the superconductor it will follow it, like it is attracting it or like if the magnet was wrapped around the superconductor. It this entirely explained by the fact that some magnetic flux goes through the superconductor,, pinning it or it something else behing the phenomenon ? $\endgroup$
    – Shelyy
    Commented Oct 25, 2021 at 7:52
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    $\begingroup$ Do you know about induced electric field and Lenz's law? $\endgroup$
    – Ján Lalinský
    Commented Oct 25, 2021 at 17:06

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The answer to the initial question: In every superconductor can exist long-lived supercurrents, because there are dissipationless charge carriers (electron pairs). An external magnetic field generates in the superconductor an additional free energy, which is directly related to the square of the magnetic field strength $H^2$. Every crystal tends to minimize its free energy, so the superconductor redistributes its fluctuations of supercurrents so that the magnetic field of the supercurrents compensates the external magnetic flux. Therefore the total magnetic field and its energy inside the crystal vanish. Thus the driving force of the Meissner effect is the energy minimization inside the superconductor.

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    $\begingroup$ There is some good insight here but you need to explain why "every crystal tends to minimize its free energy" and also why the increase in field outside does not raise the free energy more than the reduction in field inside reduces it. To do this you would also need to define the free energy. $\endgroup$
    – Andrew Steane
    Commented Jan 27, 2023 at 13:40
  • $\begingroup$ Every quantum system (including crystals) tends to take a state of minimum energy. Therefore the system emits the free energy, like an atom emits a photon reducing the electron energy. So outside the energy raises by a value of the energy decrease inside (energy conservation law). The free energy of magnetic field is directly related to B^2, the magnetic energy stored in the crystal volume. $\endgroup$
    – Stanislav Dolgopolov
    Commented Jan 27, 2023 at 15:11
  • $\begingroup$ No, systems don't go to minimum energy state in thermal equilibrium, they go to the state of least free energy, and free energy involves both energy and entropy. $\endgroup$
    – Andrew Steane
    Commented Jan 27, 2023 at 18:55
  • $\begingroup$ At absolute zero temperature the Meissner effect also works. So the entropy cannot play a driving role here. $\endgroup$
    – Stanislav Dolgopolov
    Commented Jan 30, 2023 at 11:05
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An answer to your question is contained in your own comment:

„but if you pull the magnet from the superconductor it will follow it, like it is attracting it or like if the magnet was wrapped around the superconductor. It this entirely explained by the fact that some magnetic flux goes through the superconductor, pinning it“

This is an idea worth to think about.

  • Meissner and Ochsenfeld discovered the expulsion of a magnetic field from a superconductor during its transition to the superconducting state when it is cooled below the critical temperature. They concluded this from the levitation of superconductive and ultracold materials in a magnetic field.
  • The levitation takes place also if the material is placed below the magnetic source. The superconductor is trapped on some distance (magnetic density) from the external magnetic field.
  • The levitation gets destroyed by a stronger magnetic field.
  • Last not least superconductors are such materials where electrons exist pairwise (Cooper pairs).

Especially the last point allows a deeper insight to the effect of the magnetic field on the electron pairs inside the superconductor. A strong enough magnetic field will align the electrons in the direction of the magnetic field and the superconductor gets attracted to the magnet. And than, now these electrons are influenced in the levitating state? May we have to think about an alignment of Cooper pairs perpendicular to the external field.

enter image description here

The sketch illustrates the idea. Each electron with its magnetic dipole is sketched as a tiny magnet and two of them are shown as pairs. As long as the external magnetic field is not strong enough to align both electrons of the pair along its own field, the alignment takes place between the pairs and the external field meanders inside the superconductor.

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  • $\begingroup$ Thank you for answering! I wonder why is it so that just when one electron in the cooper pair gets aligned in the the direction of the magnetic field the superconductor gets attracted to the magnet. how does this change when both the electrons are aligned ? what is the difference? $\endgroup$
    – Shelyy
    Commented Oct 26, 2021 at 13:51
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    $\begingroup$ In the sketch the external magnetic field direction is vertically. But inside the superconductor the Cooper pairs are in equilibration to this field only if the are oriented perpendicular to the external field. A stronger magnetic field will break the Cooper pairs and all the electrons get aligned with their magnetic dipoles parallel to the external field. $\endgroup$
    – HolgerFiedler
    Commented Oct 26, 2021 at 19:04

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