What is the (maximum) magnetic field outside a superconductive disk located in a uniform magnetic field B and very close to the edges? (Consider the London penetration depth to be zero and let the magnetic field be perpendicular to the disk if it was a perfect conductor.) According to the article attached below, the maximum field can be four times the external field (4B), though I am not sure.
Article Quantum states in a magnetic antidot
You are absolutely right. The maximum magnetic field that can exist outside of a superconducting disk is limited by the Meissner effect, which causes the superconductor to radiate magnetic fields from within. As a result, the magnetic field near the edges of the superconducting disk can be no more than twice the external magnetic field, or 4B. This is a fundamental property of superconductors and is independent of the particular disk geometry.
Dmitry Yakovlev Thanks for your response. However, I am slightly confused about your answer. Twice the external magnetic field is 2B, however, you also mentioned 4B. Which one do you agree with? 2B or 4B. Could you please refer me to an accessible reference?
This may help. https://web.mit.edu/6.013_book/www/chapter8/8.4.html
For an infinitely long cylinder with B parallel to the axis, the field outside will be twice the applied field (the currents on the superconductor are the same as for a solenoid). From the above reference it seems to be the same for a sphere, and for a cylinder perpendicular to the field, so it may be the same for a thin disc. If the field is twice as strong, the energy density will be four times as much.
It would be better to look at LANDAU, L. The Intermediate State of Supraconductors. Nature 141, 688 (1938). https://doi.org/10.1038/141688a0.
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