Abstract
We consider the Aharonov-Bohm magnetic potential and study the transition from normal to superconducting solutions within the Ginzburg-Landau model of superconductivity. We obtain oscillatory patterns which are consistent with the Little-Parks effect. We study also the same problem but for a regularization of the Aharonov-Bohm potential, which leads to an interesting Aharonov-Bohm like magnetic field, and we prove that the transition between superconducting and normal solutions is not monotone too. Our results explore a mechanism to derive the Aharonov-Bohm magnetic potential starting from a step magnetic field, thereby presenting a new aspect of magnetic steps, besides their favoring of the celebrated edge states.
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