Abstract
A microscopic theory of superconductivity is developed for the magnetized electron gas on a cylindrical surface. The Gibbs free energy is calculated for the superconducting system. A gap equation is derived that determines the critical temperature as a function of the quantum-cylinder dimensions and the Aharonov-Bohm parameter. It is shown that the gap not only exhibits Aharonov—Bohm oscillations, but also oscillates with varying curvature of the cylindrical surface.
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