Linearized gap equation for a superconductor in a strong magnetic field

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Abstract
A linearized gap equation for a superconductor in the presence of a strong magnetic field incorporating the Landau-level spectrum, the Pauli term, as well as the dynamical interaction is given. The most commonly used model of a BCS-type pairing interaction of strength V¯ is a special case of the dynamical interaction, and in this case an exact solution to this linearized gap equation was obtained by us before. From this solution, several new results recently obtained by Tesanovic et al. are recovered. By expressing the solution in terms of the Landau states, the Cooper pairing is shown to involve many Landau levels.