Abstract
The Green's function method and diagram technique for umklapp electron-electron scattering mediated by the screened Coulomb interaction in layered anisotropic conductors are examined. Gor'kov-type equations and their general solution for anomalous and normal temperature Green's functions are derived taking into account umklapp scattering of all orders. Explicit equations for dielectric and superconducting order parameters, including coexistent Bragg and BCS pairing, are found. The possibility of the first-order phase transition to the superconducting state is discussed. The theory elucidates the origin of Bragg-Coulomb high- T c superconductivity, proposed by the authors.
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