A microscopic theory of Abrikosov lattices. I. Basic formalism

This paper generalizes the method of using the magnetic Bloch states to obtain flux-lattice solutions of the Bogoliubov-de Gennes equations. Developed by several groups, this method has had a limited applicability to the s-wave pairing and to high-kappa; materials where the spatial variation of the magnetic field may be neglected. It is extended here so that: (i) an arbitrary anisotropic pairing can be handled; (ii) the effect of the screening current can be taken into account. Hence the formalism will enable a fully microscopic description of various Abrikosov lattices in clean type-II superconductors over H-c1 less than or equal to H less than or equal to H-c2.