Self-Consistent Approximations for Superconductivity beyond the Bardeen--Cooper--Schrieffer Theory

概要

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We develop a concise self-consistent perturbation expansion for superconductivity where all the pair processes are naturally incorporated without drawing ``anomalous'' Feynman diagrams. This simplification results from introducing an interaction vertex that is symmetric in the particle--hole indices besides the ordinary space-spin coordinates. The formalism automatically satisfies conservation laws, includes the Luttinger--Ward theory as the normal-state limit, and reproduces the Bardeen--Cooper--Schrieffer theory as the lowest-order approximation. It enables us to study the thermodynamic, single-particle, two-particle, and dynamical properties of superconductors with competing fluctuations based on a single functional \Phi[\hat{G}] of Green's function \hat{G} in the Nambu space. Specifically, we derive closed equations in the FLEX-S approximation, i.e., the fluctuation exchange approximation for superconductivity with all the pair processes, which contains extra terms besides those in the standard FLEX approximation.
2011-12-15