Order-parameter anisotropies in the pnictides: An optimization principle for multi-band superconductivity

Using general arguments of an optimization taking place between the pair wave function and the repulsive part of the electron-electron interaction, we analyze the superconducting gap in materials with multiple Fermi-surface (FS) pockets, with exemplary application to two proto-type ferropnictide setups. The main point of our work is to show that the SC state, its gap, and, in particular, its anisotropy in momentum space is determined by an optimization which determines and optimizes the interplay between the attractive interaction in the SC-channel and the Coulomb repulsion. This optimization problem is unavoidable in a multi-band SC situation: for the pnictides, it appears because of a frustration in the s(+/-)-channel, when more than two FS-pockets are involved in setting up the pairing interaction. On the basis of functional renormalization group (FRG) calculations for a wide parameter span of the bare interactions, we show that the symmetry of the gap and the nodal versus nodeless behavior is driven by this optimization requirement. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim