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In the functional Renormalization Group (fRG), one starts from the bare many-body interactions in the Hamiltonian and the pairing is dynamically generated (e. g. the important
spin-fluctuation (SF) pairing interaction) by systematically integrating out the high-energy degrees of freedom including important fluctuations (magnetic, superconducting (SC),
screening, vertex corrections) on equal footing. This contrasts other popular schemes such as the RPA, which takes right from the outset a magnetically driven SF-type of pairing interaction. Here, we report progress with the fRG in two directions: (a) on the one hand, we demonstrate for the SC state of the Fe-pnictides,how this scheme can be elevated to an "ab-initio" method by combining it with a-priori (constrained) density-functional calculations. The intricate interplay of the multi-orbital bandstructure, the Fermi Surface (FS) topology (pockets) and the many-body interactions yield competing sign-reversing s-wave and d-wave, nodal and nodeless gap states. This makes insights into a more universal versus a material-dependent understanding of SC a major challenge. Therefore, in part (b), we use general arguments of an optimization principle between the pairing-wave function and the repulsive part of the el-el interaction to analyze the gap anisotropy in the case of two proto-type Fe-pnictide families, with a 4-pocket (P-based) and 5-pocket (As-based) FS topology. It is shown that the optimization principle can help providing a more universal picture. It explains why a fully gapped s+- SC-sate is favored in the 5-pocket case, while a nodal pairing is expected for 4 pockets, consistent with the majority of experiments. |
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