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The theoretical understanding of the nematic state of iron-based superconductors and especially of FeSe is still a puzzling problem. Although a number of experiments call for a prominent role of local correlations and place iron superconductors at the entrance of a Hund's metal state, the effect of the electronic correlations on the nematic state has been theoretically poorly investigated. In this work we study the nematic phase of iron superconductors accounting for local correlations, including the effect of the Hund's coupling. We show that Hund's physics strongly affects the nematic properties of the system. It severely constrains the precise nature of the feasible orbital-ordered state and induces a differentiation in the effective masses of the zx/yz orbitals in the nematic phase. The latter effect leads to distinctive signatures in different experimental probes overlooked so far in the interpretation of experiments. As notable examples the splittings between zx and yz bands at Γ and M points are modified, with important consequences for angle-resolved photoemission spectroscopy measurements., E.B. acknowledges funding from Ministerio de Economía, Industria y Competitividad via Grants No. FIS2011-29689 and No. FIS2014-53218-P and from Fundación Ramón Areces. M.C. acknowledges funding from SISSA/Consiglio Nazionale delle Ricerche project “Superconductivity, Ferroelectricity and Magnetism in bad metals” (Protocollo 232/2015) and Ministero dell'Istruzione, dell'Università e della Ricerca through the PRIN 2015 program (Protocollo 2015C5SEJJ001).

Undoped iron superconductors accommodate n=6 electrons in five d orbitals. Experimental and theoretical evidence shows that the strength of correlations increases with hole doping, as the electronic filling approaches half filling with n=5 electrons. This evidence delineates a scenario in which the parent compound of iron superconductors is the half-filled system, in analogy to cuprate superconductors. In cuprates the superconductivity can be induced upon electron or hole doping. In this work we propose to search for high-Tc superconductivity and strong correlations in chromium pnictides and chalcogenides with n, Funding from Ministerio de Economía, Industria y Competitividad (Spain) via Grants No. FIS2012-33521, No. FIS2014-53218-P, No. FIS2015-64654-P, and No. MAT2015-66888-C3-1-R and from Fundación Ramón Areces is gratefully acknowledged. J.L. acknowledges the financial support of the National Natural Science Foundation of China (Grants No. 11374186 and No. 51231007) and the China Scholarship Council.

Oral presentation given at the 20th International Conference on Magnetism, held in Barcelona (Spain) on July 5-10th, 2015. Friday, July 10. FR.J.1_THEORY OF STRONGLY CORRELATED MATTER 09:00-10:30 (ROOM E1-E3)., A new concept has emerged in the last years in correlated electron systems: the Hund metal. This name was coined within the context of iron superconductors and refers to a strongly correlated metallic state found in multi-orbital systems with Hund¿s coupling playing a key role in setting the correlations [1]. Until very recently [2] the nature of correlations in Hund metals has been controversial and not well understood. When the atoms become spin polarized the overlap between the atomic and single particle states decreases suppressing the quasiparticle weight. Nevertheless the system seems to be far from a Mott transition as the transition is not found for moderate increase of interactions. On the other hand the strong increase of correlations as half-filling is approached has led to a description of Hund metals as doped Mott insulators. This has led to a discussion on the role of Mott physics in these systems. We have addressed the correlations in multi-orbital systems as a function of interactions, number of orbitals and electronic filling. We have clarified the nature of correlations in Hund metals and solved the controversy between Hund and Mott systems [2]. Our calculations clearly show that the suppression of coherence in Hund metals is directly connected to the Mott insulating state at half-filling. However correlations due to Hund¿s coupling are intrinsically different to those in Mott states. This is observed in the charge fluctuations, which are only weakly reduced or even enhanced in Hund metals as the quasiparticle weight is suppressed, contrary to what happens in Mott correlated systems. We have shown that the dependence of correlations, energy scales, charge and spin fluctuations can be understood by looking at the hopping processes which are suppressed or promoted by Hund's coupling.