High temperature superconductivity in iron pnictides and chalcogenides emerges when a magnetic phase is suppressed. The multi-orbital character and the strength of correlations underlie this complex phenomenology, involving magnetic softness and anis
otropies, with Hunds coupling playing an important role. We review here the different theoretical approaches used to describe the magnetic interactions in these systems. We show that taking into account the orbital degree of freedom allows us to unify in a single phase diagram the main mechanisms proposed to explain the (pi,0) order in iron pnictides: the nesting-driven, the exchange between localized spins, and the Hund induced magnetic state with orbital differentiation. Comparison of theoretical estimates and experimental results helps locate the Fe superconductors in the phase diagram. In addition, orbital physics is crucial to address the magnetic softness, the doping dependent properties, and the anisotropies.
The origin of the nematic state is an important puzzle to be solved in iron pnictides. Iron superconductors are multiorbital systems and these orbitals play an important role at low energy. The singular $C_4$ symmetry of $d_{zx}$ and $d_{yz}$ orbital
s has a profound influence at the Fermi surface since the $Gamma$ pocket has vortex structure in the orbital space and the X/Y electron pockets have $yz$/$zx$ components respectively. We propose a low energy theory for the spin--nematic model derived from a multiorbital Hamiltonian. In the standard spin--nematic scenario the ellipticity of the electron pockets is a necessary condition for nematicity. In the present model nematicity is essentially due to the singular $C_4$ symmetry of $yz$ and $zx$ orbitals. By analyzing the ($pi, 0$) spin susceptibility in the nematic phase we find spontaneous generation of orbital splitting extending previous calculations in the magnetic phase. We also find that the ($pi, 0$) spin susceptibility has an intrinsic anisotropic momentum dependence due to the non trivial topology of the $Gamma$ pocket.
Electronic interactions in multiorbital systems lead to non-trivial features in the optical spectrum. In iron superconductors the Drude weight is strongly suppressed with hole-doping. We discuss why the common association of the renormalization of th
e Drude weight with that of the kinetic energy, used in single band systems, does not hold in multi-orbital systems. This applies even in a Fermi liquid description when each orbital is renormalized differently, as it happens in iron superconductors. We estimate the contribution of interband transitions at low energies. We show that this contribution is strongly enhanced by interactions and dominates the coherent part of the spectral weight in hole-doped samples at frequencies currently used to determine the Drude weight.
Charge, spin and lattice degrees of freedom are strongly entangled in iron superconductors. A neat consequence of this entanglement is the behavior of the A_{1g} As-phonon resonance in the different polarization symmetries of Raman spectroscopy when
undergoing the magneto-structural transition. In this work we show that the observed behavior could be a direct consequence of the coupling of the phonons with the electronic excitations in the anisotropic magnetic state. We discuss this scenario within a five orbital tight-binding model coupled to phonons via the dependence of the Slater-Koster parameters on the As position. We identify two qualitatively different channels of the electron-phonon interaction: a geometrical one related to the Fe-As-Fe angle and another one associated with the modification upon As displacement of the Fe-As energy integrals pdsigma and pdpi. While both mechanisms result in a finite B_{1g} response, the behavior of the phonon intensity in the A_{1g} and B_{1g} Raman polarization geometries is qualitatively different when the coupling is driven by the angle or by the energy integral dependence. We discuss our results in view of the experimental reports.
