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Itinerant electron scenario for Fe-based superconductors

I review works on Fe-based superconductors which depart from a metal with well defined Fermi surfaces and Fermi liquid-type quasiparticles. I consider normal state instabilities -- SDW magnetism and nematic order, and superconductivity, all three as the consequences of the instability of a Fermi surface due to interactions between low-energy fermionic quasiparticles. This approach assumes that renormalizations coming from fermions from high energies, of order bandwidth, modify but do not destroy Fermi liquid behavior in the normal state and can be absorbed into the effective low-energy model of interacting fermions located near hole and electron-type Fermi surfaces. I argue that the interactions between these fermions are responsible for (i) a stripe-type SDW magnetic order (and, in some cases, a checkerboard order), (ii) a preliminary nematic-type instability, in which magnetic fluctuations break $C_4$ lattice rotational symmetry down to $C_2$, but magnetic order does not yet develop, and (iii) a superconductivity, which competes with these two orders. The experimental data on superconductivity show rich behavior with potentially different symmetry of a superconducting state even for different compositions of the same material. I argue that, despite all this, the physics of superconductivity in the itinerant scenario for Fe-based materials is governed by a single underlying pairing mechanism.