Current challenges in Fe-based superconductors

Fe-based superconductors (FeBS) are different from cuprates in many aspects, including time placement and social climate in the superconducting community. Unlike cuprates, where it took 20 years for the researchers to arrive at a reasonably broad consensus regarding their pairing symmetry and mechanism, in case of FeBS the opinions converged to the spin-fluctuation driven $s_\pm$ pairing within a few years. Unfortunately, the feeling that we have gained a fundamental understanding of FeBS turned out to be fleeting. With the broadening of superconducting materials in this class, this simple scenario has been increasingly questioned, and some of the unsolved problems of the early stage have been re-evaluated and found to be more important than it had seemed. Some parent compounds are magnetic, but it is not clear why they do not order at much higher temperatures. Others show no long range order, despite the fact that frustration and reduced dimensionality are relatively mild. Are the local $\pi,0$ correlations that survive up to the highest measurable temperatures relevant? Second, what pushes apart electron and hole pockets? A whole block of questions arises in intercalated or monolayered FeSe, with Tc up to 40 K in the bulk and at least 80 at some interfaces. Neither $d-$wave, not ``old'' $s_\pm$, not a constant-sign $s$ are apparently consistent with the experiments, and why does removing the hole pocket enhance $T_c$, in apparent contradiction to the original-consensus spin-fluctuation theory? Moreover, these FeBS feature some very small $E_F$ but no indications of BEC and pre-formed pairs. What other important effects may be triggered by a small $E_F$? What is the role of phonons, in particular the forward scattering process ascribed to the monolayers, proposed to enhance Tc over that possible by electronic excitations?