Fig: Graphical demonstration of orbital flexible superconductors .
Fig: This schematic RG flow for the ladder material BaFe2S3 illustrates that a repulsive quantum critical point is the nexus of many-body phases .
Ten years after their discovery, the mechanism of superconductivity in iron pnictides and chalcogenides is still an open puzzle. The major conundrum is the explanation of the robust appearance of the superconducting state in a diverse variety of Fermi surface morphologies, including systems with both electron and hole pockets, others with only hole pockets, and others again with only electron pockets. This is particularly confusing since repulsive interactions are substantial in these systems and require a compound independent mechanism to overcome the Coulomb repulsion.
In our recent contributions we particularly focus on the role of orbital degrees of freedom. In  we investigate the possibility of predominant interorbital s-wave pairing to overcome the Coulomb cost. Complementary, in , an RG study for the arguably most exotic of all iron-based superconductors, the ladder material BaFe2S3 is presented and unveils the importance of Hund's interaction. Going beyond the present paradigm, we propose an entirely novel mechanism for superconductivity in multiorbital systems ("triplet RVB"), which is based on the idea of doping a miniature triplet spin-liquid .
A complementary research direction on iron based superconductors regards their topological nature . As we demonstrate theoretically, the experimentally observed 3D Dirac semimetallic state of Co doped LiFeAs is expected to host helical, one dimensional Majorana fermions. These exotic quantum particles propagate along each vortex line in the flux phase and lead to a quantization of thermal conductivity.
 EJ König, P Coleman, Phys. Rev. B 99, 144522 (2019)
 EJ König, AM Tsvelik, P Coleman, Phys. Rev. B 98, 184517 (2018)
 EJ König, P Coleman, Phys. Rev. Lett. 122, 207001 (2019)
 P Coleman, Y Komijani, EJ König, arXiv:1910.03168 (2019)