High temperature superconductivity is a big challenge problem to be solved for the scientific community in the present century. It is also a field with important technological applications. There are two families of high temperature superconductivity at ambient pressure: cuprates discovered in 1986 and iron superconductors discovered in 2008. The mechanism that drives superconductivity in both systems is unknown in contrast to the standard BCS superconductors. Our group worked in the past in cuprates and at present is very active in iron superconductors. The main challenge that poses these systems is that they are strongly correlated systems in quasi-two dimensions.
Strongly correlated systems are materials where the Landau Fermi liquid description of common metals is questioned. The standard one-particle approximations implied by the Fermi liquid are not usually enough to describe these systems. They present a rich variety of phases and unconventional superconductivity is one of them. Furthermore, in low dimensions quantum fluctuations are unavoidable.
The advent of iron superconductors has initiated a new era in the study of superconductivity. They are multiorbital systems with hole and electron Fermi pockets that seem to lie between the weak and strong correlation regime, in the most difficult intermediate regime. In addition they present a strong interplay between lattice, orbital and spin degrees of freedom. A notorious example of this interplay is the electronic nematic phase that presents these compounds. The origin of electron nematicity in iron-based superconductors is one of the most interesting and controversial topics and it is thought to be related to the mechanism of superconductivity. Together with Maria José Calderón and Elena Bascones we have been worked in iron superconductors since they were discovered. We have recently written a review.
At present, our group have focused in the proposal of a field theoretical model at low energy that unveils the spin-orbital entanglement in the paramagnetic and nematic phases. The model describes the orbital content of the hole and electron pockets and an orbital selective spin-spin interaction. With this model we have been able to understand the orbital ordering found in ARPES experiments in FeSe in collaboration with an experimental group. We have also been able to understand why the 122 family of iron superconductors present a magnetic phase while FeSe does not. There is still a lot to do to check the model. In these works you can learn more about it.