Concepts relating magnetic interactions, intertwined electronic orders and strongly correlated superconductivity

Unconventional superconductivity (SC) is said to occur when Cooper pair formation is dominated by repulsive electron-electron interactions, so that the symmetry of the pair wavefunction is other than isotropic s-wave. The strong, on-site, repulsive electron-electron interactions that are the proximate cause of such superconductivity are more typically drivers of commensurate magnetism. Indeed, it is the suppression of commensurate antiferromagnetism (AF) that usually allows this type of unconventional superconductivity to emerge. Importantly, however, intervening between these AF and SC phases, intertwined electronic ordered phases of an unexpected nature are frequently discovered. For this reason, it has been extremely difficult to distinguish the microscopic essence of the correlated superconductivity from the often spectacular phenomenology of the intertwined phases. Here we introduce a model conceptual framework within which to understand the relationship between antiferromagnetic electron-electron interactions, intertwined ordered phases and correlated superconductivity. We demonstrate its effectiveness in simultaneously explaining the consequences of antiferromagnetic interactions for the copper-based, iron-based and heavy-fermion superconductors, as well as for their quite distinct intertwined phases.