A universal relationship between magnetic resonance and superconducting gap in unconventional superconductors

Superconductivity involves the formation of electron pairs (Cooper pairs) and their condensation into a macroscopic quantum state. In conventional superconductors, such as Nb 3 Ge and elemental Hg, weakly interacting electrons pair through the electron-phonon interaction. In contrast, unconventional superconductivity occurs in correlated-electron materials in which electronic interactions are significant and the pairing mechanism may not be phononic. In the cuprates, the superconductivity arises on doping charge carriers into the copper-oxygen layers of antiferromagnetic Mott insulators. Other examples of unconventional superconductors are the heavy-fermion compounds, which are metals with coupled conduction and localized f-shell electrons, and the recently discovered iron-arsenide superconductors. These unconventional superconductors show a magnetic resonance, a prominent collective spin-1 excitation mode in the superconducting state. Here we demonstrate the existence of a universal linear relation, Er2Δ, between the magnetic resonance energy (Er) and the superconducting pairing gap (Δ), which spans two orders of magnitude in energy. This relationship is valid for the three different classes of unconventional superconductors, which range from being close to the Mott-insulating limit to being on the border of itinerant magnetism. As the common excitonic picture of the resonance has not led to such universality, our observation suggests a much deeper connection between antiferromagnetic fluctuations and unconventional superconductivity.