We analyze whether and how the neutron resonance mode in unconventional superconductors is affected by higher-order corrections in the coupling between spin excitations and fermionic quasiparticles and find that in general such corrections can not be ignored. In particular, we show that in two spatial dimensions ($d=2$) the corrections are of the same order as the leading, one-loop contributions, demonstrating that the neutron resonance mode in unconventional superconductors is a strong coupling phenomenon. The origin of this behavior lies in the quantum-critical nature of the low-energy spin dynamics in the superconducting state and the feedback of the resonance mode onto the fermionic excitations. While quantum-critical fluctuations occur in any dimensionality $d⩽3$, they can be analyzed in a controlled fashion by means of the $\varepsilon$ expansion ($\varepsilon =3-d$), such that the leading corrections to the resonance mode position are small. Regardless of the strong coupling nature of the resonance mode, we show that it emerges only if the phase of the superconducting gap function varies on the Fermi surface, making it a powerful tool to investigate the microscopic structure of the pair condensate.

• Received 19 August 2013

DOI:https://doi.org/10.1103/PhysRevB.88.205104