Strong coupling behavior of the neutron resonance mode in unconventional superconductors

TL;DR

This paper demonstrates that the neutron resonance mode in unconventional superconductors is a strong coupling phenomenon influenced by quantum-critical spin dynamics, with implications for understanding the superconducting gap structure.

Contribution

It reveals that higher order corrections are significant, establishing the resonance mode as a strong coupling effect and linking its emergence to the phase variation of the superconducting gap.

Findings

Corrections to the resonance mode are of same order as leading contributions in 2D.

Quantum critical fluctuations dominate the low energy spin dynamics.

The resonance mode appears only if the superconducting gap phase varies on the Fermi surface.

Abstract

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 cannot be ignored. In particular, we find that in two spatial dimensions (d=2) the corrections are of same order as the leading, weak coupling 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 smaller than the upper critical dimension d_{uc}=3, they can be analyzed in a controlled fashion by means of the \epsilon-expansion (\epsilon =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.