Spin susceptibility in bilayered cuprates: resonant magnetic excitations

TL;DR

This paper investigates the momentum and frequency dependence of spin susceptibility in bilayer cuprate superconductors, revealing the existence of resonant modes with distinct energies and dispersions, and explaining their doping dependence.

Contribution

It provides a detailed theoretical analysis of the resonance modes in bilayer cuprates, including energy splitting, dispersion, and the origin of doping dependence, advancing understanding of magnetic excitations.

Findings

Existence of resonance modes in both odd and even channels.

Energy splitting between modes due to interaction and susceptibility differences.

Identification of a second branch of the even resonance similar to the Q*-mode.

Abstract

We study the momentum and frequency dependence of the dynamical spin susceptibility in the superconducting state of bilayer cuprate superconductors. We show that there exists a resonance mode in the odd as well as the even channel of the spin susceptibility, with the even mode being located at higher energies than the odd mode. We demonstrate that this energy splitting between the two modes arises not only from a difference in the interaction, but also from a difference in the free-fermion susceptibilities of the even and odd channels. Moreover, we show that the even resonance mode disperses downwards at deviations from ${\bf Q}=(\pi,\pi)$. In addition, we demonstrate that there exists a second branch of the even resonance, similar to the recently observed second branch (the $Q^*$-mode) of the odd resonance. Finally, we identify the origin of the qualitatively different doping dependence of the even and odd resonance. Our results suggest further experimental test that may finally resolve the long-standing question regarding the origin of the resonance peak.