Dynamical spin susceptibility and the resonance peak in the pseudogap region of the underdoped cuprate superconductors

TL;DR

This paper investigates the dynamical spin susceptibility and resonance peak behavior in the pseudogap region of underdoped cuprate superconductors, comparing different ordered states to identify phase-specific signatures.

Contribution

It provides a comparative analysis of the resonance peak in various ordered states, revealing distinct dispersion features that can distinguish between them experimentally.

Findings

Resonance peak dispersion varies significantly between DDW and DSC states.

Nearly dispersionless resonance exists only near ${f Q}=( ext{pi}, ext{pi})$ in DDW.

Coexisting DDW and DSC states alter the resonance dispersion compared to pure DSC.

Abstract

We present a study of the dynamical spin susceptibility in the pseudogap region of the high-T$_c$ cuprate superconductors. We analyze and compare the formation of the so-called resonance peak, in three different ordered states: the $d_{x^2-y^2}$-wave superconducting (DSC) phase, the $d$-density wave (DDW) state, and a phase with coexisting DDW and DSC order. An analysis of the resonance's frequency and momentum dependence in all three states reveals significant differences between them. In particular, in the DDW state, we find that a nearly dispersionless resonance excitation exists only in a narrow region around ${\bf Q}=(\pi,\pi)$. At the same time, in the coexisting DDW and DSC state, the dispersion of the resonance peak near ${\bf Q}$ is significantly changed from that in the pure DSC state. Away from $(\pi,\pi)$, however, we find that the form and dispersion of the resonance excitation in the coexisting DDW and DSC state and pure DSC state are quite similar. Our results demonstrate that a detailed experimental measurement of the resonance's dispersion allows one to distinguish between the underlying phases - a DDW state, a DSC state, or a coexisting DDW and DSC state - in which the resonance peak emerges.