Spin dynamics of possible density wave states in the pseudogap phase of the high temperature superconductors

TL;DR

This paper investigates the spin excitation spectra of various density wave states in the pseudogap phase of high-temperature superconductors, revealing nearly vertical dispersion features consistent with recent neutron scattering experiments.

Contribution

It provides a detailed theoretical analysis of spin susceptibilities in different density wave models, highlighting their distinctive vertical dispersion signatures.

Findings

Nearly vertical dispersion relations at low energies for density wave states.

Energy-dependent incommensurability at high energies.

Vertical dispersion is a common feature across different density wave models.

Abstract

In a recent inelastic neutron scattering experiment in the pseudogap state of the high temperature superconductor $\mathrm{YBa_{2}Cu_{3}O_{6.6}}$ an unusual `vertical' dispersion of the spin excitations with a large in-plane anisotropy was observed. In this paper we discuss in detail the spin susceptibility of the singlet $d$-density wave, the triplet $d$-density wave, as well as the more common spin density wave orders with hopping anisotropies. From numerical calculations within the framework of random phase approximation, we find nearly vertical dispersion relations for spin excitations with anisotropic incommensurability at low energy $\omega \le 90 meV$, which are reminiscent of the experiments. At very high energy $\omega \ge 165 meV$, we also find energy-dependent incommensurability. Although there are some important difference between the three cases, unpolarized neutron measurements cannot discriminate between these alternate possibilities; the vertical dispersion, however, is a distinct feature of all three density wave states in contrast to the superconducting state, which shows an hour-glass shape dispersion.