# A model for the neutron resonance in HgBa$_{2}$CuO$_{4+\delta}$

## TL;DR

This paper models the spin dynamics in cuprate superconductors' pseudogap phase using a Resonant Excitonic State framework, explaining neutron scattering observations and their dependence on hole doping in HgBa$_{2}$CuO$_{4+eta}$.

## Contribution

It introduces a charge order model with multiple $2{f {p}}_{ ext{F}}$ vectors to explain collective modes observed in neutron scattering in the pseudogap phase.

## Key findings

- The model reproduces the neutron scattering data in HgBa$_{2}$CuO$_{4+eta}$.
- It explains the loss of coherence in spin susceptibility at certain wave vectors.
- The hole dependence of the spin dynamics aligns with experimental observations.

## Abstract

We study the spin dynamics of the Resonant Excitonic State (RES) proposed, within the theory of an emergent SU(2) symmetry, to explain some properties of the pseudo-gap phase of cuprate superconductors. The RES can be described as a proliferation of particle-hole patches with an internal modulated structure. We model the RES modes as a charge order with multiple $2{\bf {p}}_{\text{F}}$ ordering vectors, where $2{\bf {p}}_{\text{F}}$ connects two opposite side of the Fermi surface. This simple modelization enables us to propose a comprehensive study of the collective mode observed at the antiferromagnetic (AF) wave vector $\mathbf{Q}=(\pi,\pi)$ by Inelastic Neutron Scattering (INS) in both superconducting state (SC), but also in the Pseudogap regime. In this regime, we show that the dynamic spin susceptibility accuses a loss of coherence terms except at special wave vectors commensurate with the lattice. We argue that this phenomenon could explain the change of the spin response shape around $\mathbf{Q}$. We demonstrate that the hole dependence of the RES spin dynamics is in agreement with the experimental data in HgBa$_{2}$CuO$_{4+\delta}$.