A model for the neutron resonance in HgBa$_2$ CuO$_{4+\delta}$
Résumé
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 $2_{P_{F}}$ ordering vectors, where $2_{P_{F}}$ 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 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 Q . We demonstrate that the hole dependence of the RES spin dynamics is in agreement with the experimental data in HgBa$_2$ CuO$_{4+\delta}$