Possible isotope effect on the resonance peak formation in high-T$_c$ cuprates

TL;DR

This paper investigates how isotope substitution affects the resonance peak in high-Tc cuprates, revealing a significant isotope effect driven by electron-phonon interactions and electronic correlations beyond RPA.

Contribution

It introduces an effective $t-J$ model including electron-phonon interactions to analyze isotope effects on magnetic resonance in cuprates, beyond traditional RPA methods.

Findings

Large isotope coefficient (~0.35) at optimal doping.

Electron-phonon coupling significantly influences the resonance peak.

Electronic correlations beyond RPA enhance the isotope effect.

Abstract

Starting from the three-band $p-d$ Hubbard Hamiltonian we derive an effective $t-J$ model including electron-phonon interaction of quasiparticles with optical phonons. Within the effective Hamiltonian we analyze the influence of electronic correlations and electron-phonon interaction on the dynamical spin susceptibility in layered cuprates. We find a huge isotope effect on the resonance peak in the magnetic spin susceptibility, ${Im}\chi({\bf q},\omega)$, seen by inelastic neutron scattering. It results from both the electron-phonon coupling and the electronic correlation effects taken into account beyond random phase approximation(RPA) scheme. We find at optimal doping the isotope coeffiecient $\alpha_{res} \approx 0.35$ which can be further tested experimentally.