Signatures of pairing in the magnetic excitation spectrum of strongly correlated ladders

TL;DR

This study uses advanced computational methods to link magnetic excitation spectra with pairing tendencies in a model relevant to high-temperature superconductors, providing insights for experimental detection.

Contribution

It demonstrates a quantitative correlation between low-energy magnetic spectral weight and pairing strength in a generalized Hubbard model on a ladder.

Findings

Enhanced pairing correlates with increased low-energy magnetic spectral weight near (π,π).

Spin incommensurate features develop with doping, indicating pairing tendencies.

The spectrum branch with rung wave-vector 0 remains largely unaffected by doping.

Abstract

Magnetic interactions are widely believed to play a crucial role in the microscopic mechanism leading to high critical temperature superconductivity. It is therefore important to study the signatures of pairing in the magnetic excitation spectrum of simple models known to show unconventional superconducting tendencies. Using the Density Matrix Renormalization Group technique, we calculate the dynamical spin structure factor $S({\bf k},\omega)$ of a generalized $t-U-J$ Hubbard model away from half-filling in a two-leg ladder geometry. The addition of $J$ enhances pairing tendencies. We analyze quantitatively the signatures of pairing in the magnetic excitation spectra. We found that the superconducting pair-correlation strength, that can be estimated independently from ground state properties, is closely correlated with the integrated low-energy magnetic spectral weight in the vicinity of $(\pi,\pi)$. In this wave-vector region, robust spin incommensurate features develop with increasing doping. The branch of the spectrum with rung direction wave-vector $k_{rung}=0$ does not change substantially with doping where pairing dominates, and thus plays a minor role. We discuss the implications of our results for neutron scattering experiments, where the spin excitation dynamics of hole-doped quasi-one dimensional magnetic materials can be measured, and also address implications for recent resonant inelastic X-ray scattering experiments.