Anisotropy of incommensurate spin and charge fluctuations in detwinned YBa$_2$Cu$_3$O$_{6+\delta}$

TL;DR

This study investigates the anisotropy of spin and charge fluctuations in detwinned YBa₂Cu₃O₆+δ superconductors using a theoretical model, revealing robust anisotropic behaviors linked to plane-chain coupling effects.

Contribution

It provides a detailed theoretical analysis of anisotropic spin and charge fluctuations in YBa₂Cu₃O₆+δ, highlighting the impact of plane-chain coupling on fluctuation topology and anisotropy.

Findings

Pronounced anisotropy of incommensurate spin peaks along specific directions.

Charge fluctuations are incommensurate with anisotropic peak intensities.

Incommensurate charge peaks exhibit upward dispersion, contrasting with spin peaks.

Abstract

Motivated by a recent neutron scattering experiment on detwinned YBa$_2$Cu$_3$O$_{6+\delta}$ superconductor, we examine the frequency and doping dependence of the anisotropy in the spin and charge fluctuation arising from the coupling between the plane and the chain. Starting from the two-dimensional $t$-$t^{'}$-$J$ model and using the random-phase approximation (RPA), we find a pronounced anisotropy of the incommensurate (IC) peaks in the spin channel, namely the peak intensity at the $(\pi\pm\delta,\pi)$ direction is stronger than that at the $(\pi,\pi\pm\delta)$ direction in a wide frequency range from $\omega=0.2J$ to the resonance frequency $\omega_r=0.35J$. Above the resonance frequency, the IC peaks reemerge. Their intensities shift to the diagonal direction and no anisotropy exists along the two diagonal directions. We find that this anisotropy is robust with respect to the possible variation of the RPA correction factor and to the dopings. The charge fluctuation is also found to be incommensurate for all energies considered and peak at $(0,\delta)$ and $(\delta,0)$. An anisotropy in its IC peak intensity along the $k_x$ and the $k_y$ direction exists, but in sharp contrast to the spin channel, the maximum intensity of the IC peak is along the $k_y$ direction. Moreover, the IC peak in the charge channel exhibits an upward dispersion, in contrast to the downward dispersion below the spin resonance frequency for the spin IC peak. We explain these features based on the effect of the plane-chain coupling on the topology of the Fermi surface.