Coexistence of the antiferromagnetic and superconducting order and its effect on spin dynamics in electron-doped high-$T_{c}$ cuprates

TL;DR

This study uses a slave-boson approach to analyze the coexistence of antiferromagnetic and superconducting orders in electron-doped high-$T_c$ cuprates, revealing how spin dynamics vary with frequency and doping, aligning with experimental data.

Contribution

It demonstrates the coexistence of AF and SC orders over a wide doping range and highlights the importance of two-band effects in explaining spin response and gap behavior.

Findings

Spin response is commensurate below a crossover frequency in the coexisting phase.

Spin response switches to incommensurate at frequencies above the crossover.

Including two-band effects is crucial for matching experimental spin dispersion and gap features.

Abstract

In the framework of the slave-boson approach to the $t-t'-t''-J$ model, it is found that for electron-doped high-$T_c$ cuprates, the staggered antiferromagnetic (AF) order coexists with superconducting (SC) order in a wide doping level ranged from underdoped to nearly optimal doping at the mean-field level. In the coexisting phase, it is revealed that the spin response is commensurate in a substantial frequency range below a crossover frequency $\omega_{c}$ for all dopings considered, and it switches to the incommensurate structure when the frequency is higher than $\omega_{c}$. This result is in agreement with the experimental measurements. Comparison of the spin response between the coexisting phase and the pure SC phase with a $d_{x^{2}-y^{2}}$-wave pairing plus a higher harmonics term (DP+HH) suggests that the inclusion of the two-band effect is important to consistently account for both the dispersion of the spin response and the non-monotonic gap behavior in the electron-doped cuprates.