Doping dependance of the spin resonance peak in bilayer high-$T_c$ superconductors

TL;DR

This study investigates how doping levels affect the spin resonance peaks in bilayer high-$T_c$ superconductors, revealing differences between even and odd channels and their relation to doping and critical temperature.

Contribution

The paper provides a theoretical analysis of doping dependence of spin resonance peaks in bilayer high-$T_c$ superconductors using a bilayer $t-J$ model, highlighting differences between channels.

Findings

Resonance peak intensity is weaker in the even channel than in the odd channel.

Resonance frequency in the odd channel scales linearly with $T_c$.

Resonance frequency in the even channel increases with decreasing doping and saturates in the underdoped regime.

Abstract

Motivated by a recent experiment on the bilayer Y$_{1-x}$Ca$_{x}$Ba$_2$Cu$_3$O$_y$ superconductor and based on a bilayer $t-J$ model, we calculate the spin susceptibility at different doping densities in the even and odd channels in a bilayer system. It is found that the intensity of the resonance peak in the even channel is much weaker than that in the odd one, with the resonance position being at a higher frequency. While this difference decreases as the doping increases, and both the position and amplitude of the resonance peaks in the two channels are very similar in the deeply overdoped sample. Moreover, the resonance frequency in the odd channel is found to be linear with the critical temperature $T_c$, while the resonance frequency increases as doping decreases in the even channel and tends to saturate at the underdoped sample. We elaborate the results based on the Fermi surface topology and the d-wave superconductivity.