Development of spin fluctuations under the presence of $d$-wave bond order in cuprate superconductors

TL;DR

This study investigates how $d$-wave bond order influences spin fluctuations in cuprate superconductors, revealing suppression of certain magnetic relaxation rates while minimally affecting superconducting transition temperature, aligning with experimental observations.

Contribution

The paper introduces a self-consistent FLEX calculation showing the impact of $d$-wave bond order on spin dynamics and magnetic relaxation in cuprates, providing new insights into their electronic states.

Findings

Suppression of nuclear magnetic relaxation rate $1/T_1$ due to $d$-wave bond order.

Minimal reduction in superconducting transition temperature $T_c$.

Consistency of the $d$-wave bond order scenario with experimental data.

Abstract

In cuprate superconductors, superconductivity appears below the CDW transition temperature $T_{CDW}$. However, many-body electronic states under the CDW order are still far from understood. Here, we study the development of the spin fluctuations under the presence of $d$-wave bond order (BO) with wavevector $q=(\pi/2,0),(0,\pi/2)$, which is derived from the paramagnon interference mechanism in recent theoretical studies. Based on the $4 \times 1$ and $4 \times 4$ cluster Hubbard models, the feedback effects between spin susceptibility and self-energy are calculated self-consistently by using the fluctuation-exchange (FLEX) approximation. It is found that the $d$-wave BO leads to a sizable suppression of the nuclear magnetic relaxation rate $1/T_1$. In contrast, the reduction in $T_c$ is small, since the static susceptibility $\chi^s(Q_s)$ is affected by the BO just slightly. It is verified that the $d$-wave BO scenario is consistent with the experimental electronic properties below $T_{CDW}$.