$d$-wave bond-order charge excitations in electron-doped cuprates

TL;DR

This paper investigates $d$-wave bond-order charge excitations in electron-doped cuprates using the $t$-$J$ model, revealing characteristic peaks in susceptibility and energy spectra related to charge-order tendencies near specific momenta.

Contribution

It provides a theoretical analysis of charge excitation spectra and susceptibility peaks, elucidating the charge-order phenomena observed in electron-doped cuprates.

Findings

Peaks in static susceptibility at ${f q}_1$ and ${f q}_2$ indicate charge-order tendencies.

Energy spectra show gap-like features around ${f q}_1/2$ and ${f q}_2/2$.

Charge excitations exhibit V-shaped structures and momentum-dependent features consistent with experiments.

Abstract

We study charge excitation spectra in the two-dimensional $t$-$J$ model on a square lattice to explore a charge-order tendency recently found in electron-doped cuprates around the carrier density 0.15. The static susceptibility of $d$-wave charge density, which corresponds to the nematic susceptibility at the momentum transfer ${\bf q}=(0,0)$, shows two characteristic peaks at momenta of the form ${\bf q}_{1}=(q',q')$ and ${\bf q}_{2}=(q,0)$. These two peaks originate from the so-called $2k_{F}$ scattering processes enhanced by the $d$-wave character of the bond-charge density. The peak at ${\bf q}_{1}$ is much broader, but develop to be very sharp in the vicinity of its instability, whereas the peak at ${\bf q}_{2}$ becomes sharper with decreasing temperature, but does not diverge. The equal-time correlation function, which is measured by resonant x-ray scattering, exhibits a momentum dependence similar to the static susceptibility. We also present energy-resolved charge excitation spectra. The spectra show a V-shaped structure around ${\bf q}=(0,0)$ and bend back toward close to zero energy due to the charge-order tendency at ${\bf q}_{1}$ and ${\bf q}_{2}$. The resulting spectra form gap-like features with a maximal gap at ${\bf q} \approx {\bf q}_{1}/2$ and ${\bf q}_{2}/2$. We discuss implications for the recent experiments in electron-doped cuprates.