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

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 $\mathbf{q}=(0,0)$, shows two characteristic peaks at momenta of the form ${\mathbf{q}}_1=(q^{\prime },q^{\prime })$ and ${\mathbf{q}}_2=(q,0)$. 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 ${\mathbf{q}}_1$ is much broader, but develop to be very sharp in the vicinity of its instability, whereas the peak at ${\mathbf{q}}_2$ 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 $\mathbf{q}=(0,0)$ and bend back toward close to zero energy due to the charge-order tendency at ${\mathbf{q}}_1$ and ${\mathbf{q}}_2$. The resulting spectra form gap-like features with a maximal gap at $\mathbf{q}\approx {\mathbf{q}}_1/2$ and ${\mathbf{q}}_2/2$. We discuss implications for the recent experiments in electron-doped cuprates.

6 pages, 4 figures, panel b of figure 1 corrected, added references, corrected typos, added a paragraph before summary

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