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

We study charge excitation spectra in the two-dimensional t\text-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 \textbf{q}=(0,0) , shows two characteristic peaks at momenta of the form \textbf{q}₁= (q',q') and \textbf{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 \textbf{q}₁ is much broader, but develops to be very sharp in the vicinity of its instability, whereas the peak at \textbf{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 \textbf{q}=(0,0) and bend back toward close-to-zero energy due to the charge-order tendency at \textbf{q}₁ and \textbf{q}₂ . The resulting spectra form gap-like features with a maximal gap at \textbf{q} ≈ \textbf{q}₁/2 and \textbf{q}₂/2 . We discuss implications for the recent experiments in electron-doped cuprates.