Doping dependence of d-wave bond-charge excitations in electron-doped cuprates

Motivated by the recent experiments reporting the doping dependence of the short-range charge order (CO) in electron-doped cuprates, we study the resonant x-ray scattering spectrum from d-wave bond-charge fluctuations obtained in the two-dimensional t-J model. We find that (i) the CO is short-range, (ii) the CO peak is pronounced at low temperature, (iii) the peak intensity increases with decreasing carrier doping $\delta$ down to $\delta \approx$ 0.10 and is substantially suppressed below $\delta \approx$ 0.10 due to strong damping, and (iv) the momentum of the CO decreases monotonically down to $\delta \approx$ 0.10 and goes up below $\delta \approx$ 0.10. These results reasonably capture the major features of the experimental data, and the observed short-range CO can be consistently explained in terms of bond-charge fluctuations with an internal d-wave symmetry.