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 dwave 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 δ down to δ ≈ 0.10 and is substantially suppressed below δ ≈ 0.10 due to strong damping, and (iv) the momentum of the CO decreases monotonically down to δ ≈ 0.10 and goes up below δ ≈ 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.
PACS numbers:Recently resonant x-ray scattering (RXS), resonant inelastic x-ray scattering (RIXS), and high-energy x-ray scattering revealed the presence of short-range charge order (CO) with modulation vector along the axial direction (0, 0)-(π, 0) in various hole-doped cuprates (h-cuprates) such as Y-1-5 , Bi-6-9 , and Hg-based 10,11 compounds, implying that the CO can be a universal phenomenon in h-cuprates. The understanding of the origin of those charge correlations, therefore, will likely yield an important clue to the origin of the pseudogap as well as high-T c superconductivity 12 . In fact, a large number of theoretical studies were performed 13-22 , although a consensus has not been obtained.On the other hand, a short-range CO was also observed in electron-doped cuprates [23][24][25] (e-cuprates). Since the pseudogap features similar to those in h-cuprates are much weaker in e-cuprates, a theoretical study may be less complicated in e-cuprates. However, compared to theoretical studies of h-cuprates 13-22 , the CO in e-cuprates is much less studied [26][27][28][29] . Ref. 26 showed a comprehensive study of all possible COs in the two-dimensional (2D) t-J model and found a strong tendency to d-wave bond-charge order 30 . Ref. 27 then showed that d-wave bond-charge fluctuations can capture the charge excitation spectrum observed in experiments 23 . Although the theoretical framework is different from Refs. 26 and 27, similar d-wave bond-charge fluctuations were also proposed in Ref. 28 to explain the experimental data.The d-wave bond-charge order is different from a usual textbook-like charge-densitywave because the bond charge has an internal structure characterized by a d-wave symmetry.Therefore if the short-range CO observed in e-cuprates is indeed a d-wave bond-charge order, it can be interpreted as the first observation of unconventional CO in e-cuprates. Given that d-wave bond-charge order was discussed in h-cuprates 31 , it can be a universal phenomenon in the whole cuprate family. In addition, d-wave bond-charge order would be reduced to the electronic nematic order 32 , more precisely a d-wave Pomeranchuk instability 33-35 when the momentum transfer approaches zero. In this sense, the nematic ph...