Ring-like shaped charge modulations in the t-J model with long-range Coulomb interaction

Abstract

The study of the charge excitations in cuprates is presently an interesting topic because of the development of new and precise x-ray experiments. Based on a large-N formulation of the two-dimensional t-J model, which allows us to consider all possible charge excitations on an equal footing, we investigate the charge spectrum for both electron- and hole-doped cases. In both cases, the instability toward phase separation, which has momentum modulation q=(0,0), is found to be robust in a large region of the doping-temperature phase diagram. If a short-range Coulomb repulsion is included the phase separation region shrinks, but the instability remains at q=(0,0). If on the other hand a two-dimensional long-range Coulomb interaction is included the instability sets in at q momenta forming a ring around q=(0,0). The computed charge spectrum in the translation-invariant phase shows well-formed rings. We discuss our results in the light of recent x-ray experiments in electron- and hole-doped cuprates, where ring-like shaped charge modulations have been reported.