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

TL;DR

This paper investigates charge excitations in the t-J model with long-range Coulomb interactions, revealing ring-like charge modulations consistent with recent x-ray experiments on cuprates.

Contribution

It introduces a large-N formulation of the 2D t-J model considering all charge excitations and demonstrates the emergence of ring-shaped charge modulations due to long-range Coulomb interactions.

Findings

Phase separation instability persists at q=(0,0) with short-range Coulomb repulsion.

Long-range Coulomb interaction induces ring-shaped charge modulations around q=(0,0).

Computed charge spectrum shows well-formed rings matching experimental observations.

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 ${\bf q}=(0,0)$, 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 ${\bf q}=(0,0)$. If on the other hand a two-dimensional long-range Coulomb interaction is included the instability sets in at ${\bf q}$ momenta forming a ring around ${\bf q}=(0,0)$. 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.