Coulomb-Driven Electronic Textures in Lightly Hole-Doped Cuprates

Abstract

Motivated by recent experiments on Ca$_2$CuO$_2$Cl$_2$, we present a comprehensive study of the interplay between dopants and localized Zhang-Rice singlets in lightly hole-doped cuprates. Owing to the poorly screened Coulomb potential, the interactions between dopants and localized Zhang-Rice singlets favor asymmetric electronic configurations characterized by effective electric "dipoles". Using the MPS-based Lanczos method, we show that these localized holes give rise to in-gap bound states within the charge-transfer gap. When tunneling matrix-element effects are included, the bound states exhibit a characteristic $4a_0 \times 2a_0$ internal structure, consistent with experimental observations. Our results suggest that Coulomb interactions between dopants and localized Zhang-Rice singlets, together with tunneling matrix-element effects, provide a microscopic mechanism for the observed $4a_0$ electronic structures.