Dynamically screened Coulomb interaction in the parent compounds of hole-doped cuprates: Trends and exceptions

Abstract

Although cuprate high-temperature superconductors were discovered already in 1986 the origin of the pairing mechanism remains elusive. While the doped compounds are superconducting with high transition temperatures ${T}_{c}$, the undoped compounds are insulating due to the strong effective Coulomb interaction between the Cu $3d$ holes. We investigate the dependence of the maximum superconducting transition temperature ${T}_{c\phantom{\rule{4.pt}{0ex}}\text{max}}$ on the on-site effective Coulomb interaction $U$ using the constrained random-phase approximation. We focus on the commonly used one-band model of the cuprates, including only the antibonding combination of the Cu ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and O ${p}_{x}$ and ${p}_{y}$ orbitals and find a screening-dependent trend between the static value of $U$ and ${T}_{c\phantom{\rule{4.pt}{0ex}}\text{max}}$ for the parent compounds of a large number of hole-doped cuprates. Our results suggest that superconductivity may be favored by a large on-site Coulomb repulsion. We analyze both the trend in the static value of $U$ and its frequency dependence in detail and, by comparing our results to other works, speculate on the mechanisms behind the trend.