Towards an ab initio theory of high-temperature superconductors: a study of multilayer cuprates

Benjamin Bacq-Labreuil; Benjamin Lacasse; André-Marie S. Tremblay; David Sénéchal; Kristjan Haule

paper

Towards an ab initio theory of high-temperature superconductors: a study of multilayer cuprates

arXiv:2410.10019

Abstract

Significant progress towards a theory of high-temperature superconductivity in cuprates has been achieved via the study of effective one- and three-band Hubbard models. Nevertheless, material-specific predictions, while essential for constructing a comprehensive theory, remain challenging due to the complex relationship between real materials and the parameters of the effective models. By combining cluster dynamical mean-field theory and density functional theory in a charge-self-consistent manner, here we show that the goal of material-specific predictions for high-temperature superconductors from first principles is within reach. We take on the challenge of explaining the remarkable physics of multilayer cuprates by focusing on the two representative Ca $_{(1 + n)}$ Cu $_{n}$ O $_{2 n}$ Cl $_{2}$ and HgBa $_{2}$ Ca $_{(n - 1)}$ Cu $_{n}$ O $_{(2 n + 2)}$ families. We shed light on the microscopic origin of many salient features of multilayer cuprates, in particular the $n$ -dependence of their superconducting properties. The maximum of $T_{c}$ for the tri-layer compounds is explained by an intertwined analysis of the charge-transfer gap, superexchange $J$ , and inhomogeneous doping between the CuO $_{2}$ planes. We highlight the existence of a minimal doping (4\%) required for superconductivity to emerge. We capture material-specific properties such as the larger propensity of HgBa $_{2}$ Ca $_{(n - 1)}$ Cu $_{n}$ O $_{(2 n + 2)}$ to superconduct compared with Ca $_{(1 + n)}$ Cu $_{n}$ O $_{2 n}$ Cl $_{2}$ . We also find the coexistence of arcs and pockets observed with photoemission, the charge redistribution between copper and oxygen, and the link to the pseudogap. Our work establishes a framework for comprehensive studies of cuprates, enables detailed comparisons with experiment, and, through its \emph{ab initio} settings, unlocks opportunities for theoretical material design of high-temperature superconductors.

44 pages, 19 main figures, 9 supplementary figures, revised version