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

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. To demonstrate the capabilities of our approach, we take on the challenge of explaining the remarkable physics of multilayer cuprates by focusing on the two representative Ca_1+nCu_nO_2nCl₂ and HgBa₂Ca_n-1Cu_nO_2n+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. Our work establishes a framework for comprehensive studies of high-temperature superconducting cuprates, enables detailed comparisons with experiment, and, through its ab initio settings, unlocks opportunities for theoretical material design of high-temperature superconductors.