Ab initio Studies on Cuprate High-T_c Superconductors

Understanding the materials dependence and the universal controlling parameter of superconductivity (SC) in cuprate high-T_c superconductors is a major challenge in physics. Without adjustable parameters, we numerically analyze the SC by using ab initio low-energy effective Hamiltonians consisting of the antibonding combination of Cu 3d_x2−y2 and O 2p_σ orbitals [1,2]. We apply a state-of-the-art variational Monte Carlo method combined with the Boltzmann-machine neural network for four cuprates (carrier doped CaCuO₂, Bi₂Sr₂CuO₆, Bi₂Sr₂CaCu₂O₈, and HgBa₂CuO₄), which show diverse experimental optimal SC critical temperature T_c ranging from ~10K to 120K. Calculated materials and hole doping concentration (δ) dependencies of the SC order parameter F_SC and severe competitions with spin orand charge orders show essential and quantitative agreement with the available experiments on the four materials: The amplitudes of F_SC and its δ dependence show quantitative agreement with the results of the muon spin resonance, tunneling and photoemission measurements. Then, we find realistic insights into the universal SC mechanism: (I) The principal component controlling the F_SC is U/|t|, which accounts for the diverse materials dependence. Here, U and t are the on-site Coulomb repulsion and the nearest neighbor hopping, respectively, in the ab initio Hamiltonians. (II) A universal scaling for the optimal T_c ~ 0.16|t|F_SC holds. (III) SC is enhanced and optimized for larger U and for smaller off-site interactions beyond most of the real available materials, while the off-site interaction stabilizes the SC against the competing states providing useful clues for designing higher T_c materials. Effective local attraction arising emergently from the strong onsite repulsion through the Mottness is identified as the origin of Cooper pairing and electron fractionalization, which constitute the keys for the SC mechanism. This work was obtained in collaboration with J.-B. Moree, M.T. Schmid, M. Hirayama, R. Kaneko and Y. Yamaji.

[1] .B. Moree et al. Phys. Rev. B 106, 235150 (2022). [2] M. T. Schmid et al. Phys. Rev. X 13, 041036 (2023).