Superconductivity Studied by Solving Ab Initio Low-Energy Effective Hamiltonians for Carrier Doped CaCuO2, Bi2Sr2CuO6, Bi2Sr2CaCu2O8, and HgBa2CuO4

Understanding the materials dependence together with the universal controlling parameter of superconductivity (SC) in copper oxide superconductors is one of the major challenges in condensed matter physics. Here, we numerically analyze SC by using ab initio low-energy effective Hamiltonians consisting of the antibonding combination of Cu 3dx2-y2 and O 2p sigma orbitals without adjustable parameters. We have performed the state-of-the-art variational Monte Carlo calculations for the four carrier doped cuprates with diverse experimental optimal SC critical temperature Topt c : CaCuO2 (Topt c '' 110 K), Bi2Sr2CuO6 (Topt c '' 10-40 K), Bi2Sr2CaCu2O8 (Toptc '' 85-100 K), and HgBa2CuO4 (Topt c '' 90 K). Materials and hole doping concentration (5) dependencies of the SC order parameter FSC and the competition with spin or charge order show essential and quantitative agreement with the available experiments on the four materials in the following points. (1) In a wide range 0.05 <= 5 <= 0.25, the ground state is commonly the uniform SC state, which is severely competing with the charge or spin stripe and antiferromagnetic states. (2) FSC at the optimum doping shows amplitude consistent with the superfluid density measured in the muon spin resonance and its dome structure found in 5 dependence shows consistency with that of the SC gap in the tunneling and photoemission measurements. Based on the confirmed materials dependence, we further find insights into the universal SC mechanism. (I) FSC increases with the ratio U/It1I within the available realistic materials, indicating that U/It1I is the principal component controlling the strength of the SC in the real materials dependence. Here, U and t1 are the on-site Coulomb repulsion and the nearestneighbor hopping, respectively, in the ab initio Hamiltonians. (II) A universal scaling Topt c '' 0.16It1IFSC holds. (III) SC is enhanced and optimized if U is increased beyond the real available materials, and it is further enhanced when the off-site interaction is reduced, while the presence of the off-site interaction is important to make the SC ground state against other competing states. The present findings provide useful clues for the design of new SC materials with even higher Topt c.