Ab initio low-energy effective Hamiltonians for the high-temperature superconducting cuprates Bi2Sr2CuO6, Bi2Sr2CaCu2O8, HgBa2CuO4, and CaCuO2

We derive ab initio low-energy effective Hamiltonians (LEH) for high-temperature superconducting (SC) copper oxides Bi2Sr2CuO6 (Bi2201, N-l = 1, T-c(exp) similar to 10 K), Bi2Sr2CaCu2O8 (Bi2212, N-l = 2, T-c(exp) similar to 84 K), HgBa2CuO4 (Hg1201, N-l = 1, T-c(exp) similar to 90 K), and CaCuO2 (Ca11, N-l = infinity, T-c(exp) similar to 110 K), with substantially different values of experimental optimal SC transition temperature T-c(exp) and number N-l of laminated CuO2 planes between the two neighboring block layers. We apply the latest methodology of the multiscale ab initio scheme for correlated electron systems (MACE), and focus on the LEH consisting of one antibonding (AB) Cu3d(x2-y2)/O2p(sigma) orbital centered on each Cu atom. We discuss prominent features of this LEH: (1) The ratio U/|t(1)| between the onsite effective Coulomb repulsion (ECR) U and amplitude of nearest-neighbor hopping t(1) increases with T-c(exp) and N-l, consistently with the expected increase in d-wave SC correlation function P-dd with U/|t(1)|. One possible cause of the increase of U/|t(1)| with N-l is the replacement of apical O atoms by Cu atoms from neighboring CuO2 planes when N-l increases. Furthermore, we show that the increase in distance between Cu and apical O atoms decreases the effective screening (ES) defined as the screening by electrons outside of the LEH and increases U/|t(1)|. (2) For Hg1201 and Ca11, we examine the variation in U/|t(1)| with hole doping per AB orbital delta, and show that U/|t(1)| decreases when delta increases, which may partly account for the disappearance of SC when delta exceeds the optimal value in experiment. (3) For N-l >= 2, offsite inter-CuO2 plane ECR is comparable to off-site intra-CuO2 plane ECR. We discuss contributions of inter-CuO2 plane ECR to both P-dd and the stability of the SC state.