(Ab\) \(initio\) low-energy effective Hamiltonians for high-temperature superconducting cuprates Bi\(_2\)Sr\(_2\)CuO\(_6\), Bi\(_2\)Sr\(_2\)CaCu\(_2\)O\(_8\), HgBa\(_2\)CuO\(_4\) and CaCuO\(_2\)

• Published in: arXiv.org 2022-11
• Main Authors: Jean-Baptiste Morée, Hirayama, Motoaki, Schmid, Michael Thobias, Yamaji, Youhei, Imada, Masatoshi
• Format: Article
• Language: English
• Subjects: Bismuth strontium calcium copper oxide; Copper; Copper oxides; Cuprates; High temperature; Inspection; Laminates; Orbitals; Order parameters; Phase diagrams; Superconductivity; Transition temperature
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2206.01510

We derive \(ab\) \(initio\) low-energy effective Hamiltonians (LEH) for high-temperature superconducting (SC) copper oxides Bi\(_2\)Sr\(_2\)CuO\(_6\) (Bi2201, \(N_{\ell}=1\), \(T_c^{\rm exp} \sim 10\) K), Bi\(_2\)Sr\(_2\)CaCu\(_2\)O\(_8\) (Bi2212, \(N_{\ell}=2\), \(T_c^{\rm exp} \sim 84\) K), HgBa\(_2\)CuO\(_4\) (Hg1201, \(N_{\ell}=1\), \(T_c^{\rm exp} \sim 90\) K) and CaCuO\(_2\) (Ca11, \(N_{\ell}=\infty\), \(T_c^{\rm exp} \sim 110\) K), with different experimental optimal SC transition temperature \(T_c^{\rm exp}\) and number \(N_{\ell}\) of laminated CuO\(_2\) 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) Cu\(3d_{x^2-y^2}\)/O\(2p_{\sigma}\) 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 neighbour hopping \(t_1\) increases with \(T^{\rm exp}_c\) and \(N_{\ell}\), consistently with the expected increase in \(d\)-wave SC correlation function \(P_{dd}\) with \(U/|t_1|\). One possible cause of the increase of \(U/|t_1|\) is the replacement of apical O atoms by Cu atoms from neighbouring CuO\(_2\) planes when \(N_{\ell}\) increases. Furthermore, we show that the increase in distance between Cu and apical O atoms decreases the effective screening (ES) by electrons outside of the LEH and increases \(U/|t_1|\). (2) For Hg1201 and Ca11, we show that \(U/|t_1|\) decreases when hole doping per AB orbital \(\delta\) increases, which may partly account for the disappearance of SC when \(\delta\) exceeds the optimal value in experiment. (3) For \(N_{\ell} \geq 2\), off-site inter-CuO\(_2\) plane ECR is comparable to off-site intra-CuO\(_2\) plane ECR. We discuss contributions of inter-CuO\(_2\) plane ECR to both \(P_{dd}\) and the stability of the SC state.