We formulate a method of deriving an effective low-energy Hamiltonian for nonperiodic systems such as interfaces for strongly correlated electron systems by extending a conventional multiscale ab initio scheme for correlated electrons (MACE). We apply the formalism to copper-oxide high Tc superconductors in an example of the interface between overdoped La2-xSrxCuO4 and Mott insulating La2CuO4 recently realized experimentally and derive the two-band effective Hamiltonian (Eg Hamiltonian) from the Cu 3dx2-y2-like and 3d3r2-z2-like orbitals near the Fermi level. We show that the parameters of the Eg Hamiltonian derived for the La2CuO4/La1.55Sr0.45CuO4 superlattice differ considerably from those for the bulk La2CuO4, particularly significant in the partially screened Coulomb parameters and the level offset between the dx2-y2 and dz2 orbitals, ΔE. In addition, we investigate the effect of the lattice relaxation on the Eg Hamiltonian by carefully comparing the parameters derived before and after the structure optimization. We find that the CuO6 octahedra distort after the relaxation as a consequence of the Madelung potential difference between the La2CuO4 and La1.55Sr0.45CuO4 sides, by which the layer dependence of the hopping and Coulomb parameters becomes more gradual than the unrelaxed case. Furthermore, the structure relaxation dramatically changes the ΔE value and the occupation number at the interface. This study not only evidences the importance of the ionic relaxation around interfaces but also provides a set of layer-dependent parameters of the Eg Hamiltonian, which is expected to provide further insight into the interfacial superconductivity when solved with low-energy solvers.
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