Effective of charge doping in the LaNiO$_3$/SrTiO$_3$ superlattices

In this study we investigate the charge doping effect on the crystal and electronic structure of LaNiO$_3$/SrTiO$_3$ superlattice with density-functional theory calculations. It is found that the doped charge favors Ni $d_{3z^2 - r^2}$ orbital, and that the NiO$_6$ octahedron is elongated or compressed along the $z$-direction in order to reduce the energy. Under the fixed in-plane lattice constant, the octahedral distortion upon charge doping can be understood as a doping-induced effective epitaxial strain. The rotation of the NiO$_6$ octahedra is affected by the charge doping and the resulting doping-induced effective strain. Inclusion of the electron correlations enhances the orbital-lattice coupling and the structural changes. Possible cuprate-like Fermi surfaces induced by hole doping will also be discussed. Our work provides insights on the effect of charge doping on the nickelate superlattices, and suggests a doping-controlled structural evolution in these systems.