Abstract
A set of broken symmetry two-dimensional ground states are predicted in (111)-oriented (LaNiO$_3$)$_N$/(LaAlO$_3$)$_M$ ($N$/$M$) superlattices, based on density functional theory (DFT) calculations including a Hubbard $U$ term. An unanticipated Jahn-Teller distortion with $d_{z^2}$ orbital polarization and a FM Mott insulating (and multiferroic) phase emerges in the double perovskite (1/1), that shows strong susceptibility to strain-controlled orbital engineering. The LaNiO$_3$ bilayer with graphene topology has a switchable multiferroic (ferromagnetic (FM) and ferroelectric) insulating ground state with inequivalent Ni sites. Beyond $N=3$ the confined LaNiO$_3$ slab undergoes a metal-to-insulator transition through a half-semimetallic phase with conduction originating from the interfaces. Antiferromagnetic arrangements allow combining motifs of the bilayer and single trigonal layer band structures in designed artificial mixed phases.
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