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

Confinement-driven transitions between topological and Mott phases in (LaNiO3)$_N$/(LaAlO3)$_M$(111) superlattices