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The diverse functionality emerging at oxide interfaces calls for a fundamental understanding of the mechanisms and control parameters of electronic reconstructions. Here, we explore the evolution of electronic phases in (LaAlO3)M/(SrTiO3)N (001) superlattices as a function of strain and confinement of the SrTiO3 quantum well. Density functional theory calculations including a Hubbard U term reveal a charge ordered Ti(3+) and Ti(4+) state for N = 2 with an unanticipated orbital reconstruction, displaying alternating d(xz) and d(yz) character at the Ti(3+) sites, unlike the previously reported d(xy) state, obtained only for reduced c-parameter at a(STO). At aLAO c-compression leads to a Dimer-Mott insulator with alternating d(xz), d(yz) sites and an almost zero band gap. Beyond a critical thickness of N = 3 (a(STO)) and N = 4 (aLAO) an insulator-to-metal transition takes place, where the extra e/2 electron at the interface is redistributed throughout the STO slab with a d(xy) interface orbital occupation and a mixed d(xz) + d(yz) occupation in the inner layers. Chemical variation of the SrTiO3 counterpart (LaAlO3 vs. NdGaO3) proves that the significant octahedral tilts and distortions in the SrTiO3 quantum well are induced primarily by the electrostatic doping at the polar interface and not by variation of the SrTiO3 counterpart.

Density functional theory calculations with an on-site Coulomb repulsion term reveal competing ground states in (111)-oriented (LaAlO(3))(M)/(SrTiO(3))(N) superlattices with n-type interfaces, ranging from spin, orbitally polarized (with selective e(g)('), a(1g), or d(xy) occupation), Dirac point Fermi surface, to charge-ordered flat band phases. These phases are steered by the interplay of (i) Hubbard U, (ii) SrTiO(3) quantum well thickness, and (iii) crystal field splitting tied to in-plane strain. In the honeycomb lattice bilayer N = 2 under tensile strain, inversion symmetry breaking drives the system from a ferromagnetic Dirac point (massless Weyl semimetal) to a charge-ordered multiferroic (ferromagnetic and ferroelectric) flat band massive (insulating) phase. With increasing SrTiO(3) quantum well thickness an insulator-to-metal transition occurs.