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Design of Mott and topological phases on buckled 3d-oxide honeycomb lattices

Perovskite bilayers with (111)-orientation combine a honeycomb lattice as a key feature with the strongly correlated, multiorbital nature of electrons in transition metal oxides. In a systematic DFT+$U$ study of (111)-oriented (La$X$O$_3$)$_2$/(LaAlO$_3$)$_4$ superlattices, we establish trends in the evolution of ground states versus band filling in (111)-oriented (La$X$O$_3$)$_2$/(LaAlO$_3$)$_4$ superlattices, with $X$ spanning the entire $3d$ transition metal series. The competition between local quasi-cubic and global triangular symmetry triggers unanticipated broken symmetry phases, with mechanisms ranging from Jahn-Teller distortions, to charge-, spin-, and orbital-ordering. LaMnO$_3$, where spin-orbit coupling opens a sizable gap in the Dirac-point Fermi surface, emerges as a topological Chern insulator.