Design of Mott and topological phases on buckled \textit{3d}-oxide honeycomb lattices

The honeycomb lattice, as realized e.g. in graphene, has rendered a robust platform for innovative science and potential applications. A much richer generalization of this lattice arises in (111)-oriented bilayers of perovskites, adding the complexity of the strongly correlated, multiorbital nature of electrons in transition metal oxides. Based on first principles calculations with an on-site Coulomb repulsion, here we provide trends in the evolution of ground states versus band filling in (111)-oriented (La$X$O$_{\mathrm{3}})_{\mathrm{2}}$/(LaAlO$_{\mathrm{3}})_{\mathrm{4}}$ superlattices, with $X$ spanning the entire \textit{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 distortion, to charge-, spin-, and orbital-ordering. LaMnO$_{\mathrm{3}}$ and LaCoO$_{\mathrm{3}}$ bilayers, where spin-orbit coupling opens a sizable gap in the Dirac-point Fermi surface, emerge as much desired oxide-based Chern insulators, the latter displaying a gap capable of supporting room-temperature applications [1] Further realizations of the honeycomb lattice and geometry patterns beyond the perovskite structure will be addressed. [1] D. Doennig, S. Baidya, W.E. Pickett and R. Pentcheva, arXiv: 1510.09177.