Correlated transition metal oxides have been a hot topic in condensed matter physics for decades, since they display complex ordering in orbital, spin and charge states. Numerous remarkable phenomena in such materials have been found and studied extensively, such as high-temperature superconductivity, electron-electron correlation driven metal-insulator transition, a rich variety of exotic topological states, and so on. Recently, new growth techniques have successfully created various correlated oxide heterostructures with transition metal and rare earth materials. They offer a promising new platform for correlation, magnetism and new emergent phenomena, and the study of it has become the new hot subject.

Bulk rare earth nickelates, RNiO3(R=rare earth element), display an interesting coexistence of charge and spin ordering and a canonical metal-insulator transition. Guided by experiment and band structure, we introduce and study a phenomenological Landau theory. The unusual magnetic periodicity is simply explained due to Fermi surface nesting of the eg band, and the observed charge order is a secondary order parameter proportional to the degree of orthorhombicity of the material structure. We also predict transport anisotropy resulted from the spin density wave order.

Titanate heterostructures have caught many peoples attention by hosting extremely high sheet carrier density two-dimensional electron gases, with strong correlations evidenced by, for example, a thickness dependent mass enhancement, and even a metal-insulator transition. Even in the extreme limit of quantum confinement, a single SrO layer in a GdTiO3 matrix, the high sheet carrier density n2d = 3.5 x 1014cm-2 is still half of the usual filling fraction for a Mott insulator. Inspired by this experimental observation, a new many-body ground state is discovered in a SrTiO3/GdTiO 3 superlattice: the dimer Mott insulator. In the dimer Mott insulator, electrons are localized not to individual atoms but to bonding orbitals on molecular dimers formed across a bilayer of two TiO2 planes. Dimer formation halves the charge density needed to reach the Mott state, and the combined effects of polar discontinuity, strong structural relaxation, and electron correlations all contribute to the realization of this unique ground state.

The 4d and 5d transition metal oxides are interesting because these materials incorporate both strong spin-orbit coupling and strong correlations, and consequently display distinctive physical properties and the tantalizing possibility of novel topological phases. A paramagnetic band calculation predicts that Pr2Ir2O 7 is a strong candidate for a nodal quadratic band touching state, in which the doubly degenerate conduction and valence bands touch at the zone center, right at the Fermi level. This nodal state is also independently observed in angle-resolved photoemission spectroscopy. The degeneracy point suggests that Pr2Ir2O7 is very sensitive to perturbations, such as time reversal symmetry or cubic symmetry, giving rise to the possibility of many novel phases. Indeed, we demonstrate using first-principles calculations that uniaxial strain applied along the (111) direction opens a band gap and converts the material to a strong topological insulator.