Transition metal oxides (TMOs) have long been one of the main subjects of material science because of their novel functionalities such as high-Tc superconductivity in cuprates and the colossal magnetoresistance effect in manganites. A new era for the study of novel oxides was opened by the recent developments in thin film growth techniques with the atomic precision. A variety of heterostructures involving TMOs have been fabricated and characterized, leading to, for example, the discovery of 2-dimensional electron gases at interfaces between two dissimilar insulators . Thus, further novel phenomena may emerge in such TMO heterostructures. In this talk, I will present our recent theoretical developments on oxide heterostructures along with this direction. Specifically, I consider bilayers of TMOs grown along the  crystallographic axis. A variety of novel phenomena are predicted, including quantum spin Halll effects  and anomalous Hall effects . The effect of strong correlation is also discussed in the presence of strong spin-orbit coupling. For some cases, the low-energy effective Hamiltonian is given by the sum of the Heisenberg interaction and the Kitaev interaction . Detailed phase behavior for such a model is discussed for a wide range of parameters .
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Research supported by the U.S. Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division.