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 [1]. 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 [111] crystallographic axis. A variety of novel phenomena are predicted, including quantum spin Halll effects [2] and anomalous Hall effects [3]. 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 [4]. Detailed phase behavior for such a model is discussed for a wide range of parameters [5].

[1] A. Ohtomo & H. Y. Hwang, Nature 427, 423?426 (2004).

[2] D. Xiao, W. Zhu, Y. Ran, N. Nagaosa, and S. Okamoto, Nat. Commun. 2:596 doi: 10.1038/ncomms1602 (2011).

[3] K.-Y. Yang, W. Zhu, D. Xiao, S. Okamoto, Z. Wang, and Y. Ran, Phys. Rev. B 84, 201104(R) (2011).

[4] S. Okamoto, arXiv:1210.2290.

[5] S. Okamoto, arXiv:1212.5218

Research supported by the U.S. Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division.