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Topological Crystalline Insulators in Transition Metal Oxides

Topological crystalline insulators (TCI) possess electronic states protected by crystal symmetries, rather than time-reversal symmetry. We show that the transition metal oxides with heavy transition metals are able to support nontrivial band topology resulting from mirror symmetry of the lattice. As an example, we consider pyrochlore oxides of the form A$_2$M$_2$O$_7$. As a function of spin-orbit coupling strength, we find two $Z_2$ topological insulator phases can be distinguished from each other by their mirror Chern numbers, each of which indicates a different TCI. We also derive an effective $\bf{k\cdot p}$ Hamiltonian, similar to the model introduced for $\mathrm{Pb_{1-x}Sn_{x}Te}$, and discuss the effect of an on-site Hubbard interaction on the topological crystalline insulator phase using slave-rotor mean-field theory, which predicts new classes of topological quantum spin liquids.