Topological and magnetic phases of interacting electrons in the pyrochlore iridates

We construct a model for interacting electrons with strong spin-orbit coupling in the pyrochlore iridates. We establish the importance of the direct hopping process between the Ir atoms, and use the relative strength of the direct and indirect hopping as a generic tuning parameter to study the correlation effects across the iridates family. We predict quantum phase transitions between conventional and/or topologically nontrivial phases. At weak coupling, we find topological insulator and metallic phases. As one increases the interaction strength, various magnetic orders emerge. The topological Weyl semimetal phase is found to be realized in these different orders, one of them being the all-in/all-out pattern. Our findings establish the possible magnetic ground states for the iridates and suggest the generic presence of the Weyl semimetal phase in correlated magnetic insulators on the pyrochlore lattice. We discuss the implications for existing and future experiments.