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We study the finite temperature and magnetic field phase diagram of electronson the pyrochlore lattice subject to a local repulsion as a model for thepyrochlore iridates. We provide the most general symmetry-allowed Hamiltonian,including next-nearest neighbour hopping, and relate it to a Slater-Kosterbased Hamiltonian for the iridates. It captures Lifshitz and/or thermaltransitions between several phases such as metals, semimetals, topologicalinsulators and Weyl semimetals, and gapped antiferromagnets with differentorders. Our results on the charge conductivity, both DC and optical, Hallcoefficient, magnetization and susceptibility show good agreement with recentexperiments and provide new predictions. As such, our effective model shedslight on the pyrochlore iridates in a unified way.

Pyrochlore electrons under pressure, heat and field: shedding light on the iridates