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

We study the finite temperature and magnetic-field phase diagram of electrons on the pyrochlore lattice subject to a local repulsion as a model for the pyrochlore iridates. We provide the most general symmetry-allowed Hamiltonian, including next-nearest-neighbor hopping, and relate it to a Slater-Koster-based Hamiltonian for the iridates. It captures Lifshitz and/ or thermal transitions among several phases, such as metals, semimetals, topological insulators andWeyl semimetals, and gapped antiferromagnets with different orders. Our results on the charge conductivity, both dc and optical, Hall coefficient, magnetization, and susceptibility show good agreement with recent experiments and provide new predictions. As such, our effective model sheds light on the pyrochlore iridates in a unified way.