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In 5d transition metal oxides such as the iridates, novel properties arisefrom the interplay of electron correlations and spin-orbit interactions. Weinvestigate the electronic structure of the pyrochlore iridates, (such asY$_{2}$Ir$_{2}$O$_{7}$) using density functional theory, LDA+U method, andeffective low energy models. A remarkably rich phase diagram emerges on tuningthe correlation strength U. The Ir magnetic moment are always found to benon-collinearly ordered. However, the ground state changes from a magneticmetal at weak U, to a Mott insulator at large U. Most interestingly, theintermediate U regime is found to be a Dirac semi-metal, with vanishing densityof states at the Fermi energy. It also exhibits topological properties -manifested by special surface states in the form of Fermi arcs, that connectthe bulk Dirac points. This Dirac phase, a three dimensional analog ofgraphene, is proposed as the ground state of Y$_{2}$Ir$_{2}$O$_{7}$ and relatedcompounds. A narrow window of magnetic `axion' insulator, with axion parameter$\theta=\pi$, may also be present at intermediate U. An applied magnetic fieldinduces ferromagnetic order and a metallic ground state.

Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator