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Ashivin Vishwanath We investigate novel phases that emerge from the interplay of electron correlations and strong spin-orbit interactions. We find a novel phase, the topological semimetal, a three-dimensional magnetic phase, and argue that it may be realized in a class of pyrochlore iridates (such as Y2Ir2O7) based on LDA + U calculations. This state is a three-dimensionalanalog of graphene with linearly dispersing excitations and provides a condensed-matter realization of Weyl fermions that obeys a two-component Dirac equation. It also exhibits remarkable topological properties manifested by surface states in the form of Fermi arcs, which are impossible to realize in purely two-dimensional band structures. |