Interactions and Spin Orbit: from Weyls to Helical Spin Liquids

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Novel phases can result from the interplay of electronic interactions and spin orbit coupling. In the first part, we discuss a simple Hubbard model for the pyrochlore iridates, whose phase diagram contains topological insulator (TI) and various magnetic phases. The latter host the novel topological Weyl semimetal, whose excitations behave like Weyl fermions. In the second part we study a novel spin liquid that was proposed to arise in the iridates, the 3D topological Mott insulator: a fractionalized TI where the neutral spinons acquire a topologically non-trivial band structure. The low-energy behavior is dominated by the 2D surface spinons strongly coupled to a bulk gauge field. This phase is characterized by the helical nature of the spinon surface states and the dimensional mismatch between the latter and the gauge bosons. We discuss experimental signatures as well as the possibility of dyonic excitations and a non-trivial magneto-electric response.