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Abstract

We investigate interaction-driven integer quantum Hall states realized in Landau levels of monolayer graphene when two out of its four nearly degenerate spin-valley flavors are filled. By employing a model that accounts for interactions beyond pure delta-functions as well as Zeeman and substrate-induced valley potentials, we demonstrate the existence of a delicate competition of several phases with spontaneous generation of spin-valley entangle-ment, akin to the spontaneous appearance of spin-orbit coupling driven by interactions. We encounter a particular phase that we term the entangled-Kekule-antiferromagnet (E-KD-AF) which only becomes spin-valley entangled under the simultaneous presence of Zeeman and substrate potentials, because it gains energy by simultaneously canting in the spin and valley spaces, by combining features of a canted antiferromagnet and a canted Kekule state. We quantify the degree of spin-valley entanglement of the many competing phases by computing their bipartite concurrence.