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Remarkable recent experiments have observed Mott insulating behavior and superconductivity in moire superlattices of twisted bilayer graphene near a magic twist angle. However, the nature of the Mott insulator, origin of superconductivity and an effective model remain to be determined. I will present our understanding of these phenomena. We propose a Mott insulator with intervalley coherence that spontaneously breaks U(1) valley symmetry, and describe a mechanism that selects this order over the competing magnetically ordered states favored by the Hunds coupling. We also identify symmetry related features of the nearly flat bands that are key to understanding the strong correlation physics and constrain any lattice model description. First, although the charge density is concentrated on the triangular lattice sites of the moire pattern, the Wannier states of a tight-binding model must be centered on different sites which form a honeycomb lattice. Next, spatially localizing electrons derived from the nearly flat bands necessarily breaks valley and other symmetries within any mean-field treatment, which is suggestive of a valley-ordered Mott state, and also dictates that additional symmetry breaking is present to remove symmetry-enforced band contacts. Tight-binding models describing the nearly flat mini-band are derived, which highlight the importance of further neighbor hopping and interactions. We discuss the consequences of this picture.

Recently, a web of quantum field theory dualities was proposed linking several problems in the study of strongly correlated quantum critical points and phases in two spatial dimensions. These dualities follow from a relativistic flux attachment duality, which relates a Wilson-Fisher boson with a unit of attached flux to a free Dirac fermion. While several derivations of members of the web of dualities have been presented thus far, none explicitly involve the physics of flux attachment, which in relativistic systems affects both statistics and spin. We discuss how this can be achieved in models of relativistic current loops, where the concept of relativistic flux attachment can be made precise. In this context, we provide simple, explicit “derivations” of members of the web of dualities. We describe some implications of this work for relativistic composite fermion theories arising in condensed matter physics, as well as new possibilities for deriving additional dualities using these techniques.