Superconductivity, correlated insulators, and Wess-Zumino-Witten terms in twisted bilayer graphene

Recent experiments on twisted bilayer graphene have shown a high-temperature parent state with massless Dirac fermions and broken electronic flavor symmetry. Superconductivity and correlated insulators are thought to emerge from this parent state at lower temperatures. We propose that the superconducting and correlated insulating orders are connected by Wess-Zumino-Witten terms, so that defects of one order contain quanta of another order and skyrmion fluctuations of the correlated insulator are a ‘mechanism’ for superconductivity. We will present a comprehensive listing of plausible low-temperature orders for the correlated insulators, and the possible parent flavor symmetry breaking orders at charge neutrality and half-filling. We consider both singlet and triplet pairings for the superconducting state. We will also discuss how our classification may constrain possible order parameters for correlated insulators, superconductivity, and the high-temperature parent state in experiments.