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We argue that the combination of strong repulsive interactions and high magnetic fields can generate electron pairing and superconductivity. Inspired by the large lattice constants of moiré materials, which make large flux per unit cell accessible at laboratory fields, we study the triangular lattice Hofstadter–Hubbard model at one-quarter flux quantum per plaquette, where previous literature has argued that a chiral spin liquid separates a weak-coupling integer quantum Hall phase and a strong-coupling topologically trivial antiferromagnetic insulator at a density of one electron per site. We argue that topological superconductivity emerges upon doping in the vicinity of the integer quantum Hall to chiral spin liquid transition. We employ exact diagonalization and density matrix renormalization group methods to examine this theoretical scenario and find that electronic pairing indeed occurs on both sides of criticality over a remarkably broad range of interaction strengths. On the chiral spin liquid side, our results provide a concrete model realization of the long-hypothesized mechanism of anyon superconductivity. Our study thus establishes a beyond-Bardeen-Cooper-Schrieffer route to electron pairing in a well-controlled limit, relying crucially on the interplay between electron correlations and band topology. 

Quantum spin liquids are exotic phases of quantum matter especially pertinent to many modern condensed matter systems. Dirac spin liquids (DSLs) are a class of gapless quantum spin liquids that do not have a quasi-particle description and are potentially realized in a wide variety of spin 1 / 2 magnetic systems on 2 d lattices. In particular, the DSL in square lattice spin- 1 / 2 magnets is described at low energies by ( 2 + 1 ) d quantum electrodynamics with N f = 4 flavors of massless Dirac fermions minimally coupled to an emergent U ( 1 ) gauge field. The existence of a relevant, symmetry-allowed monopole perturbation renders the DSL on the square lattice intrinsically unstable. We argue that the DSL describes a stable continuous phase transition within the familiar Neel phase (or within the Valence Bond Solid (VBS) phase). In other words, the DSL is an "unnecessary" quantum critical point within a single phase of matter. Our result offers a novel view of the square lattice DSL in that the critical spin liquid can exist within either the Neel or VBS state itself, and does not require leaving these conventional states. 

The recent observation of fractional quantum anomalous Hall (FQAH) states in tunable moiré materials encourages study of several new phenomena that may be uniquely accessible in these platforms. Here, we show that an isolated localized anyon of the FQAH state will nucleate a “halo” of charge-density-wave (CDW) order around it. We demonstrate this effect using a recently proposed quantum Ginzburg-Landau theory that describes the interplay between the topological order of the FQAH state and the broken-symmetry order of a CDW. The spatial extent of the CDW order will, in general, be larger than the length scale at which the fractional charge of the anyon is localized. The strength and the decay length of the CDW order around anyons induced by doping or the magnetic field differ qualitatively from those nucleated by a random potential. Our results leverage a precise mathematical analogy to earlier studies of the superfluid-CDW competition of a system of lattice bosons which has been used to interpret the observed CDW halos around vortices in high-Tc superconductors. We show that measurement of these patches of CDW order can give an indirect route to measuring the fractional charge of the anyon. Such a measurement may be possible by scanning tunneling microscopy in moiré systems.