Microscopic Mechanism of Anyon Superconductivity Emerging from Fractional Chern Insulators

Abstract

Fractional quantum Hall (FQH) states and superconductors typically require contrasting conditions, yet recent experiments have observed them in the same device. A natural explanation is that mobile anyons give rise to superconductivity; however, this mechanism requires binding of minimally charged anyons to establish an unusual energy hierarchy. This scenario has mostly been studied with effective theories, leaving open the question of how anyon superconductivity can arise from repulsive interactions. Here, we show that such an energy hierarchy of anyons arises naturally in fractional Chern insulators (FCIs) at fillings $\nu =2/(4p\mp 1)$ when they are driven toward a quantum phase transition into a ``semion crystal'' -- an exotic charge-density-wave (CDW) insulator with semion topological order. Near the transition, Cooper-pair correlations are enhanced, so that a conventional charge-2e superconductor appears with doping. Guided by these insights, we analyze a microscopic realization in a repulsive Hubbard-Hofstadter model. Tensor network simulations at $\nu =2/3$ reveal a robust FCI that, with increasing interactions, transitions into the semion crystal. Finding a stable semion crystal in such a minimal model highlights it as a viable state competing with conventional CDW and FQH states. In the vicinity of this transition, we find markedly enhanced Cooper pairing, consistent with our theory that the 2e/3 anyon is cheaper than a pair of isolated e/3 anyons. Doping near the transition should in general lead to doping Cooper pairs and charge-2e superconductivity, with chiral edge modes of alternating central charge $c=\pm 2$, which can coexist with translation symmetry breaking. Our framework unifies recent approaches to anyon superconductivity, reconciles it with strong repulsion and provides guidance for flat band moiré materials such as recent experiments in twisted MoTe${}_2$.

19 pages main text + 9 pages Appendix and References; 7 + 2 figures

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Cited by in corpus (7)

• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
• Pathways from a chiral superconductor to a composite Fermi liquid
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Quantum Hall to Chiral Spin Liquid transition in a Triangular Lattice Hofstadter-Hubbard Model
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor