Doping a fractional quantum anomalous Hall insulator

Abstract

We study novel itinerant phases that can be accessed by doping a fractional quantum anomalous Hall (FQAH) insulator, with a focus on the experimentally observed Jain states at lattice filling $\nu =p/(2p+1)$. Unlike in the lowest Landau level, where charge motion is confined into cyclotron orbits, the charged excitations in the FQAH occupy Bloch states with well-defined crystal momenta. At a non-zero doping density, this enables the formation of itinerant states of the doped anyons just beyond the FQAH plateau region. Specializing to the vicinity of $\nu =2/3$, we describe a few possible such itinerant states. These include a topological superconductor with chiral neutral fermion edge modes as well as a more exotic Pair Density Wave (PDW) superconductor with non-trivial non-Abelian topological order. A Fermi liquid metal with a doping-induced period-3 charge density wave also occurs naturally in our analysis. This Fermi liquid (as well as the PDW) arises from pairing instabilities of a composite Fermi liquid metal that can emerge near filling $2/3$. Though inspired by the theory of anyon superconductivity, we explain how our construction is qualitatively different. At a general Jain filling $\nu =p/(2p+1)$, the same analytical framework leads to a wider variety of phases including higher-charge superconductors and generalized composite Fermi liquids. We predict unusual physical signatures associated with each phase and analyze the crossover between different temperature regimes. These results provide a proof-of-principle that exotic itinerant phases can be stabilized by correlations intrinsic to the FQAH setup.

33 pages + 18 pages appendices, 5 figures. (v2) minor edits and typo fixes (v3) journal version with streamlined discussion of SC* states from doping higher Jain states

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Cited by in corpus (12)

• Molecular anyons in fractional quantum Hall effect
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Apparent inconsistency between Streda formula and Hall conductivity in reentrant integer quantum anomalous Hall effect in twisted MoTe${}_2$
• Pathways from a chiral superconductor to a composite Fermi liquid
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Sensing the binding and unbinding of anyons at impurities
• Family of multilayer graphene superconductors with tunable chirality: Momentum-space vortices nucleated by a ring of Berry curvature
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Generalizing the composite fermion theory for fractional Chern insulators
• Quantized Transport of $\nu =2/3$ Fractional Quantum Hall Edge with Disordered Superconducting Proximity
• Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$