Doping a Fractional Quantum Anomalous Hall Insulator

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>ν</a:mi><a:mo>=</a:mo><a:mi>p</a:mi><a:mo>/</a:mo><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:mi>p</a:mi><a:mo>+</a:mo><a:mn>1</a:mn><a:mo stretchy="false">)</a:mo></a:math>. 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 nonzero doping density, this feature enables the formation of itinerant states of the doped anyons just beyond the FQAH plateau region. Focusing on the vicinity of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>ν</e:mi><e:mo>=</e:mo><e:mn>2</e:mn><e:mo>/</e:mo><e:mn>3</e:mn></e:math>, we describe a few possible itinerant states, including a topological superconductor with chiral neutral fermion edge modes as well as a more exotic pair density wave (PDW) superconductor with 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mn>2</g:mn><g:mo>/</g:mo><g:mn>3</g:mn></g:math>. Though inspired by the theory of anyon superconductivity, we explain how our construction is qualitatively different. At a general Jain filling <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>ν</i:mi><i:mo>=</i:mo><i:mi>p</i:mi><i:mo>/</i:mo><i:mo stretchy="false">(</i:mo><i:mn>2</i:mn><i:mi>p</i:mi><i:mo>+</i:mo><i:mn>1</i:mn><i:mo stretchy="false">)</i:mo></i:math>, 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.