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Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
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Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
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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 moir\'e 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-BCS mechanism for electron pairing in a well-controlled limit, relying crucially on the interplay between electron correlations and band topology.
Forward citations
Cited by 11 Pith papers
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Anyon Dispersion in Aharonov-Casher Bands and Implications for Twisted MoTe${}_2$
Laughlin quasiholes in an Aharonov-Casher band acquire a finite dispersion, of order 1 meV in twisted MoTe2, produced by non-uniform quantum geometry and the anyon Berry phase.
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Anyon superfluidity of excitons in quantum Hall bilayers
Finite density of anyonic excitons in bilayer Laughlin states at total filling 2/3 yields an exciton superfluid with specific bulk topological order, edge spectrum, and stiffness scaling as |δν|^{1/2} near Halperin (1...
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Fractionalized metals from doped anyons: Application to tMoTe2
Lightly doped 2/3 FQAH anyons form U(3)-symmetric Z3 Orthogonal Metals of charge-1/3 fermions that explain large resistivity and pair into ordinary 2e superconductors.
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Coloring in anyon superconductivity
Doping the ν=2/3 FQAH state produces a unifying 'quark metal' of charge-e/3 fermions whose superconducting and ferromagnetic instabilities reproduce and extend the known zoo of anyon-driven superconductors.
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Color superconductors and holon metals from doping a Fractional Chern insulator
Doping a C=1/3 fractional Chern insulator can produce charge-2e superconductors and holon metals described by a nine-pocket SU(3) parton theory.
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Topological superconductivity from Abelian fractional Chern insulators
U(3) infrared parton theory unifies a ν=1/3 FCI with topological superconductors (SC* preserving U(1)_3, chiral TSC with c_-=3/2, strong-pairing with c_-=3) and a σ_xy=0 CDW.
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Non-Abelian topological superconductivity from melting Abelian fractional Chern insulators
Bandwidth tuning can melt a single ν=2/3 Jain fractional Chern insulator into five distinct superconductors, two with non-Abelian order, with higher-charge variants predicted at general Jain fillings.
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Topological Chiral Superconductivity in the Triangular-Lattice Hofstadter-Hubbard Model
DMRG and quantum Monte Carlo show that the lightly doped triangular Hofstadter-Hubbard model supports chiral superconductivity with power-law pairing and spin Chern number 2.
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Pairing around a Single Dirac Point: A Unifying View of Kohn-Luttinger Superconductivity in Chern Bands, Quarter Metals, and Topological Surface States
Higher-order k corrections to Dirac dispersion enable Kohn-Luttinger superconductivity, producing topological p-ip pairing in broken-TR systems and anisotropic or warped pairings on TI surfaces.
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Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
Disorder effects on anyon composite fermion bands drive plateau transitions that explain observed superconductivity and RIQAH phases near doped nu_e=2/3 FQAH states in twisted MoTe2.
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Superconductivity and non-Fermi liquid metals in a charge-1/3 anyon fluid
Doping a fractional Chern insulator yields an anyon fluid that can form an SC* superconductor with residual Z2 order or a non-Fermi liquid Z3 orthogonal metal.
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