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Doping lattice non-abelian quantum Hall states

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arxiv 2505.02893 v2 pith:5V4VMTHN submitted 2025-05-05 cond-mat.str-el cond-mat.supr-conhep-th

Zhengyan Darius Shi , Carolyn Zhang , T. Senthil This is my paper
classification cond-mat.str-elcond-mat.supr-conhep-th
keywords non-abeliandopingquantumstatestatesanyonchargecsgl
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abstract

We study quantum phases of a fluid of mobile charged non-abelian anyons, which arise upon doping the lattice Moore-Read quantum Hall state at lattice filling $\nu = 1/2$ and its generalizations to the Read-Rezayi ($\mathrm{RR}_k$) sequence at $\nu = k/(k+2)$. In contrast to their abelian counterparts, non-abelian anyons present unique challenges due to their non-invertible fusion rules and non-abelian braiding structures. We address these challenges using a Chern-Simons-Ginzburg-Landau (CSGL) framework that incorporates the crucial effect of energy splitting between different anyon fusion channels at nonzero dopant density. For the Moore-Read state, we show that doping the charge $e/4$ non-abelion naturally leads to a fully gapped charge-$2$ superconductor without any coexisting topological order. The chiral central charge of the superconductor depends on details of the interactions determining the splitting of anyon fusion channels. For general $\mathrm{RR}_k$ states, our analysis of states obtained by doping the basic non-abelion $a_0$ with charge $e/(k+2)$ reveals a striking even/odd pattern in the Read-Rezayi index $k$. We develop a general physical picture for anyon-driven superconductivity based on charge-flux unbinding, and show how it relates to the CSGL description of doped abelian quantum Hall states. Finally, as a bonus, we use the CSGL formalism to describe transitions between the $\mathrm{RR}_k$ state and a trivial period-$(k+2)$ CDW insulator at fixed filling, driven by the gap closure of the fundamental non-abelian anyon $a_0$. Notably, for $k=2$, this predicts a period-4 CDW neighboring the Moore-Read state at half-filling, offering a potential explanation of recent numerical observations in models of twisted MoTe$_2$.

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Charge-6e superconductivity from doping SU(3) spin liquids

    cond-mat.str-el 2026-07 conditional novelty 7.0 of 10

    Doping SU(3) spin liquids can yield charge-6e superconductors, including a non-Abelian chiral version with h/(6e) vortices.

  2. Topological Charge-2ne Superconductors

    cond-mat.str-el 2025-12 conditional novelty 7.0 of 10

    Topological charge-2ne superconductors are shown to be realizable from Read–Green ingredients and from cluster quantum Hall states, with explicit Chern–Simons/CFT descriptions and non-Abelian anyon content.

  3. Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor

    cond-mat.str-el 2025-10 conditional novelty 7.0 of 10

    Repulsive interactions turn a half-filled Rashba-coupled Landau level proximitized by an s-wave superconductor into a topological superconductor.

  4. Anyon dispersion from non-uniform magnetic field on the sphere

    cond-mat.str-el 2025-06 conditional novelty 7.0 of 10

    For a specifically chosen non-uniform magnetic field on the sphere, Laughlin quasiholes acquire an analytically computed, interaction-generated energy dispersion whose functional form is exact up to a fitted overall scale.

  5. Fractionalized metals from doped anyons: Application to tMoTe2

    cond-mat.str-el 2026-07 conditional novelty 6.5 of 10

    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.

  6. Coloring in anyon superconductivity

    cond-mat.str-el 2026-07 conditional novelty 6.0 of 10

    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.

  7. Color superconductors and holon metals from doping a Fractional Chern insulator

    cond-mat.str-el 2026-07 conditional novelty 6.0 of 10

    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.

  8. Non-Abelian topological superconductivity from melting Abelian fractional Chern insulators

    cond-mat.str-el 2025-12 conditional novelty 6.0 of 10

    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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