TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.6.150
TI  - Doping lattice non-Abelian quantum Hall states
PY  - 2025/12/09
UR  - https://scipost.org/SciPostPhys.19.6.150
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 6
SP  - 150
A1  - Shi, Zhengyan Darius
AU  - Zhang, Carolyn
AU  - Todadri, Senthil
AB  - 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 ($RR_k$) 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 $RR_k$ 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 $RR_k$ 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$_2$.
ER  -

@Article{10.21468/SciPostPhys.19.6.150,
	title={{Doping lattice non-Abelian quantum Hall states}},
	author={Zhengyan Darius Shi and Carolyn Zhang and Senthil Todadri},
	journal={SciPost Phys.},
	volume={19},
	pages={150},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.6.150},
	url={https://scipost.org/10.21468/SciPostPhys.19.6.150},
}