SciPost Submission Page
Doping lattice non-abelian quantum Hall states
by Zhengyan Darius Shi, Carolyn Zhang, Senthil Todadri
Submission summary
| Authors (as registered SciPost users): | Zhengyan Darius Shi · Carolyn Zhang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202507_00022v1 (pdf) |
| Date accepted: | Oct. 13, 2025 |
| Date submitted: | July 7, 2025, 10:01 p.m. |
| Submitted by: | Zhengyan Darius Shi |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
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$_2$.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2025-9-17 (Invited Report)
The referee discloses that the following generative AI tools have been used in the preparation of this report:
check grammar.
Strengths
Report
My only suggestion is that it would strengthen the paper if the authors could propose a clear “smoking-gun” experimental signature of the anyon superconductor. In particular, what experiment could unambiguously identify that the mechanism of the charge-2e superconductivity arises from doping charge-e/4 non-Abelian anyons, rather than form other mechanism?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
1- The paper deals with the problem of doping non-abelian quantum Hall states. Building on the work by some of the authors on doping abelian quantum Hall states, the paper presents a general framework for analyzing this conceptually and experimentally important problem.
2- The paper is written with good pedagogy in mind, carefully introducing important concepts in the main text, which is supported by a number of appendices.
3- In keeping with the aforementioned prior work, this work carefully considers the effect of the underlying lattice and the fractionalization of translation symmetry.
4- The paper tackles both Moore-Read states and general k Read-Rezayi states, showcasing distinct behavior between odd/even k's. The field theoretic derivation is complemented by a heuristic argument for the origin of this difference.
5- The paper also presents a heuristic charge-flux unbinding picture for the origin of superconductivity, but also presents the limit of this approach.
Weaknesses
1- Relative to the analysis of the field theory when the components fields go into insulators (such as bIQH), the argument around bosonic CFL seemed a little less tight. On the other hand, it is probably a consequence of Fermi liquids generally being more difficult to deal with than insulators, and I don't think any improvement is needed to make the paper suitable for a publication.
2- As the paper admits itself, the analysis depends strongly on mean-field assumptions about the nature of the ground states. While the assumptions look reasonable, it is sometime hard to keep track of how many assumptions are being made. For example, what happens when the bosons do not go into bIQH? How reasonable is that scenario? The paper touches on some of these questions (e.g. when discussing k->infinity limit), but it is a bit opaque in my opinion.
Report
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
We thank the referee for their insightful comments and criticisms. Let us address them in order.
Regarding the first criticism, we agree that it is more difficult to justify the formation of bosonic CFL phases that appear in our analysis. However, we remark that the bosonic CFL phase is in any case only used as an intermediate step towards obtaining a charge-ordered Fermi liquid ground state. In other words, we can view the bosonic CFL as a valid description at some intermediate energy scales which exposes an inevitable pairing instability at the lowest temperature. The paired state ends up being an ordinary Fermi liquid, over which we have much better analytical control.
Regarding the second criticism, we agree that there is some freedom in choosing the mean-field state. We have added a comment in the discussion section emphasizing that we are always choosing the simplest translation-preserving mean-field consistent with filling constraints. For example, when bosons are at an even-integer filling, we always assume that it forms the simplest invertible phase which is the boson IQH state. If we allow ourselves to consider more complicated states with symmetry-breaking and/or topological order, the number of possible phases proliferates and there is no definite conclusion to be drawn. It would be great to have a more rigorous justification for this Occam's razor approach in the future, either through numerics or some more sophisticated analytical methods.
Author: Zhengyan Shi on 2025-11-21 [id 6059]
(in reply to Report 2 on 2025-09-17)We thank the referee for their insightful comments. Following their suggestion, we have included an extended discussion of experimental signatures, supported by a new Appendix F. Indeed, in the absence of disorder, the charge-2e superconductor obtained from doping e/4 anyons in the Pfaffian state is smoothly connected to a regular p-ip BCS superconductor (i.e. all the universal low-energy properties match). However, when impurities are present, the superconductor in the vicinity of the Pfaffian-SC transition is a novel anomalous vortex glass phase, with randomly pinned vortices carrying vorticity h/2e or -3h/2e. The density of these vortices have a 3:1 ratio, such that the global vorticity vanishes. This pattern is difficult to obtain through conventional BCS/Kohn-Luttinger pairing and may be viewed as a smoking-gun for the anyon-driven mechanism. In the new discussion, we derive this phase and also comment on other experimental probes for more exotic higher-charge superconductors and higher-charge Fermi liquids obtained from doping Read-Rezayi states at filling k/(k+2).