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Topological states in double monolayer graphene
by Ying-Hai Wu
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Submission summary
| Authors (as registered SciPost users): | Yinghai Wu |
| Submission information | |
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| Preprint Link: | scipost_202111_00063v1 (pdf) |
| Date submitted: | 2021-11-30 15:52 |
| Submitted by: | Wu, Yinghai |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Motivated by the experiments on double monolayer graphene that observe a variety of fractional quantum Hall states [Liu et al., Nat. Phys. 15, 893 (2019); Li et al., Nat. Phys. 15, 898 (2019)], we study the special setting in which two monolayers have different areas. It has not been considered before and allows us to construct a class of exotic topological states. The elementary excitations of these states do not carry fractional charges but obey fractional statistics. This is in sharp contrast to all previously studied cases, where the two properties are intimately connected and serve as hallmarks of fractional quantum Hall states. Numerical calculations are performed to demonstrate that some states can be realized with realistic parameters.
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Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2022-4-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202111_00063v1, delivered 2022-04-07, doi: 10.21468/SciPost.Report.4882
Report
Inspired by recent experiments on fractional quantum Hall states in double-layer graphene, in this manuscript, the author proposed a new topological state where excitations obey fractional statistics but do not carry a fractional U(1) charge. The model is realized by two graphene layers where electrons cannot hop to the other layer but interact with electrons in the other layer. A key setup to realize the proposed state is that the two layers have different areas such that they can have different fluxes under a uniform magnetic field in the z-direction. I can recommend this work for publication if the authors can address my main concern:
1. Suppose the top layer has a smaller area. Then, in Eq. (1), r1 is restricted in this smaller area (A1) while r2 is not restricted. That means an inhomogeneous Coulomb potential for the bottom layer: r2 inside A1 feels a much stronger Coulomb potential than r2 outside A1. However, in the author's numerical calculation, the two layers are treated as two homocentric spheres with a radius difference of D. Clearly, the bottom layer feels a homogeneous Coulomb potential from the top layer in the numerical setup. My question is, will the inhomogeneity change the true ground state in the realistic system? In the limit where D is much smaller than the sample size, it is hard to believe that all the electrons in the second layer interact equally with the top layer.
2. If a large D comparable to the system size is needed to justify the homogeneity, will it be a reasonable number for the realistic system?
Besides the above concerns, I also have some questions/suggestions:
1. Even though the excitations do not carry a fractional global U(1) charge, they do carry some fractional charge (Eq. (7)) because the system has a U(1)xU(1) symmetry since there are no hoppings between the two layers. Is the fractional statistic stable if one breaks the individual U(1) symmetries?
2. Suppose the U(1)xU(1) symmetry is respected. Is it possible to detect the fractional e_up/e_down from transport measurement inside a single layer?
Report #1 by Anonymous (Referee 3) on 2022-3-23 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202111_00063v1, delivered 2022-03-23, doi: 10.21468/SciPost.Report.4762
Report
The manuscript by Y.-H. Wu studied a bilayer quantum Hall system motivated by recent experiments on double monolayer graphene quantum Hall effect. The author used various approaches including numerical methods, composite fermion mean field, and Chern-Simons theory to analyze bilayer quantum Hall systems with each layer having different areas. A class of bilayer quantum Hall states was proposed and was found to be a promising candidate ground state of a realistic Hamiltonian. An interesting feature of such quantum Hall states is the existence of anyons that carry integer charge. The manuscript studied an experimentally relevant problem and has interesting discoveries, I am happy to recommend the manuscript after minor revisions are made (see below).
1. It is not too rare that a topological ordered state has no symmetry fractionalization. Examples I know of are various non-Abelian chiral spin liquids in spin systems with Ising anyons (eg. $SU(2)_2$ in spin-1 system and Kitaev's sixteen fold way), in which the Ising anyon is charge neutral. I think there might be examples of fractional quantum Hall states of fermions as well. It would be good if the author can include some of such references.
2. On page 3 before Eq.(1), the author assumed that $N_e^t=N_e^b$. Is this assumption realistic for experiments, and how much would the conclusion change if this assumption is relaxed?
3. I am a bit confused by the analysis of flux attachment in the first paragraph of Sec. 3 Results. The author wrote, "For the top monolayer, $2N_e^t+N_e^b$ fluxes are attached to each electron so $\widetilde N_\phi^t = -N_e^t$, ...". The counting doesn't seem to be right: the total effective flux should be $N_e^t+N_e^b - N_e^t(2N_e^t+N_e^b)$. I guess there is a typo about how many fluxes are attached to each electron?