SciPost Submission Page
Role of scaling dimensions in generalized noises in fractional quantum Hall tunneling due to a temperature bias
by Matteo Acciai, Gu Zhang, Christian Spånslätt
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Matteo Acciai |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202408_00011v1 (pdf) |
| Date submitted: | 2024-08-12 12:29 |
| Submitted by: | Acciai, Matteo |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Continued improvement of heat control in mesoscopic conductors brings novel tools for probing strongly correlated electron phenomena. Motivated by these advances, we comprehensively study transport due to a temperature bias in a quantum point contact device in the fractional quantum Hall regime. We compute the charge-current noise (so-called delta-$T$ noise), heat-current noise, and mixed noise and elucidate how these observables can be used to infer strongly correlated properties of the device. Our main focus is the extraction of so-called scaling dimensions of the tunneling anyonic quasiparticles, of critical importance to correctly infer their anyonic exchange statistics.
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:
Reports on this Submission
Report #2 by Kyrylo Snizhko (Referee 2) on 2024-9-23 (Invited Report)
Strengths
1. Systematic consideration of:
- various observables;
- in both limiting regimes;
- of a general class of models.
2. Detailed theoretical expressions. Useful for future reference.
Weaknesses
1. No clear punchline. It is not clear which of the observables show the most promise.
Report
The paper is of very high quality. It systematically addresses the question of transport observables induced by a temperature bias in a quantum Hall tunnelling contact. The authors address multiple observables: the charge noise, the heat current, the heat current noise, and even the mixed charge-heat noise. The authors analyse the limiting cases of small and large temperature bias and compare the asymptotic predictions with the exact solutions.
Further, the authors systematically introduce an effective single-particle picture, where the tunnelling properties of fractional quasiparticles are represented in terms of a Fermi distribution and power-law density of states.
Despite the high quality of the work, I do not feel it meets the SciPost acceptance criteria.
The authors state that their work meets two:
(i) Present a breakthrough on a previously-identified and long-standing research stumbling block;
(ii) Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work.
Concerning (i), I fail to see a long-standing stumbling block in the paper's consideration.
Concerning (ii). The paper does bring a systematic consideration of the scaling dimension into the temperature bias studies - which is an important aspect previously absent for the works in the area. However, the potential for follow-up work is rather narrow: performing experiments (potentially, on various observables considered in the work).
The paper may barely surpass criterion (ii), yet I do not see it opening a large space for thought.
However, I feel significantly more comfortable recommending the work to be published in SciPost Physics Core. It easily meets both acceptance criteria: addressing an important problem with a high degree of originality and significantly advance the knowledge in the field.
This will be an important reference work in the future for the people interested to perform one or another experiment and compare it to the theoretical predictions.
Requested changes
1. In the discussion of $|\mathcal{C}^{(4)}| \ll |\mathcal{C}^{(2)}|$ after Eq. (28), this relation is not evident from the expressions. It would be appropriate to refer the reader to Fig. 2.
2. When citing [77-79], it would be appropriate to cite also https://link.aps.org/doi/10.1103/PhysRevB.61.10929. This is the earliest work on the topic that I know.
3. In Eq. (67), the formula needs to be amended to account for the possibility of negative energies.
4. The expression in Eq. (77) looks like a conventional Landauer-Buttiker formula: all the Fermi functions and DOS correspond to the energy $E$, offset by the appropriate chemical potentials. At the same time, Eqs. (68-69) include integrands evaluated at $E$ and $-E$, which ruins the analogy with the Landauer-Buttiker formalism. I ask the authors to check the validity of these formulas; and if the mismatch persists, to comment about it in the text.
5. Ref. 102 is the same as Ref. 31. Please remove the duplicate.
Recommendation
Accept in alternative Journal (see Report)
Strengths
1- treats an important and current subject of research in the physics of nano electronic devices
2- develops an approach to quantum charge and heat transport in fractional quantum Hall quantum point contacts using the standard approach of chiral Luttinger liquids
3- provides a comprehensive overview of noise characteristics of heat and charge transport
4- develops a picture based on an effective density of states and noninteracting tunneling to explain the physics
Weaknesses
1- contains a huge amount of results and it is not clear what is the main focus
2- many results are presented as lengthy formulas and they are not interpreted
3- results are mainly of theoretical interest since quantities like the mixed noise are not measurable currently
4- only results in the perturbative regime of weak backscattering or weak tunneling are presented
Report
The authors study the charge and heat transport in a quantum point contact formed between two edge channels in the fractional quantum Hall regime. They focus on noise correlations in the transport, which should provide additional insight into the average currents. To this end, they present a comprehensive overview of the auto- and cross-correlations of charge and energy currents in a wide range of scaling parameters. The main goal is to show how the different quantities reflect the scaling dimensions and how they could be extracted experimentally.
In my opinion, the authors present a solid work that deserves to be published more or less in its present form. Regarding the acceptance criteria highlighted by the author, I find it less clear that they are all fulfilled: the manuscript does not really open a new path or research direction, but rather further develops a well-defined and established theoretical approach to study the various noise quantities. It is certainly a contribution to the field of fractional quantum Hall physics, but will most likely not lead to follow-up work outside this field. I'm also not convinced that it represents an important breakthrough of a research stumbling block. The way to relate the rather complicated results of the fully interacting theory to the effective non-interacting picture might have an impact on future research, but is somewhat hidden in the vast amount of results.
Given the strict criteria for acceptance in SciPost Physics, I would recommend that the authors make a substantial revision and highlight the main results in a compact form at the beginning. It is important that this summary be comprehensible to readers who are not specialists in chiral Luttinger liquids. Otherwise, the manuscript in its current form is acceptable for SciPost Physics Core, where it could be published without further review.
Recommendation
Ask for major revision
Author: Matteo Acciai on 2024-11-21 [id 4978]
(in reply to Report 1 on 2024-09-08)
We thank the Referee for the overall positive assessment of the quality our work, in particular that it is "a solid work that deserves to be published more or less in its present form". We would like to reply here in depth to the Referee's concerns about the relevance of our paper considering the journal's acceptance criteria.
The determination of scaling dimensions is an important problem in strongly correlated, one-dimensional systems, and in the FQH effect it has been a notorious stumbling block to match experimental results with theoretical predictions. Clearly, solving this problem calls for models that could explain the discrepancies, an avenue that has been explored in some detail in previous works [e.g., Phys. Rev. Lett. 88, 096404 (2002)]. At the same time, it is critical to assemble a broad range of complementary physical observables that can probe the scaling dimensions. This latter need is the main motivation for our work, and the spirit with which we present our results: highlighting a set of complementary tools that can be used to extract scaling dimensions in the FQH effect. In doing so, we have provided a systematic analysis of several noise observables under general conditions with temperature and voltage biases, which has been missing in the FQH literature. As acknowledged by the second Referee, our detailed analysis paves the way for detailed comparison to both state-of-the-art and future experiments.
Moreover, our work extends naturally towards using temperature-biased noise to identify the scaling dimension in a variety of tunneling setups. The most relevant and important extensions involve probing more complicated edge structures with non-Abelian character, where the presence of neutral modes requires the use of charge-insensitive observables, like the heat-current fluctuations that we have analyzed here. We remark here that several non-Abelian candidate edge structures, e.g., at filling $\nu=5/2$, involve such neutral modes. Having at hand tools to probe their presence is thus an important step towards distinguishing between such candidates and realizing non-Abelian anyons, a major goal in the broader physics community. Our work thus sets the stage to compute temperature-biased noise for such edges. Furthermore, our work can be adapted to related systems of interest, like quantum wires and quantum spin Hall edges, where the quantities presented are of clear relevance.
Following the Referee's recommendation, we have rewritten both the introduction and the outlook sections of the manuscript. We think that these improvements provide non-expert readers with a general understanding of the main results, together with the appropriate context in which they find applications.
As for the introduction, we made two main modifications: - We have provided a more complete and accessible description of the key physical quantities of interest (particularly the scaling dimension), together with a broader context explaining why the determination of this parameter is both important and challenging. - We have made a clearer summary of our results in a list format, with references to key equations, allowing readers to more easily navigate the main results.
In the outlook, we now explicitly discuss the advantages and disadvantages of the different types of noise that we address, suggesting possible follow-up work, and we also comment in more detail on the experimental relevance of our predictions.
With these modifications, we are confident that the main message of the work is both clearer and more accessible to a non-expert readership. We are therefore convinced that the work meets the criteria of Scipost Physics.
Author: Matteo Acciai on 2024-11-21 [id 4977]
(in reply to Report 2 by Kyrylo Snizhko on 2024-09-23)We thank the Referee for the very positive assessment of our work, in particular that it "is of very high quality".
Given that the criticism is mainly concerned with the journal's acceptance criteria and is thus similar to that of the first Referee, we refer to our response to Report#1, where we reply to this criticism in detail.
Here, we reply to the second Referee's listed points with requested changes: 1. We have implemented this change, below Eq. (28). 2. We have added the reference suggested by the Referee. 3. We thank the Referee for spotting this mistake. The formula is now correct. 4. The analogy works in both cases. We have modified the text below Eq. (70) to emphasize that both (77) and (68-69) can indeed be written as a standard Landauer Büttiker formula, with an appropriate energy-dependent effective transmission which is due to the correlated nature of the system. The main feature that we exploit in these formulas is that the particle-hole symmetry of the FQH edge Hamiltonian produces effective "transmission functions" that are even in energy. 5. The duplicate reference has been removed.