# Mechanisms of Andreev reflection in quantum Hall graphene

### Submission summary

 As Contributors: Anton Akhmerov · Antonio Manesco Arxiv Link: https://arxiv.org/abs/2103.06722v3 (pdf) Code repository: https://doi.org/10.5281/zenodo.4597080 Data repository: https://doi.org/10.5281/zenodo.4597080 Date submitted: 2022-02-16 11:43 Submitted by: Manesco, Antonio Submitted to: SciPost Physics Core Academic field: Physics Specialties: Condensed Matter Physics - Theory Condensed Matter Physics - Computational Approaches: Theoretical, Computational

### Abstract

We simulate a hybrid superconductor-graphene device in the quantum Hall regime to identify the origin of downstream resistance oscillations in a recent experiment [Zhao et. al. Nature Physics 16, (2020)]. In addition to the previously studied Mach-Zehnder interference between the valley-polarized edge states, we consider disorder-induced scattering, and the previously overlooked appearance of the counter-propagating states generated by the interface density mismatch. Comparing our results with the experiment, we conclude that the observed oscillations are induced by the interfacial disorder, and that lattice-matched superconductors are necessary to observe the alternative ballistic effects.

###### Current status:
Editor-in-charge assigned

Dear editor,

We thank the referees for their evaluation. We reviewed our manuscript according to the reports. Hopefully, the implemented changes made our manuscript suitable for publication.

We also want to bring to the referees' and readers' attentions that this work was recently presented as a satellite talk the "Andreev reflection in quantum Hall systems: 2021 state of the union" workshop hosted by the Virtual Science Forum. The video recording includes discussions about the work that might be relevant during the evaluation of the manuscript.

### List of changes

Explicitly wrote the conditions to observe the phenomenon described in Sec. 4. Reformulated the justification for a small coupling between chiral edge states in the clean limit. Added a figure panel to show approximate valley conservation in disorder boundaries. Added further details about our simulations.

### Submission & Refereeing History

Resubmission 2103.06722v3 on 16 February 2022
Submission 2103.06722v2 on 1 October 2021

## Reports on this Submission

### Report

The authors have addressed several, but not all, of my concerns.

One I would like to insist on, namely point 1 of my first report regarding smoothness of the confining potential. The authors replied, "The only important effect of a smooth confining potential is to introduce additional counter-propagating modes, as analyzed in Sec. 4. ...".

I do not agree. For instance, smoothness is certainly required for the derivation of Eq. (2) given in App. B, where the superconductor is taken to be a honeycomb lattice with the same chemical potential as the graphene. Furthermore, since the spectrum of the two modes in Eq. (2) is degenerate (with respect to $k_0$), Eq. (2) is written for the situation in which the NS coupling is valley isotropic. The usual argument for valley isotropic coupling given in, e.g., Titov and Beenakker relies on a smooth interface. The authors may have other arguments for Eq. (2) in mind but these are not given---the argument written in the paper depends on smoothness.

The authors decided not to implement several of the changes that I brought up in my first report. I think that these would have been beneficial to the reader-- I'm sure I'm not the only reader who was curious about how many disorder configurations were studied, confused by the distinction between the "N" and "QH" in the figures, or had trouble finding the tight-binding parameters, for instance---but I do not feel strongly about them. Likewise, while I still find the authors' qualitative argument for the magnitude of intervalley scattering at the top of p. 4 confusing and suspect, I am willing to give it a pass.

In summary, there is one issue that still requires attention---the smoothness of the potential. Once this is taken care of, the paper will be suitable for publication.

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