Mechanisms of Andreev reflection in quantum Hall graphene

We thank the referee for the feedback.

The main remaining concern of the referee is our claim that the main role of the smooth electrostatic potential is limited to introducing additional counter-propagating modes. The referee lists the valley-isotropic superconducting pairing used in the App. B as an additional important effect of the smoothness of the electrostatic potential. The referee then argues that because we use the appendix to support Eq. 2, the said equation therefore also relies on the smoothness of the electrostatic potential.

Furthermore, the referee noticed missing details on how the simulations were performed. We now provide them in the manuscript.

We provide a detailed answer to the report below.

Part 1: Electrostatic potential at the NS interface

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.

Following the referee's remarks we have realized that the manuscript did not present our argument in a clear fashion. We have used this opportunity to clarify our logic.

The form of Eq. 2 is completely constrained by the particle-hole symmetry. However, in order to relate it to the NS conductance one needs to identify the degrees of freedom in terms of valleys and electrons or holes. Our claim that the two modes are nearly valley-polarized is supported on the one hand by the qualitative argument that we have discussed in the previous review round (the one that the referee is "willing to give it a pass"), and on the other hand by the numerical evidence where we explicitly compute the valley polarization of different eigenstates in presence of strong intervalley scattering due to the lattice mismatch. To fully addrees the referee concerns regarding abrupt potential changes we have now also demostrated the same approximate valley conservation in presence of an atomically sharp potential step (the newly added Fig. 7). The referee, however, is correct in claiming that the App. B relies on the valley-isotropic pairing. The logical relation between the App. B and the Eq. 2 was not clear in the previous version. Specifically, the App. B serves only as an illustration of how Eq. 2 can be derived, rather than as its foundation.

We have rewritten the discussion to make the above points clear. In addition, we have rewritten the discussion in the App. B, and we now include intervalley coupling in the Eq. (12). We improved the presentation of the results by computing the valley polarization of the chiral Andreev states, once again confirming our qualitative argument.

Part 2: Missing information in the manuscript

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

We verified that the qualitative behavior reported is independent on the random seed used to generate the disorder landscape. We now provide in the Zenodo repository the data from one more calculation and modified the code to set the chosen seed as an extra parameter and state in the manuscript that the results are representative. However, we did not perform a sufficient amount of calculations to be able to address universal quantitative behavior. Since this work aims to report possible mechanisms for the experimental observations, a systematic quantitative analysis is beyond the scope of the current mansucript. A quantitative analysis was recently done elsewhere (arXiv:2201.00273).

Figure 1. Downstream conductance with the same system parameters as Fig. 3 (d) in the manuscript but with a different disorder realization. Image available here.

[I'm not the only reader...] confused by the distinction between the "N" and "QH" in the figures

As long as the contact resistance of the normal leads is negligible, the distinction is irrelevant. There are two possible choices to obtain a vanishing reflection probability: 1. create a semi-infinite metallic lead with large density of states; 2. create a semi-infinite lead with the same tight-binding description as the scattering region.

Option 1 has the disadvantage of resulting in a large scattering matrix due to the large number of propagating modes. Therefore, in our transport simulations, we choose option 2 to keep a reduced computational cost. We now explicitly state it in the manuscript.

[I'm not the only reader... who] had trouble finding the tight-binding parameters

In the previous response we added all the missing parameters we could find. We reviewed our manuscript one more time and added system's dimensions that were missing.

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.

As outlined in our response in the first part, we have expanded the argument. While we agree with the referee that this argument only qualitative, we also demonstrate that it fully agrees with the numerical simulations.

* Computed the corresponding valley expectation value in the bandstructure calculations.
* Added Fig. 7 with bandstructure and downstream conductance of a system interface with sharp electrostatic potential.
* Clarified the logic to obtain the effective Hamiltonian in Eq. 2.
* Clarified the logic in App. B and emphasized that the Appendix serves only as an illustration of how Eq. 2 can be derived, rather than as its foundation.
* Refactored the code to the user to generate multiple disorder realizations and added an illustrative case in the reply to the referee.
* Added missing parameters in the manuscript.

The changes in the manuscript are highlighted in the PDF available here: https://surfdrive.surf.nl/files/index.php/s/9H0b4Ytaf5rfypI