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Reconstructing the potential configuration in a high-mobility semiconductor heterostructure with scanning gate microscopy

by Gaëtan J. Percebois, Antonio Lacerda-Santos, Boris Brun, Benoit Hackens, Xavier Waintal, Dietmar Weinmann

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Dietmar Weinmann
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-11-28
Date submitted: 2023-11-10 12:38
Submitted by: Weinmann, Dietmar
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Experiment
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Experimental, Computational


The weak disorder potential seen by the electrons of a two-dimensional electron gas in high-mobility semiconductor heterostructures leads to fluctuations in the physical properties and can be an issue for nanodevices. In this paper, we show that a scanning gate microscopy (SGM) image contains information about the disorder potential, and that a machine learning approach based on SGM data can be used to determine the disorder. We reconstruct the electric potential of a sample from its experimental SGM data and validate the result through an estimate of its accuracy.

Published as SciPost Phys. 15, 242 (2023)

Author comments upon resubmission

Following the editorial recommendation, we have replied to the three reports on our work, and we have revised the manuscript taking into account the comments made by the referees. We herewith resubmit our paper "Reconstructing the potential configuration in a high-mobility semiconductor heterostructure with scanning gate microscopy" for publication in SciPost Physics.

List of changes

- We have extended the description of SGM in the introduction.

- We have added a new footnote (2) in Sec. 2.1, stating that the tip never touches the surface of the sample.

- We have added information about the experimental determination of the Fermi wavelength in Sec. 2.1.

- We have mentioned the value of the ratio between the Fermi wavelength and the tight-binding lattice constant in Sec. 3.

- A remark about the limited importance of electronic correlations has been added at the end of Sec. 2.

- In the first paragraph of Sec. 4, we mention Figure 9 that shows the training-set size dependence of the accuracy.

- The risk of possible general bias of the method mentioned by referee 3 is discussed in the new second-to-last paragraph in Sec. 5.

- At the end of Sec. 5, a new paragraph mentions some possible uses of the proposed method.

- We have corrected a few typos. We have also updated the list of references and funding information.

Reports on this Submission

Anonymous Report 3 on 2023-11-21 (Invited Report)


I appreciate the effort of the authors to address the points raised in my previous report and the reports of the other referees. This adds to the high quality of the paper.
I recomment publication in the present form.

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Anonymous Report 2 on 2023-11-13 (Invited Report)


I appreciate the authors' comprehensive consideration of all suggestions from the referees and their adequate response to them. This work is significant, and I recommend its publication in SciPost Physics.

I would like to hear the authors' thoughts on the issue of 'locality' that I raised in the last round of review. Although I acknowledge that it might be beyond the scope of this work and a definitive answer is not obligatory, it remains an interesting point:
Specifically, if the SGM of an area A produces a random potential related to A, and the data is then cropped into a sub-area B⊆A (potentially close to a feature-rich side), will the machine learning algorithm still produce an accurate random potential for the cropped area B⊆A? If not, how can this violation of locality be understood?

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Author:  Dietmar Weinmann  on 2023-11-29  [id 4158]

(in reply to Report 2 on 2023-11-13)
answer to question

The referee asks about the locality of the relation between the disorder potential and the SGM-response. Following the remark, we have investigated the dependence of the disorder prediction quality on the size of the SGM scan. The results of that study are presented in the attached file.



Anonymous Report 1 on 2023-11-13 (Invited Report)


The authors have significantly improved the manuscript and incorporated all the requests made by the referees. It is my understanding that the manuscript meets all the acceptance criteria for publication. This is a timely contribution to both mesoscopic physics as well as to the use of machine learning techniques for solving inverse problems.

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