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Detecting Nematic Order in STM/STS Data with Artificial Intelligence
by Jeremy B. Goetz, Yi Zhang, Michael J. Lawler
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Submission summary
| Authors (as registered SciPost users): | Michael Lawler |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1901.11042v2 (pdf) |
| Date submitted: | 2020-01-16 01:00 |
| Submitted by: | Lawler, Michael |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Detecting the subtle yet phase defining features in Scanning Tunneling Microscopy and Spectroscopy data remains an important challenge in quantum materials. We meet the challenge of detecting nematic order from local density of states data with supervised machine learning and artificial neural networks for the difficult scenario without sharp features such as visible lattice Bragg peaks or Friedel oscillation signatures in the Fourier transform spectrum. We train the artificial neural networks to classify simulated data of isotropic and anisotropic two-dimensional metals in the presence of disorder. The supervised machine learning succeeds only with at least one hidden layer in the ANN architecture, demonstrating it is a higher level of complexity than nematic order detected from Bragg peaks which requires just two neurons. We apply the finalized ANN to experimental STM data on CaFe2As2, and it predicts nematic symmetry breaking with 99% confidence (probability 0.99), in agreement with previous analysis. Our results suggest ANNs could be a useful tool for the detection of nematic order in STM data and a variety of other forms of symmetry breaking.
Author comments upon resubmission
Dear Editor,
Attached please find our manuscript "Detecting nematic order in STM/STS data with artificial intelligence". We are sorry for the delay in responding to the referee comments. We were confused by the latest statement from you on the main page of our manuscript "With only this short report I cannot formulate a recomendation for this manuscript, therefore I am oblished to contact additional referees. I'm sorry if this takes more time." But it seems this statement is out of date and that you have been waiting for our response to the referee who posted a report for some time now. We include this response here and apologize for the delay.
The referee requested both a thorough comparison with experimental data, an explanation for why the performance of the artificial neural network (ANN) on trained data was poor and that we correct a typo.
On the comparison with experimental data, we opted not to compare with additional experiments but instead to argue that the experimental data we did analyze was robustly predicted to be in the nematic phase by the ANN. We now added a subfigure to our report on this analysis which shows the distribution of results from 1000 randomly extracted 16x16 images from the experimental data which cover both different locations on the surface of the material and sampling at different length scales. We believe the results are now convincing that the ANN robustly identifies nematic order in STM data.
As for the poor performance of the ANN on trained data, we believe the referee misinterpreted what we were trying to say in the first version of the manuscript. The ANN performed very well on trained data (we now show a distribution of the ANN predictions on about 10000 images in Fig. 2). What we were trying to do in the first manuscript was to show a case where it didn't do well but still made the correct prediction to demonstrate the hard cases. We search through 10000 images for a few where it performed poorly to do this. In the new version of the manuscript, we dropped this discussion both to avoid any misunderstanding and because isolated examples are not as meaningful as a statistical analysis of how the ANN performs.
Lastly, we have corrected the typo and made many other minor changes throughout the manuscript. Below is our specific response to the referee's report. We hope this new submission can be published without any further delay.
Sincerely, Jeremy B. Goetz Yi Zhang Michael J. Lawler
The manuscript by Goetz et al. reports on detecting subtle nematic order from the local density of states (LDOS) data measured by scanning tunneling microscopy (STM) using supervised machine learning. They simulate LDOS data using various tight-binding methods to train and test their artificial neural network (ANN). They obtain 95% accuracy score with an ANN with a single hidden layer. They test the ANN on a real STM data that is observed to be anisotropic in previous studies. The ANN is able to identify the nematic order with 99% confidence.
The manuscript is well written, the subject is novel and the results are compelling in my opinion.
We thank this referee for his/her encouraging comments and suggestions.
However, the authors test the ANN only on a single anisotropic STM image. I would like to see its performance on a few other isotropic as well as anisotropic STM images. The fact that the ANN performs poorly on simulated data (only %65 Fig. 2) which is trained on compared to the real STM data (%99) is a bit controversial.
We agree with the referee. In the revised manuscript, we show the statistics of neuron outputs across a large number of input samples for both the simulated and the experimental data, instead of referring to the output of a single data sample. Also, the authors have cross-checked their results for consistency. We hope such visualization of statistics offer more clarity and persuasive power for our claims and conclusions.
Typo: For example, inhomogeneous behavior found in strongly correlated materials [can lead] to ...
We thank this referee for pointing this out. We have fixed this typo and other typos, as we carefully revised through the entire manuscript.
List of changes
1. We add the histograms in Fig. 2, Fig. 3 and Fig. 4 to show data statistics.
2. We correct typos and grammar across the manuscript.
3. We have changed the section and subsection labels for consistency with the catalog at the end of Sec. I.
4. We have revised Appendix C to make the presentation more succinct.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2020-2-16 (Invited Report)
- Cite as: Anonymous, Report on arXiv:1901.11042v2, delivered 2020-02-16, doi: 10.21468/SciPost.Report.1514
Strengths
1 - well written
2 - a useful result with a clear answer for experimental data; approach is generic
Weaknesses
1 - see below under requested changes
2- see below under requested changes
3- see below under requested changes -- this amounts to the fact that the ANN output is difficult to interpret for humans
4 - not entirely clear to me whether the modelling by a non-interacting model is sufficient in case no Bragg peaks or Friedel oscillations are observed.
Report
In "Detecting nematic order in STM/STS data with artificial intelligence" the authors want to enhance the classification of experimentally observed STM images through the use of artificial intelligence.
The problem setting is clear. The authors want do distinguish symmetric from nematic data, or more precisely, data that has $C_4$ symmetry vs data that has $C_2$ symmetry. Detecting nematic order can sometimes become a challenge because of instrumental reasons or large amounts of disorder. To this end the authors train an artificial neural network containing one hidden layer and two output neurons with simulated STM images generated from non-interacting fermionic models. They then let the machine decide on realistic STM data of CaFe2As2 and find a nematic symmetry with confidence. The method is particularly useful in cases where there are no Bragg peaks nor Friedel oscillations.
The non-interacting fermionic models, which can be isotropic or anisotropic, are supplemented with a disorder Hamiltonian. The input parameter is the local density of states. In a first step, the authors show that two neurons are insufficient to detect nematic order (in case of Bragg peaks), ie that a hidden layer is necessary. Next they show that one hidden layer is also sufficient. Finally, they apply the machine to the experimental data.
The paper is well written and easy to follow. The analysis of the ANN appears to be correct.
Requested changes
I have a couple of questions that must be answered prior to any decision on publication.
(1) Upon coarse-graining the pixels the authors write that the confidence of the ANN gradually wanes. Is this also seen in the data from the non-interacting model? Or does one have to include disorder that changes over a scale of a dozen lattice sites to reproduce this?
(2) One of the main conclusions of this work is that the ANN remains successful in distinguishing nematic from symmetric samples even when standard approaches fail, say in case of strong disorde. This is remarkable. Imagine a sample with very strong disorder. Then, and this is a typical argument for disordered systems, it is impossible to say whether this sample was generated from phase A or from phase B in case the disorder distribution is generic (in which case one can continuously change the parameters of the disorder distribution, and hence generate the sample from either phase with equal probability). I therefore do not understand that the ANN can learn something that mathematically is not supposed to exist. And so it is fair to ask if the disorder modelling is sufficiently generic in this paper: it is written that $\delta t$ and $\delta {\mu}$ are constant and isotropic, ie they do not make a further distinction between symmetric and nematic phases. If one makes these distributions broad and anisotropic, do the conclusions of this work still hold?
(3) on p8 the authors write: "In comparison, machine learning approaches are base upon the original real-space LDOS data and thus may look beyond merely the Fermi wave vectors." (note the typo: base --> based). But what do the authors think that distinguishes the two cases? Looking at Fig 9d (please add the color scale to fig 9c), Fig 7d, and Fig 6d, it seems that there is a difference between the x and y direction for k-values in the range 2 to 3. Is this true, and if so, can it be explained?