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 the 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 symmetric and nematic 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 a nematic order detected from Bragg peaks, which requires just two neurons. We apply the finalized ANN to experimental STM data on CaFe_22As_22, and it predicts nematic symmetry breaking with dominating confidence, 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.
Highlights
The specific choices of model parameters are presented in Appendix A. This model is too simple for non-trivial local density of states (LDOS) Nr(ω), since it is invariant under translation and scalar under rotation - spatially isotropic even with hopping t x = t y
We have trained artificial neural networks (ANNs) with either no hidden layer or one hidden layer via a supervised machine learning algorithm to detect the presence of nematic order in materials based upon the simulated LDOS data sets
artificial intelligence (AI) architecture with a hidden layer can successfully distinguish the nematic order from a symmetric phase, likely relying on nontrivial correlations in the data
Summary
Scanning Tunneling Microscopy (STM) and spectroscopy (STS) data is difficult to fit to theory. After training on simulated data from diverse microscopic models categorized into a series of classes following respective hypothetical claims, artificial neural networks (ANNs) can extract information from ‘big’ STM experimental data, and determine the characteristic symmetries of the realistic electronic quantum matter [6]. The recent trend of applying machine learning techniques to condensed matter physics, beginning with its use in density function theory [7,8,9,10] and its extension to strongly correlated electrons models [5,11] suggests a new route to extracting information from STM data [6,12]. Much like following a renormalization group flow, through machine learning, the ANN summarizes the relevant phase defining features automatically [4] With this in mind, consider the case of detecting nematic order in STM data.
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