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Title: Machine learning in electronic-quantum-matter imaging experiments

Abstract

For centuries, the scientific discovery process has been based on systematic human observation and analysis of natural phenomena. Today, however, automated instrumentation and large-scale data acquisition are generating datasets of such large volume and complexity as to defy conventional scientific methodology. Radically different scientific approaches are needed, and machine learning (ML) shows great promise for research fields such as materials science. Given the success of ML in the analysis of synthetic data representing electronic quantum matter (EQM), the next challenge is to apply this approach to experimental data—for example, to the arrays of complex electronic-structure images17 obtained from atomic-scale visualization of EQM. Here we report the development and training of a suite of artificial neural networks (ANNs) designed to recognize different types of order hidden in such EQM image arrays. These ANNs are used to analyse an archive of experimentally derived EQM image arrays from carrier-doped copper oxide Mott insulators. In these noisy and complex data, the ANNs discover the existence of a lattice-commensurate, four-unit-cell periodic, translational-symmetry-breaking EQM state. Further, the ANNs determine that this state is unidirectional, revealing a coincident nematic EQM state. Here, strong-coupling theories of electronic liquid crystals are consistent with these observations.

Authors:
 [1];  [2];  [3];  [4];  [5];  [6];  [7];  [8];  [9];  [6];  [1]
  1. Cornell Univ., Ithaca, NY (United States)
  2. Cornell Univ., Ithaca, NY (United States); Univ. Paris-Sud, Orsay (France)
  3. Brookhaven National Lab. (BNL), Upton, NY (United States)
  4. Cornell Univ., Ithaca, NY (United States); Stanford Univ., Stanford, CA (United States)
  5. Cornell Univ., Ithaca, NY (United States); Harvard Univ., Cambridge, MA (United States)
  6. San Jose State Univ., San Jose, CA (United States)
  7. National Institute of Advanced Industrial Science and Technology, Tsukuba (Japan)
  8. National Institute of Advanced Industrial Science and Technology, Tsukuba (Japan); Univ. of Tokyo, Tokyo (Japan)
  9. Cornell Univ., Ithaca, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States); Univ. College Cork, Cork (Ireland); Univ. of Oxford, Oxford (United Kingdom)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States); Cornell Univ., Ithaca, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1546043
Alternate Identifier(s):
OSTI ID: 2322500
Report Number(s):
BNL-211896-2019-JAAM
Journal ID: ISSN 0028-0836
Grant/Contract Number:  
SC0012704; SC0018946
Resource Type:
Accepted Manuscript
Journal Name:
Nature (London)
Additional Journal Information:
Journal Name: Nature (London); Journal Volume: 570; Journal Issue: 7762; Journal ID: ISSN 0028-0836
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Zhang, Yi, Mesaros, A., Fujita, Kazuhiro, Edkins, S. D., Hamidian, M. H., Ch’ng, K., Eisaki, H., Uchida, S., Davis, J. C. Séamus, Khatami, Ehsan, and Kim, Eun -Ah. Machine learning in electronic-quantum-matter imaging experiments. United States: N. p., 2019. Web. doi:10.1038/s41586-019-1319-8.
Zhang, Yi, Mesaros, A., Fujita, Kazuhiro, Edkins, S. D., Hamidian, M. H., Ch’ng, K., Eisaki, H., Uchida, S., Davis, J. C. Séamus, Khatami, Ehsan, & Kim, Eun -Ah. Machine learning in electronic-quantum-matter imaging experiments. United States. https://doi.org/10.1038/s41586-019-1319-8
Zhang, Yi, Mesaros, A., Fujita, Kazuhiro, Edkins, S. D., Hamidian, M. H., Ch’ng, K., Eisaki, H., Uchida, S., Davis, J. C. Séamus, Khatami, Ehsan, and Kim, Eun -Ah. Wed . "Machine learning in electronic-quantum-matter imaging experiments". United States. https://doi.org/10.1038/s41586-019-1319-8. https://www.osti.gov/servlets/purl/1546043.
@article{osti_1546043,
title = {Machine learning in electronic-quantum-matter imaging experiments},
author = {Zhang, Yi and Mesaros, A. and Fujita, Kazuhiro and Edkins, S. D. and Hamidian, M. H. and Ch’ng, K. and Eisaki, H. and Uchida, S. and Davis, J. C. Séamus and Khatami, Ehsan and Kim, Eun -Ah},
abstractNote = {For centuries, the scientific discovery process has been based on systematic human observation and analysis of natural phenomena. Today, however, automated instrumentation and large-scale data acquisition are generating datasets of such large volume and complexity as to defy conventional scientific methodology. Radically different scientific approaches are needed, and machine learning (ML) shows great promise for research fields such as materials science. Given the success of ML in the analysis of synthetic data representing electronic quantum matter (EQM), the next challenge is to apply this approach to experimental data—for example, to the arrays of complex electronic-structure images17 obtained from atomic-scale visualization of EQM. Here we report the development and training of a suite of artificial neural networks (ANNs) designed to recognize different types of order hidden in such EQM image arrays. These ANNs are used to analyse an archive of experimentally derived EQM image arrays from carrier-doped copper oxide Mott insulators. In these noisy and complex data, the ANNs discover the existence of a lattice-commensurate, four-unit-cell periodic, translational-symmetry-breaking EQM state. Further, the ANNs determine that this state is unidirectional, revealing a coincident nematic EQM state. Here, strong-coupling theories of electronic liquid crystals are consistent with these observations.},
doi = {10.1038/s41586-019-1319-8},
journal = {Nature (London)},
number = 7762,
volume = 570,
place = {United States},
year = {2019},
month = {6}
}

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Figures / Tables:

Figure 1 Figure 1: Electronic quantum matter imaging in hole-doped CuO2. a, Schematic phase diagram of hole-doped Cu02. At $\mathcal{p}$=0 a single electron is localized at each Cu site in a Mott insulator [MI] state. As holes are introduced (electrons removed) the MI disappears quickly. The high temperature superconductivity (SC) emerges atmore » slightly higher p, reaching its maximum critical temperature Tc near $\mathcal{p}$~0.16. However, in the range p<0.19 and up to temperatures T* an enigmatic phase of EQM, dubbed the pseudogap (PG) phase, is known to contain periodic charge density modulations of imprecise wavevector $\mathrm{Q}$. b, In the CuO2 Brillouin zone, the Fermi surface is defined as the $\mathcal{k}$-space contour $\mathcal{k}$(E = 0) that separates the occupied from unoccupied electronic states, and its locus changes rapidly with changing carrier density $\mathcal{p}$. Density wave (DW) states may then appear at a wavevector $Q(k_i(E = 0)$ — $k_f(E = 0))$ if the electron states $k_i(E)$ and $k_f(E)$ are ’’nested” (red and yellow arrows), c, Strongly correlated electrons may be fully localized in the Mott insulator phase, or self-organized into electronic liquid crystal states in r -space. Schematically shown here is a simple example of a state with unidirectional charge density modulations in the CuO2 plane, having wavelength $\lambda$ = 4$a_0$ or wavevector $\mathrm{Q}$ = $\frac{2π}{a_0}$ (0.25,0) (Methods section 1). d, Typical 24.4nmX24.4nm SISTM image of electronic structure $R(r,E = 150mV)$ from the CuO2 plane of Bi2Sr2CaCu2O8 with $\mathcal{p}$=0.08 (TC=45K). Complex spatial patterns, which to human visual perception look like highly disordered "tweed”, dominate. The contrast with simple periodic arrangement of the simultaneously visualized atoms of the same crystal in the topograph (upper inset) is arresting, e, Typical image-array of simultaneously measured $Z(r,E)$ for $\mathcal{p}$=0.08, each 16nmX16nm but at a different electron energy E, spanning the range 6meV < E < 150meV in steps of 12 meV. Such arrays are the basic type of data-set for which efficient ML analysis and discovery techniques are required« less

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