Machine learning in electronic-quantum-matter imaging experiments

For centuries, the scientific discovery process has been based on systematic human observation and analysis of natural phenomena1. 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 science2–5. Given the success of ML in the analysis of synthetic data representing electronic quantum matter (EQM)6–16, 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. Strong-coupling theories of electronic liquid crystals18,19 are consistent with these observations.A machine-learning approach is used to train artificial neural networks to analyse experimental scanning tunnelling microscopy image arrays of quantum materials.

[1]  Stefano Curtarolo,et al.  SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates , 2017, Physical Review Materials.

[2]  R. Melko,et al.  Machine Learning Phases of Strongly Correlated Fermions , 2016, Physical Review X.

[3]  John M. Tranquada,et al.  Colloquium : Theory of intertwined orders in high temperature superconductors , 2014, 1407.4480.

[4]  K. Fujita,et al.  Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state , 2015, Nature Physics.

[5]  F. Bacon,et al.  The Advancement of Learning [1605] , 1949 .

[6]  David J. Schwab,et al.  Supervised Learning with Tensor Networks , 2016, NIPS.

[7]  Andrea Damascelli,et al.  Resonant X-Ray Scattering Studies of Charge Order in Cuprates , 2015, 1509.03313.

[8]  Juan Carrasquilla,et al.  Machine learning quantum phases of matter beyond the fermion sign problem , 2016, Scientific Reports.

[9]  Eric R. Homer,et al.  Discovering the building blocks of atomic systems using machine learning: application to grain boundaries , 2017, npj Computational Materials.

[10]  Giacomo Torlai,et al.  Neural Decoder for Topological Codes. , 2016, Physical review letters.

[11]  Matthias Troyer,et al.  Solving the quantum many-body problem with artificial neural networks , 2016, Science.

[12]  S. Huber,et al.  Learning phase transitions by confusion , 2016, Nature Physics.

[13]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[14]  J. Zaanen,et al.  Self-Organized One Dimensionality , 1999, Science.

[15]  Michael J. Lawler,et al.  Nematic Fermi Fluids in Condensed Matter Physics , 2009, 0910.4166.

[16]  Hiroshi Eisaki,et al.  Commensurate 4a0-period charge density modulations throughout the Bi2Sr2CaCu2O8+x pseudogap regime , 2016, Proceedings of the National Academy of Sciences.

[17]  Roger G. Melko,et al.  Machine learning phases of matter , 2016, Nature Physics.

[18]  D. Deng,et al.  Quantum Entanglement in Neural Network States , 2017, 1701.04844.

[19]  Adolfo Avella,et al.  Strongly correlated systems : experimental techniques , 2015 .

[20]  Bernd Rosenow,et al.  From stripe to checkerboard ordering of charge-density waves on the square lattice in the presence of quenched disorder , 2006, cond-mat/0603029.

[21]  Yi Zhang,et al.  Quantum Loop Topography for Machine Learning. , 2016, Physical review letters.

[22]  G. Tarjus,et al.  Quenched disorder and vestigial nematicity in the pseudogap regime of the cuprates , 2013, Proceedings of the National Academy of Sciences.

[23]  M. R. Norman,et al.  From quantum matter to high-temperature superconductivity in copper oxides , 2015, Nature.

[24]  V. J. Emery,et al.  Electronic liquid-crystal phases of a doped Mott insulator , 1998, Nature.

[25]  Titus Neupert,et al.  Probing many-body localization with neural networks , 2017, 1704.01578.

[26]  Aharon Kapitulnik,et al.  Distinguishing patterns of charge order : Stripes or checkerboards , 2006 .

[27]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[28]  Fa Wang,et al.  The Electron-Pairing Mechanism of Iron-Based Superconductors , 2011, Science.

[29]  Manh Cuong Nguyen,et al.  On-the-fly machine-learning for high-throughput experiments: search for rare-earth-free permanent magnets , 2014, Scientific Reports.

[30]  Matthias Troyer,et al.  Neural-network quantum state tomography , 2018 .

[31]  Corey Oses,et al.  Machine learning modeling of superconducting critical temperature , 2017, npj Computational Materials.