Topological Data Analysis in Materials Science: The Case of High-Temperature Cuprate Superconductors

Pattern Recognition and Image Analysis - Tập 30 - Trang 264-276 - 2020
I. Yu. Torshin1, K. V. Rudakov1
1Dorodnicyn Computing Centre, Federal Research Center “Informatics and Control,”, Russian Academy of Sciences, Moscow, Russia

Tóm tắt

Adequate formalization of problems is the most important task that has to be solved in order to apply the modern methods of so-called “machine learning” to real problems. The effective application of the metric, logical, regression, and other algorithms of machine learning becomes possible only when feature generation procedures and classes of objects are adequately defined. In this study, the theory of topological analysis of poorly formalized problems and the theory of analysis of labeled graphs were applied to the problem of predicting numerical characteristics of crystalline materials. The methods developed were tested on the problem of predicting the critical temperature of superconducting transition (Tc) of high-temperature cuprate superconductors (1450 structures). As a result, in a tenfold 6 : 1 cross-validation, the best model with a linear recognition operator yielded quite high average value of the correlation coefficient (r = 0.77) between the predicted and experimentally determined values of Tc.

Tài liệu tham khảo

I. Yu. Torshin and K. V. Rudakov, “On the theoretical basis of metric analysis of poorly formalized problems of recognition and classification,” Pattern Recogn. Image Anal. 25 (4), 577–587 (2015). Yu. I. Zhuravlev, K. V. Rudakov, and I. Yu. Torshin, “Algebraic criteria for local solvability and regularity as an instrument for researching amino acid sequence morphology,” Trudy Mosk. Fiz.-Tekhn. Inst. 3 (4), 45–54 (2011). Yu. I. Zhuravlev, “Correct algebras over sets of incorrect (heuristic) algorithms,” I: Cybern. 13 (4), 489–497 (1977). I. Yu. Torshin and K.V. Rudakov, “Combinatorial analysis of the solvability properties of the problems of recognition and completeness of algorithmic models. Part 1: Factorization approach,” Pattern Recognition and Image Anal. 27 (1), 16–28 (2017). I. Yu. Torshin and K.V. Rudakov, “Combinatorial analysis of the solvability properties of the problems of recognition and completeness of algorithmic models. Part 2: Metric approach within the framework of the theory of classification of feature values,” Pattern Recogn. Image Anal. 27 (2), 184–199 (2017). I. Yu. Torshin and K. V. Rudakov, “On metric spaces arising during formalization of recognition and classification problems. Part 1: Properties of compactness,” Pattern Recogn. Image Anal. 26 (2), 274–284 (2016). I. Yu. Torshin and K. V. Rudakov, “On metric spaces arising during formalization of problems of recognition and classification. Part 2: Density properties,” Pattern Recognit. Image Anal. 26 (3), 483–496 (2016). I. Yu. Torshin and K. V. Rudakov, “On the application of the combinatorial theory of solvability to the analysis of chemographs. Part 1: Fundamentals of modern chemical bonding theory and the concept of the chemograph,” Pattern Recogn. Image Anal. 24 (1), 11–23 (2014). I. Yu. Torshin and K. V. Rudakov, “On the application of the combinatorial theory of solvability to the analysis of chemographs. Part 2. Local completeness of invariants of chemographs in view of the combinatorial theory of solvability,” Pattern Recogn. Image Anal. 24 (2), 196–208 (2014). I. Yu. Torshin and K. V. Rudakov, “On the procedures of generation of numerical features over partitions of sets of objects in the problem of predicting numerical target variables,” Pattern Recognit. Image Anal. 29 (4), 654–667 (2019). H. Fröhlich, “On the theory of superconductivity: the one-dimensional case,” Proc. R. Soc. Lond. Ser. A 223 (1154), 296–305 (1954). https://doi.org/10.1098/rspa.1954.0116 F. von Oppen, Y. Peng, and F. Pientka, “Topological superconducting phases in one dimension,” in Topological Aspects of Condensed Matter Physics, École de Physique des Houches, Session CIII, 4–29 August 2014, Ed. by C. Chamon, M. O. Goerbig, R. Moessner, and L. F. Cugliandolop (Oxford University Press, Oxford, 2017), pp. 387–447. https://doi.org/10.1093/acprof:oso/9780198785781.003.0009 K. Nishi, “Possible higher temperature superconductivity in the modulation-doped superlattice structure of cuprate superconductors,” Phys. Lett. A 382 (45), 3293–3297 (2018). https://doi.org/10.1016/j.physleta.2018.09.024 V. A Khodel., J. W. Clark, and M. V. Zverev, “Toward a topological scenario for high-temperature superconductivity of copper oxides,” Phys. Lett. A 382 (45), 3281–3286 (2018). https://doi.org/10.1016/j.physleta.2018.09.017 V. Lakhno, “A translation invariant bipolaron in the Holstein model and superconductivity,” SpringerPlus 5, Article 1277, 1–18 (2016). https://doi.org/10.1186/s40064-016-2975-x Y. Li, J. Terzic, P. G. Baity, D. Popović, G. D. Gu, Q. Li, A. M. Tsvelik, and J. M. Tranquada, “Tuning from failed superconductor to failed insulator with magnetic field,” Sci. Adv. 5 (6), eaav7686, 1–5 (2019). https://doi.org/10.1126/sciadv.aav7686 H.-H. Kim, S. M. Souliou, M. E. Barber, E. Lefrancois, M. Minola, M. Tortora, R. Heid, N. Nandi, R. A. Borzi, G. Garbarino, A. Bosak, J. Porras, T. Loew, M. Konig, P. M. Moll, A. P. Mackenzie, B. Keimer, C. W. Hicks, and M. Le Tacon. “Uniaxial pressure control of competing orders in a high-temperature superconductor,” Sci. 362 (6418), 1040–1044 (2018). https://doi.org/10.1126/science.aat4708 W. Ruan, X. Li, C. Hu, Z. Hao, H. Li, P. Cai, X. Zhou, D.-H. Lee, and Y. Wang. “Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor,” Nat. Phys. 14 (12), 1178–1182 (2018). https://doi.org/10.1038/s41567-018-0276-8 J. Wu, A. T. Bollinger, X. He, and I. Bozovic, “Spontaneous breaking of rotational symmetry in copper oxide superconductors,” Nat. 547 (7664), 432–435 (2017). https://doi.org/10.1038/nature23290 P. Giraldo-Gallo, J. A. Galvis, Z. Stegen, K. A. Modic, F. F. Balakirev, J. B. Betts, X. Lian, C. Moir, S. C. Riggs, J. Wu, A. T. Bollinger, X. He, I. Bozovic, B. J. Ramshaw, R. D. McDonald, G. S. Boebinger, and A. Shekhter, “Scale-invariant magnetoresistance in a cuprate superconductor,” Sci. 361 (6401), 479–481 (2018). https://doi.org/10.1126/science.aan3178 Y. He, M. Hashimoto, D. Song, S.-D. Chen, J. He, I. M. Vishik, B. Moritz, D.-H. Lee, N. Nagaosa, J. Zaanen, T. P. Devereaux, Y. Yoshida, H. Eisaki, D. H. Lu, and Z.-X. Shen, “Rapid change of superconductivity and electron-phonon coupling through critical doping in Bi-2212,” Sci. 362 (6410), 62–65 (2018). https://doi.org/10.1126/science.aar3394 H. C. Po, A. Vishwanath, and H. Watanabe, “Symmetry-based indicators of band topology in the 230 space groups,” Nat. Commun. 8, Article 50 (2017). https://doi.org/10.1038/s41467-017-00133-2 K. Gotlieb, C.-Y. Lin, M. Serbyn, W. Zhang, C. L. Smallwood, C. Jozwiak, H. Eisaki, Z. Hussain, A. Vishwanath, and A. Lanzara A. “Revealing hidden spin-momentum locking in a high-temperature cuprate superconductor,” Sci. 362 (6420), 1271–1275 2018. https://doi.org/10.1126/science.aao0980 P. Popčević, D. Pelc, Y. Tang, K. Velebit, Z. Anderson, V. Nagarajan, G. Yu, M. Požek, N. Barišić, and M. Greven, “Percolative nature of the direct-current paraconductivity in cuprate superconductors,” Quantum Mater. 3, Article 42, 1–6 (2018). https://doi.org/10.1038/s41535-018-0115-2 M. G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B. A. Bernevig, and Z. Wang, “A complete catalogue of high-quality topological materials,” Nat. 566 (7745), 480–485 (2019). https://doi.org/10.1038/s41586-019-0954-4 Yu. I. Zhuravlev, “Correct algebras over sets of incorrect (heuristic) algorithms,” I: Cybern. 13 (4), 489–497 (1977); II: Cybern. 13 (6), 814–821 (1977); III: Cybern. 14 (2), 188–197 (1978). K. T Butler, D. W. Davies, H. Cartwright, O. Isayev, and A. Walsh, “Machine learning for molecular and materials science,” Nat. 559 (7715), 547–555 (2018). https://doi.org/10.1038/s41586-018-0337-2 J. Hill, G. Mulholland, K. Persson, R. Seshadri, C. Wolverton, and B. Meredig, “Materials science with large-scale data and informatics: Unlocking new opportunities,” MRS Bull. 41 (5), 399–409 (2016). https://doi.org/10.1557/mrs.2016.93 Yu. I. Zhuravlev, N. N. Kiselyova, V. V. Ryazanov, O. V. Sen’ko, and A. A. Dokukin, “Design of inorganic compounds with the use of precedent-based pattern recognition methods,” Pattern Recogn. Image Anal. 21 (1), 95–103 (2011). https://doi.org/10.1134/S1054661811010135 P. V. Balachandran, J. Theiler, J. M. Rondinelli, and T. Lookman, “Materials prediction via classification learning,” Sci. Rep. 5, Article 13285, 1–16 (2015). https://doi.org/10.1038/srep13285 B. Bradlyn, L Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, “Topological quantum chemistry,” Nat. 547 (7663), 298–305 (2017). https://doi.org/10.1038/nature23268 F. Grasselli and S. Baroni, “Topological quantization and gauge invariance of charge transport in liquid insulators,” Nat. Phys. 15, 967–972 (2019). https://doi.org/10.1038/s41567-019-0562-0 I. Yu. Torshin, “The study of the solvability of the genome annotation problem on sets of elementary motifs,” Pattern Recogn. Image Anal. 21 (4), 652–662 (2011). https://doi.org/10.1134/S1054661811040171 I. Yu. Torshin, “On solvability, regularity, and locality of the problem of genome annotation,” Pattern Recogn. Image Anal. 20 (3), 386–395 (2010). T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, (Springer, New York, 2001). A. Belsky, M. Hellenbrandt, V. L. Karen, and P. Luksch, “New developments in the Inorganic Crystal Structure Database (ICSD): accessibility in support of materials research and design,” Acta Crystallogr., Sect. B: Struct. Sci., Cryst. Eng. Mater. B58, Part 3 (1), 364–369 (2002). https://doi.org/10.1107/S0108768102006948 Y. Xu, M. Yamazaki, and P. Villars, “Inorganic materials database for exploring the nature of material,” Jpn. J. Appl. Phys. 50 (11S), Article 11RH02 (2011). https://doi.org/10.1143/JJAP.50.11RH02 I. Yu. Torshin, V. A. Alyoshin, and E. V. Antipov, “Synthesis and properties of the high-temperature superconductor HgBa2CuO4+d,” Sverkhprovodimost: Fiz., Khim., Tekh. 7 (10-12), 1579–1587 (1994). S. N. Putilin, E. V. Antipov, O. Chmaissem, and M. Marezio, “Superconductivity at 94 K in HgBa2Cu04+δ,” Nat. 362, 226–228 (1993). https://doi.org//10.1038/362226a0 H. Maeda; Y. Tanaka; M. Fukutomi, and T. Asano, “A new high-Tc oxide superconductor without a rare Earth element,” Jpn. J. Appl. Phys. 27, Part 2 (2), L209–L210 (1988). https://doi.org/10.1143/JJAP.27.L209 Ch. Chen, B. M. Wanklyn, E. Dieguez, A. J. Cook, J. W. Hodby, A. Schwartzbrod, A. Dabkowski, and H. Dabkowska, “Phase diagram and crystal growth of Pb2Sr2(YxCa1-x) Cu3O8+y,” J. Cryst. Growth 118 (1–2), 101–108 (1992). https://doi.org//10.1016/0022-0248(92)90054-M