[1] Thouless D J, Kohmoto M, Nightingale M P and den Nijs M 1982 Phys. Rev. Lett. 49405 [2] Tsui D C, Stormer H L and Gossard A C 1982 Phys. Rev. Lett. 481559 [3] Laughlin R B 1983 Phys. Rev. Lett. 501395 [4] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95146802 [5] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 823045 [6] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 831057 [7] Bansil A, Lin H and Das T 2016 Rev. Mod. Phys. 88021004 [8] Kitaev A 2009 Periodic table for topological insulators and superconductors, AIP conference proceedings (American Institute of Physics) Vol. 1134 pp. 22–30 [9] Konig M, Wiedmann S, Brune C, Roth A, Buhmann H, Molenkamp L W, Qi X L and Zhang S C 2007 Science 318766 [10] Fu L, Kane C L and Mele E J 2007 Phys. Rev. Lett. 98106803 [11] Zhang H, Liu C X, Qi X L, Dai X, Fang Z and Zhang S C 2009 Nat. Phys. 5438 [12] Xia Y, Qian D, Hsieh D, Wray L, Pal A, Lin H, Bansil A, Grauer D, Hor Y S, Cava R J, et al. 2009 Nat. Phys. 5398 [13] Chen Y, Analytis J G, Chu J H, Liu Z, Mo S K, Qi X L, Zhang H, Lu D, Dai X, Fang Z, et al. 2009 Science 325178 [14] Benalcazar W A, Bernevig B A and Hughes T L 2017 Science 35761 [15] Wan X, Turner A M, Vishwanath A and Savrasov S Y 2011 Phys. Rev. B 83205101 [16] Wang Z, Sun Y, Chen X Q, Franchini C, Xu G, Weng H, Dai X and Fang Z 2012 Phys. Rev. B 85195320 [17] Young S M, Zaheer S, Teo J C, Kane C L, Mele E J and Rappe A M 2012 Phys. Rev. Lett. 108140405 [18] Wang Z, Weng H, Wu Q, Dai X and Fang Z 2013 Phys. Rev. B 88125427 [19] Liu Z, Jiang J, Zhou B, Wang Z, Zhang Y, Weng H, Prabhakaran D, Mo S K, Peng H, Dudin P, et al. 2014 Nat. Mater. 13677 [20] Lv B, Muff S, Qian T, Song Z, Nie S, Xu N, Richard P, Matt C E, Plumb N C, Zhao L, et al. 2015 Phys. Rev. Lett. 115217601 [21] Hohenberg P and Kohn W 1964 Phys. Rev. 136 B864 [22] Kohn W and Sham L J 1965 Phys. Rev. 140 A1133 [23] Bradlyn B, Elcoro L, Cano J, Vergniory M G, Wang Z, Felser C, Aroyo M I and Bernevig B A 2017 Nature 547298 [24] Hellenbrandt M 2004 Crystallogr. Rev. 1017 [25] Jain A, Ong S, Hautier G, Chen W, Richards W, Dacek S, Cholia S, Gunter D, Skinner D, Ceder G and Persson K 2013 APL Mater. 1011002 [26] Zhang T, Jiang Y, Song Z, Huang H, He Y, Fang Z, Weng H and Fang C 2019 Nature 566475 [27] Vergniory M G, Elcoro L, Felser C, Regnault N, Bernevig B A and Wang Z 2019 Nature 566480 [28] Tang F, Po H C, Vishwanath A and Wan X 2019 Nature 566486 [29] Vergniory M G, Wieder B J, Elcoro L, Parkin S S, Felser C, Bernevig B A and Regnault N 2022 Science 376 eabg9094 [30] Watanabe H, Po H C and Vishwanath A 2018 Science Advances 4 aat8685 [31] Elcoro L, Wieder B J, Song Z, Xu Y, Bradlyn B and Bernevig B A 2021 Nat. Commun. 125965 [32] Peng B, Jiang Y, Fang Z, Weng H and Fang C 2022 Phys. Rev. B 105235138 [33] Samuel A L 1959 IBM J. Res. Dev. 3210 [34] Zhang Y and Kim E A 2017 Phys. Rev. Lett. 118216401 [35] Zhang Y, Ginsparg P and Kim E A 2020 Phys. Rev. Res. 2023283 [36] Zhang P, Shen H and Zhai H 2018 Phys. Rev. Lett. 120066401 [37] Scheurer M S and Slager R J 2020 Phys. Rev. Lett. 124226401 [38] Donoho D 2006 IEEE Transactions on Information Theory 521289 [39] Acosta C M, Ouyang R, Fazzio A, Scheffler M, Ghiringhelli L M and Carbogno C 2018 arXiv 1805.10950 [40] Ouyang R, Curtarolo S, Ahmetcik E, Scheffler M and Ghiringhelli L M 2018 Phys. Rev. Mater. 2083802 [41] Cao G, Ouyang R, Ghiringhelli L M, Scheffler M, Liu H, Carbogno C and Zhang Z 2020 Phys. Rev. Mater. 4034204 [42] Liu J, Cao G, Zhou Z and Liu H 2021 J. Phys. Condens. Matter 33325501 [43] Claussen N, Bernevig B A and Regnault N 2020 Phys. Rev. B 101245117 [44] Marrazzo A, Gibertini M, Campi D, Mounet N and Marzari N 2019 Nano Lett. 198431 [45] Haastrup S, Strange M, Pandey M, Deilmann T, Schmidt P S, Hinsche N F, Gjerding M N, Torelli D, Larsen P M, Riis-Jensen A C, et al. 20182D Mater. 5042002 [46] Zhou J, Shen L, Costa M D, Persson K A, Ong S P, Huck P, Lu Y, Ma X, Chen Y, Tang H, et al. 2019 Scientific Data 686 [47] Olsen T, Andersen E, Okugawa T, Torelli D, Deilmann T and Thygesen K S 2019 Phys. Rev. Mater. 3024005 [48] Wang D, Tang F, Ji J, Zhang W, Vishwanath A, Po H C and Wan X 2019 Phys. Rev. B 100195108 [49] Schleder G R, Focassio B and Fazzio A 2021 Appl. Phys. Rev. 8031409 [50] Andrejevic N, Andrejevic J, Bernevig B A, Regnault N, Han F, Fabbris G, Nguyen T, Drucker N C, Rycroft C H and Li M 2022 Adv. Mater. 342204113 [51] Ma A, Zhang Y, Christensen T, Po H C, Jing L, Fu L and Soljacic M 2023 Nano Lett. 23772 [52] Wu Q S, Autes G, Mounet N and Yazyev O V 2019 TopoMat: A Database of High-Throughput First-Principles Calculations of Topological Materials, Materials Cloud Archive 2019.0019/v1 [53] He Y, De Breuck P P, Weng H, Giantomassi M and Rignanese G M 2025 npj Computational Materials 11181 [54] Ong S P, Richards W D, Jain A, Hautier G, Kocher M, Cholia S, Gunter D, Chevrier V L, Persson K A and Ceder G 2013 Comput. Mater. Sci. 68314 [55] Ho T K 1995 Random decision forests, Proceedings of 3rd International Conference on Document Analysis and Recognition (Montreal, Canada, 14–16 August 1995) (IEEE) pp. 278–282 [56] McCulloch W S and Pitts W 1943 The bulletin of mathematical biophysics 5115 [57] Knobbe A J, Siebes A, van der Wallen D 1999 Multi-relational Decision Tree Induction In: Zytkow J M, Rauch J (eds) · Principles of Data Mining and Knowledge Discovery. PKDD 1999 Lecture Notes in Computer Science, Vol. 1704(Berlin: Springer) [58] Barnard J and Meng X L 1999 Statistical methods in medical research 817 [59] Ward L, Dunn A, Faghaninia A, Zimmermann N E, Bajaj S, Wang Q, Montoya J, Chen J, Bystrom K, Dylla M, Chard K, Asta M, Persson K A, Snyder G J, Foster I and Jain A 2018 Comput. Mater. Sci. 15260 [60] De Breuck P P, Hautier G and Rignanese G M 2021 npj Comput. Mater. 783 [61] De Breuck P P 2025 Vibrational properties of solids: a machine learning approach (UCLouvain) [62] Talirz L, Kumbhar S, Passaro E, Yakutovich A V, Granata V, Gargiulo F, Borelli M, Uhrin M, Huber S P, Zoupanos S, Adorf C S, Andersen C W, Schutt O, Pignedoli C A, Passerone D, VandeVondele J, Schulthess T C, Smit B, Pizzi G and Marzari N 2020 Scientific Data 7 [63] Fraux G, Cersonsky R and Ceriotti M 2020 Journal of Open Source Software 52117 [64] Ye C, Wang Y, Xie X, Zhu T, Liu J, He Y, Zhang L, Zhang J, Fang Z, Wang L, et al. 2025 npj Computational Materials 1263 [65] Kresse G and Furthmuller J 1996 Computational Materials Science 615 [66] He Y, Jiang Y, Zhang T, Huang H, Fang C and Jin Z 2019 Chin. Phys. B 28087102 [67] Perdew J P, Burke K and Ernzerhof M 1996 Phys. Rev. Lett. 773865 [68] Wang Z 2021 Vasp2trace https://github.com/zjwang11/irvsp [69] Vergniory M Check topological mat https://www.cryst.ehu.es/cgibin/cryst/programs/magnetictopo.pl?tipog=gesp |