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Frontiers of Physics

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ISSN 2095-0470(Online)

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Front. Phys.    2021, Vol. 16 Issue (6) : 63503    https://doi.org/10.1007/s11467-021-1075-8
RESEARCH ARTICLE
Predication of topological states in the allotropes of group-IV elements
Chengyong Zhong1,2,3()
1. National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
2. Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
3. Institute for Advanced Study, Chengdu University, Chengdu 610106, China
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Abstract

Three-dimensional (3D) topological insulators (TIs) have been studied for approximately fifteen years, but those made from group-IV elements, especially Ge and Sn, seem particularly attractive owing to their nontoxicity, sizable intrinsic spin–orbit coupling (SOC) strength and natural compatibility with the current semiconductor industry. However, group-IV elemental TIs have rarely been reported, except for the low temperature phase of α-Sn under strain. Here, based on first-principles calculations, we propose new allotropes of Ge and Sn, named T5-Ge/Sn, as desirable TIs. These new allotropes are also highly anisotropic Dirac semimetals if the SOC is turned off. To the best of our knowledge, T5-Ge/Sn are the first 3D allotropes of Ge/Sn that possess topological states in their equilibrium states at room temperature. Additionally, their isostructures of C and Si are metastable indirect and direct semiconductors. Our work not only reveals two promising TIs, but more profoundly, we justify the advantages of group-IV elements as topological quantum materials (TQMs) for fundamental research and potential practical applications, and thus reveal a new direction in the search for desirable TQMs.

Keywords topological insulators      topological semimetals      group-IV elements      first-principles calculations     
Corresponding Author(s): Chengyong Zhong   
Issue Date: 18 June 2021
 Cite this article:   
Chengyong Zhong. Predication of topological states in the allotropes of group-IV elements[J]. Front. Phys. , 2021, 16(6): 63503.
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https://academic.hep.com.cn/fop/EN/10.1007/s11467-021-1075-8
https://academic.hep.com.cn/fop/EN/Y2021/V16/I6/63503
1 M. Z. Hasan and C. L. Kane, Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)
https://doi.org/10.1103/RevModPhys.82.3045
2 N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90(1), 015001 (2018)
https://doi.org/10.1103/RevModPhys.90.015001
3 P. Liu, J. R. Williams, and J. J. Cha, Topological nanomaterials, Nat. Rev. Mater. 4(7), 479 (2019)
https://doi.org/10.1038/s41578-019-0113-4
4 C. N. Lau, F. Xia, and L. Cao, Emergent quantum materials, MRS Bull. 45(5), 340 (2020)
https://doi.org/10.1557/mrs.2020.125
5 Q. Niu, Advances on topological materials, Front. Phys. 15(4), 43601 (2020)
https://doi.org/10.1007/s11467-020-0979-z
6 Y. X. Zhao, Equivariant PT-symmetric real Chern insulators, Front. Phys. 15(1), 13603 (2020)
https://doi.org/10.1007/s11467-019-0943-y
7 Y. X. Zhao and Z. D. Wang, Novel Z2 topological metals and semimetals, Phys. Rev. Lett. 116(1), 016401 (2016)
https://doi.org/10.1103/PhysRevLett.116.016401
8 Y. X. Zhao and A. P. Schnyder, Nonsymmorphic symmetry-required band crossings in topological semimetals, Phys. Rev. B 94(19), 195109 (2016)
https://doi.org/10.1103/PhysRevB.94.195109
9 F. Giustino, J. H. Lee, F. Trier, M. Bibes, S. M. Winter, R. Valentí,Y. W. Son, L. Taillefer, C. Heil, A. I. Figueroa, B. Plaçais, Q. S. Wu, O. V. Yazyev, E. P. A. M. Bakkers, J. Nygård, P. Forn-Díaz, S. De Franceschi, J. W. McIver, L. E. F. F. Torres, T. Low, A. Kumar, R. Galceran, S. O. Valenzuela, M. V. Costache, A. Manchon, E. A. Kim, G. R. Schleder, A. Fazzio, and S. Roche, The 2021 quantum materials roadmap, J. Phys. Mater. 3(4), 042006 (2021)
https://doi.org/10.1088/2515-7639/abb74e
10 F. Tang, H. C. Po, A. Vishwanath, and X. Wan, Comprehensive search for topological materials using symmetry indicators, Nature 566(7745), 486 (2019)
https://doi.org/10.1038/s41586-019-0937-5
11 M. G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B. A. Bernevig, and Z. Wang, A complete catalogue of highquality topological materials, Nature 566(7745), 480 (2019)
https://doi.org/10.1038/s41586-019-0954-4
12 T. Zhang, Y. Jiang, Z. Song, H. Huang, Y. He, Z. Fang, H. Weng, and C. Fang, Catalogue of topological electronic materials, Nature 566(7745), 475 (2019)
https://doi.org/10.1038/s41586-019-0944-6
13 H. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S. C. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface, Nat. Phys. 5(6), 438 (2009)
https://doi.org/10.1038/nphys1270
14 H. Lin, L. A. Wray, Y. Xia, S. Xu, S. Jia, R. J. Cava, A. Bansil, and M. Z. Hasan, Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena, Nat. Mater. 9(7), 546 (2010)
https://doi.org/10.1038/nmat2771
15 D. Xiao, Y. Yao, W. Feng, J. Wen, W. Zhu, X. Q. Chen, G. M. Stocks, and Z. Zhang, Half-Heusler compounds as a new class of three-dimensional topological insulators, Phys. Rev. Lett. 105(9), 096404 (2010)
https://doi.org/10.1103/PhysRevLett.105.096404
16 B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells, Science 314(5806), 1757 (2006)
https://doi.org/10.1126/science.1133734
17 C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene , Phys. Rev. Lett. 95(22), 226801 (2005)
https://doi.org/10.1103/PhysRevLett.95.226801
18 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature 438(7065), 197 (2005)
https://doi.org/10.1038/nature04233
19 S. Balendhran, S. Walia, H. Nili, S. Sriram, and M. Bhaskaran, Elemental analogues of graphene: Silicene, germanene, stanene, and phosphorene, Small 11(6), 640 (2015)
https://doi.org/10.1002/smll.201402041
20 A. J. Mannix, B. Kiraly, M. C. Hersam, and N. P. Guisinger, Synthesis and chemistry of elemental 2D materials, Nat. Rev. Chem. 1, 0014 (2017)
https://doi.org/10.1038/s41570-016-0014
21 J. R. Chelikowsky and M. L. Cohen, Nonlocal pseudopotential calculations for the electronic structure of eleven diamond and zinc-blende semiconductors, Phys. Rev. B 14(2), 556 (1976)
https://doi.org/10.1103/PhysRevB.14.556
22 F. Kiefer, V. Hlukhyy, A. J. Karttunen, T. F. Fässler, C. Gold, E. W. Scheidt, W. Scherer, J. Nylén, and U. Häussermann, Synthesis, structure, and electronic properties of 4H-germanium, J. Mater. Chem. 20(9), 1780 (2010)
https://doi.org/10.1039/b921575a
23 B. C. Johnson, B. Haberl, S. Deshmukh, B. D. Malone, M. L. Cohen, J. C. McCallum, J. S. Williams, and J. E. Bradby, Evidence for the R8 phase of germanium, Phys. Rev. Lett. 110(8), 085502 (2013)
https://doi.org/10.1103/PhysRevLett.110.085502
24 A. Mujica, C. J. Pickard, and R. J. Needs, Low-energy tetrahedral polymorphs of carbon, silicon, and germanium, Phys. Rev. B 91(21), 214104 (2015)
https://doi.org/10.1103/PhysRevB.91.214104
25 Z. Zhao, H. Zhang, D. Y. Kim, W. Hu, E. S. Bullock, and T. A. Strobel, Properties of the exotic metastable ST12 germanium allotrope, Nat. Commun. 8(1), 13909 (2017)
https://doi.org/10.1038/ncomms13909
26 Z. Tang, A. P. Litvinchuk, M. Gooch, and A. M. Guloy, Narrow gap semiconducting germanium allotrope from the oxidation of a layered zintl phase in ionic liquids, J. Am. Chem. Soc. 140(22), 6785 (2018)
https://doi.org/10.1021/jacs.8b03503
27 C. He, X. Shi, S. J. Clark, J. Li, C. J. Pickard, T. Ouyang, C. Zhang, C. Tang, and J. Zhong, Complex low energy tetrahedral polymorphs of group IV elements from first principles, Phys. Rev. Lett. 121(17), 175701 (2018)
https://doi.org/10.1103/PhysRevLett.121.175701
28 A. Barfuss, L. Dudy, M. R. Scholz, H. Roth, P. Höpfner, C. Blumenstein, G. Landolt, J. H. Dil, N. C. Plumb, M. Radovic, A. Bostwick, E. Rotenberg, A. Fleszar, G. Bihlmayer, D. Wortmann, G. Li, W. Hanke, R. Claessen, and J. Schäfer,, Elemental topological insulator with tunable Fermi level: Strained α-Sn on InSb(001), Phys. Rev. Lett. 111(15), 157205 (2013)
https://doi.org/10.1103/PhysRevLett.111.157205
29 C. Z. Xu, Y. H. Chan, Y. Chen, P. Chen, X. Wang, C. Dejoie, M. H. Wong, J. A. Hlevyack, H. Ryu, H. Y. Kee, N. Tamura, M. Y. Chou, Z. Hussain, S. K. Mo, and T. C. Chiang, Elemental topological Dirac semimetal: α-Sn on InSb(111), Phys. Rev. Lett. 118(14), 146402 (2017)
https://doi.org/10.1103/PhysRevLett.118.146402
30 D. Zhang, H. Wang, J. Ruan, G. Yao, and H. Zhang, Engineering topological phases in the Luttinger semimetal α-Sn, Phys. Rev. B 97(19), 195139 (2018)
https://doi.org/10.1103/PhysRevB.97.195139
31 Q. Barbedienne, J. Varignon, N. Reyren, A. Marty, C. Vergnaud, M. Jamet, C. Gomez-Carbonell,A. Lemaître, P. Le Fèvre, F. Bertran, A. Taleb-Ibrahimi, H. Jaffrès, J. M. George, and A. Fert, Angular-resolved photoemission electron spectroscopy and transport studies of the elemental topological insulator α-Sn, Phys. Rev. B 98(19), 195445 (2018)
https://doi.org/10.1103/PhysRevB.98.195445
32 I. Madarevic, U. Thupakula, G. Lippertz, N. Claessens, P. C. Lin, H. Bana, S. Gonzalez, G. Di Santo, L. Petaccia, M. N. Nair, L. M. C. Pereira, C. Van Haesendonck, and M. J. Van Bael, Structural and electronic properties of the pure and stable elemental 3D topological Dirac semimetal α-Sn, APL Mater. 8(3), 031114 (2020)
https://doi.org/10.1063/1.5142841
33 J. F. Nye, Physical Properties of Crystals, Clarendon Press, 1985
34 B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, Topological quantum chemistry, Nature 547(7663), 298 (2017)
https://doi.org/10.1038/nature23268
35 J. Doherty, S. Biswas, E. Galluccio, C. A. Broderick, A. Garcia-Gil, R. Duffy, E. P. O’Reilly, and J. D. Holmes, Progress on germanium–tin nanoscale alloys, Chem. Mater. 32(11), 4383 (2020)
https://doi.org/10.1021/acs.chemmater.9b04136
36 J. Wagner and M. Núñez-Valdez,Ab initio study of band gap properties in metastable BC8/ST12 SixGe1−x alloys, Appl. Phys. Lett. 117(3), 032105 (2020)
https://doi.org/10.1063/5.0010311
37 A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, Classification of topological insulators and superconductors in three spatial dimensions, Phys. Rev. B 78(19), 195125 (2008)
https://doi.org/10.1103/PhysRevB.78.195125
38 C. Zhong, W. Wu, J. He, G. Ding, Y. Liu, D. Li, S. A. Yang, and G. Zhang, Two-dimensional honeycomb borophene oxide: Strong anisotropy and nodal loop transformation, Nanoscale 11(5), 2468 (2019)
https://doi.org/10.1039/C8NR08729F
39 Y. Chen, Y. Xie, S. A. Yang, H. Pan, F. Zhang, M. L. Cohen, and S. Zhang, Nanostructured carbon allotropes with Weyl-like loops and points, Nano Lett. 15(10), 6974 (2015)
https://doi.org/10.1021/acs.nanolett.5b02978
40 H. Weng, Y. Liang, Q. Xu, R. Yu, Z. Fang, X. Dai, and Y. Kawazoe, Topological node-line semimetal in three-dimensional graphene networks, Phys. Rev. B 92(4), 045108 (2015)
https://doi.org/10.1103/PhysRevB.92.045108
41 C. Zhong, Y. Chen, Y. Xie, S. A. Yang, M. L. Cohen, and S. B. Zhang, Towards three-dimensional Weyl-surface semimetals in graphene networks, Nanoscale 8(13), 7232 (2016)
https://doi.org/10.1039/C6NR00882H
42 C. Zhong, Y. Chen, Z. M. Yu, Y. Xie, H. Wang, S. A. Yang, and S. Zhang, Three-dimensional pentagon carbon with a genesis of emergent fermions, Nat. Commun. 8(1), 15641 (2017)
https://doi.org/10.1038/ncomms15641
43 W. Wu, Y. Liu, S. Li, C. Zhong, Z. M. Yu, X. L. Sheng, Y. X. Zhao, and S. A. Yang, Nodal surface semimetals: Theory and material realization, Phys. Rev. B 97(11), 115125 (2018)
https://doi.org/10.1103/PhysRevB.97.115125
44 Z. Liu, H. Xin, L. Fu, Y. Liu, T. Song, X. Cui, G. Zhao, and J. Zhao, All-silicon topological semimetals with closed nodal line, J. Phys. Chem. Lett. 10(2), 244 (2019)
https://doi.org/10.1021/acs.jpclett.8b03345
45 S. Z. Chen, S. Li, Y. Chen, and W. Duan, Nodal flexiblesurface semimetals: Case of carbon nanotube networks, Nano Lett. 20(7), 5400 (2020)
https://doi.org/10.1021/acs.nanolett.0c01786
46 B. Liu, G. Zhao, Z. Liu, and Z. F. Wang, Twodimensional quadrupole topological insulator in gammagraphyne, Nano Lett. 19(9), 6492 (2019)
https://doi.org/10.1021/acs.nanolett.9b02719
47 X. L. Sheng, C. Chen, H. Liu, Z. Chen, Z. M. Yu, Y. X. Zhao, and S. A. Yang, Two-dimensional second-order topological insulator in graphdiyne, Phys. Rev. Lett. 123(25), 256402 (2019)
https://doi.org/10.1103/PhysRevLett.123.256402
48 P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, Quantum ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21(39), 395502 (2009)
https://doi.org/10.1088/0953-8984/21/39/395502
49 P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli,M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. Dal Corso, S. de Gironcoli, P. Delugas, R. A. Jr DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer, U. Gerstmann, F. Giustino, T. Gorni, J. Jia, M. Kawamura, H. Y. Ko, A. Kokalj, E. Küçükbenli, M. Lazzeri, M. Marsili, N. Marzari, F. Mauri, N. L. Nguyen, H. V. Nguyen, A. Otero-de-la-Roza, L. Paulatto, S. Poncé, D. Rocca, R. Sabatini, B. Santra, M. Schlipf, A. P. Seitsonen, A. Smogunov, I. Timrov, T. Thonhauser, P. Umari, N. Vast, X. Wu, and S. Baroni, Advanced capabilities for materials modelling with Quantum ESPRESSO, J. Phys.: Condens. Matter 29(46), 465901 (2017)
https://doi.org/10.1088/1361-648X/aa8f79
50 J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77(18), 3865 (1996)
https://doi.org/10.1103/PhysRevLett.77.3865
51 H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations,Phys. Rev. B 13(12), 5188 (1976)
https://doi.org/10.1103/PhysRevB.13.5188
52 J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118(18), 8207 (2003)
https://doi.org/10.1063/1.1564060
53 A. Togo, F. Oba, and I. Tanaka, First-principles calculations of the ferroelastic transition between rutile-type and CaCl2-type SiO2 at high pressures, Phys. Rev. B 78(13), 134106 (2008)
https://doi.org/10.1103/PhysRevB.78.134106
54 Q. Wu, S. Zhang, H.-F. Song, M. Troyer, and A. A. Soluyanov, WannierTools: An open-source software package for novel topological materials, Comput. Phys. Commun. 224, 405 (2018)
https://doi.org/10.1016/j.cpc.2017.09.033
55 G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Ibañez-Azpiroz, H. Lee, J. M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, S. Poncé, T. Ponweiser, J. Qiao, F. Thöle, S. S. Tsirkin, M. Wierzbowska, N. Marzari, D. Vanderbilt, I. Souza, A. A. Mostofi, and J. R. Yates, Wannier90 as a community code: New features and applications, J. Phys.: Condens. Matter 32(16), 165902 (2020)
https://doi.org/10.1088/1361-648X/ab51ff
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