Predication of topological states in the allotropes of group-IV elements

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.

Graphical abstract

Keywords

topological insulators / topological semimetals / group-IV elements / first-principles calculations

References

[1] M. Z. Hasan and C. L. Kane, Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)

[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)

[3] P. Liu, J. R. Williams, and J. J. Cha, Topological nanomaterials, Nat. Rev. Mater. 4(7), 479 (2019)

[4] C. N. Lau, F. Xia, and L. Cao, Emergent quantum materials, MRS Bull. 45(5), 340 (2020)

[5] Q. Niu, Advances on topological materials, Front. Phys. 15(4), 43601 (2020)

[6] Y. X. Zhao, Equivariant PT-symmetric real Chern insulators, Front. Phys. 15(1), 13603 (2020)

[7] Y. X. Zhao and Z. D. Wang, Novel Z2 topological metals and semimetals, Phys. Rev. Lett. 116(1), 016401 (2016)

[8] Y. X. Zhao and A. P. Schnyder, Nonsymmorphic symmetry-required band crossings in topological semimetals, Phys. Rev. B 94(19), 195109 (2016)

[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)

[10] F. Tang, H. C. Po, A. Vishwanath, and X. Wan, Comprehensive search for topological materials using symmetry indicators, Nature 566(7745), 486 (2019)

[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)

[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)

[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)

[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)

[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)

[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)

[17] C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene , Phys. Rev. Lett. 95(22), 226801 (2005)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[46] B. Liu, G. Zhao, Z. Liu, and Z. F. Wang, Twodimensional quadrupole topological insulator in gammagraphyne, Nano Lett. 19(9), 6492 (2019)

[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)

[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)

[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)

[50] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77(18), 3865 (1996)

[51] H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations,Phys. Rev. B 13(12), 5188 (1976)

[52] J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, J. Chem. Phys. 118(18), 8207 (2003)

[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)

[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)

[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)

RIGHTS & PERMISSIONS

2021 Higher Education Press