Effective models for nearly ideal Dirac semimetals

Abstract

Topological materials (TMs) have gained intensive attention due to their novel behaviors compared with topologically trivial materials. Among various TMs, Dirac semimetal (DSM) has been studied extensively. Although several DSMs have been proposed and verified experimentally, the suitable DSM for realistic applications is still lacking. Thus finding ideal DSMs and providing detailed analyses to them are of both fundamental and technological importance. Here, we sort out 8 (nearly) ideal DSMs from thousands of topological semimetals in Nature 566(7745), 486 (2019). We show the concrete positions of the Dirac points in the Brillouin zone for these materials and clarify the symmetryprotection mechanism for these Dirac points as well as their low-energy effective models. Our results provide a useful starting point for future study such as topological phase transition under strain and transport study based on these effective models. These DSMs with high mobilities are expected to be applied in fabrication of functional electronic devices.

Keywords

Dirac semimetal / symmetry / effective model

References

[1] K. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45(6), 494 (1980)

[2] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a twodimensional periodic potential, Phys. Rev. Lett. 49(6), 405 (1982)

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

[4] X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)

[5] Y. Ando and L. Fu, Topological crystalline insulators and topological superconductors: From concepts to materials, Annu. Rev. Condens. Matter Phys. 6(1), 361 (2015)

[6] N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90(1), 015001 (2018)

[7] T. O. Wehling, A. M. Black-Schaffer, and A. V. Balatsky, Dirac materials, Adv. Phys. 63(1), 1 (2014)

[8] S. M. Young, S. Zaheer, J. C. Y. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, Dirac semimetal in three dimensions, Phys. Rev. Lett. 108(14), 140405 (2012)

[9] Z. Wang, Y. Sun, X.Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Dirac semimetal and topological phase transitions in A₃Bi (A= Na, K, Rb), Phys. Rev. B 85(19), 195320 (2012)

[10] Z. Wang, H. Weng, Q. Wu, X. Dai, and Z. Fang, Threedimensional Dirac semimetal and quantum transport in Cd₃As₂, Phys. Rev. B 88(12), 125427 (2013)

[11] Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S. K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, Discovery of a threedimensional topological Dirac semimetal, Na₃Bi, Science 343(6173), 864 (2014)

[12] Z. K. Liu, J. Jiang, B. Zhou , Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin6 , T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, A stable three-dimensional topological Dirac semimetal Cd₃As₂, Nat. Mater. 13, 677C681 (2014)

[13] B. J. Yang and N. Nagaosa, Classification of stable threedimensional Dirac semimetals with nontrivial topology, Nat. Commun. 5(1), 4898 (2014)

[14] M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Chiral tunnelling and the Klein paradox in graphene, Nat. Phys. 2(9), 620 (2006)

[15] M. Yan, H. Huang, K. Zhang, E. Wang, W. Yao, K. Deng, G. Wan, H. Zhang, M. Arita, H. Yang, Z. Sun, H. Yao, Y. Wu, S. Fan, W. Duan, and S. Zhou, Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe₂, Nat. Commun. 8(1), 257 (2017)

[16] H. J. Noh, J. Jeong, E. J. Cho, K. Kim, B. I. Min, and B. G. Park, Experimental realization of type-II Dirac fermions in a PdTe₂ superconductor, Phys. Rev. Lett. 119(1), 016401 (2017)

[17] F. Fei, X. Bo, R. Wang, B. Wu, J. Jiang, D. Fu, M. Gao, H. Zheng, Y. Chen, X. Wang, H. Bu, F. Song, X. Wan, B. Wang, and G. Wang, Nontrivial Berry phase and type- II Dirac transport in the layered material PdTe₂, Phys. Rev. B 96(4), 041201 (2017)

[18] Q. D. Gibson, L. M. Schoop, L. Muechler, L. S. Xie, M. Hirschberger, N. P. Ong, R. Car, and R. J. Cava, Threedimensional Dirac semimetals: Design principles and predictions of new materials, Phys. Rev. B 91(20), 205128 (2015)

[19] Q. S. Wu, C. Piveteau, Z. Song, and O. V. Yazyev, MgTa₂N₃: A reference Dirac semimetal, Phys. Rev. B 98, 081115(R) (2018)

[20] W. D. Cao, P. Z. Tang, S.-C. Zhang, W. H. Duan, and A. Rubio, Stable Dirac semimetal in the allotropes of group-IV elements, Phys. Rev. B 93, 241117(R) (2016)

[21] X. Zhang, Q. Liu, Q. Xu, X. Dai, and A. Zunger, Topological insulators versus topological Dirac semimetals in honeycomb compounds, J. Am. Chem. Soc. 140(42), 13687 (2018)

[22] X. L. Sheng, Z. Wang, R. Yu, H. Weng, Z. Fang, and X. Dai, Topological insulator to Dirac semimetal transition driven by sign change of spin–orbit coupling in thallium nitride, Phys. Rev. B 90(24), 245308 (2014)

[23] Y. Du, B. Wan, D. Wang, L. Sheng, C.G. Duan, and X. Wan, Dirac and Weyl semimetal in XY Bi (X= Ba, Eu; Y= Cu, Ag and Au), Sci. Rep. 5(1), 14423 (2015)

[24] Y. P. Du, F. Tang, D. Wang, L. Sheng, E. J. Kan, C.- G. Duan, S. Y. Savrasov, and X. G. Wan, CaTe: A new topological node-line and Dirac semimetal, npj Quant. Mater. 2, 3 (2017)

[25] R. Chen, H. C. Po, J. B. Neaton, and A. Vishwanath, Topological materials discovery using electron filling constraints, Nat. Phys. 14(1), 55 (2018)

[26] 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)

[27] M. G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B. A. Bernevig, and Z. Wang, A complete catalogue of high-quality topological materials, Nature 566(7745), 480 (2019)

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

[29] J. Xiong, S. K. Kushwaha, T. Liang, J. W. Krizan, M. Hirschberger, W. Wang, R. J. Cava, and N. P. Ong, Evidence for the chiral anomaly in the Dirac semimetal Na₃Bi, Science 350(6259), 413 (2015)

[30] M. Neupane, S. Y. Xu, R. Sankar, N. Alidoust, G. Bian, C. Liu, I. Belopolski, T. R. Chang, H. T. Jeng, H. Lin, A. Bansil, F. Chou, and M. Z. Hasan, Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd₃As₂, Nat. Commun. 5(1), 3786 (2014)

[31] H. C. Po, A. Vishwanath, and H. Watanabe, Symmetrybased indicators of band topology in the 230 space groups, Nat. Commun. 8(1), 50 (2017)

[32] F. Tang, H. C. Po, A. Vishwanath, and X. Wan, Efficient topological materials discovery using symmetry indicators, Nat. Phys. 15, 470 (2019)

[33] O. Muller and R. Roy, Synthesis and crystal chemistry of some new complex palladium oxides, Adv. Chem. Ser. 98, 28 (1971)

[34] P. Norby, R. E. Dinnebier, and A. N. Fitch, Decomposition of silver carbonate: the crystal structure of two high-temperature modifications of Ag₂CO₃, Inorg. Chem. 41(14), 3628 (2002)

[35] C. J. Bradley and A. P. Cracknell, The Mathematical Theory of Symmetry in Solids, Oxford: Claredon Press, 1972

[36] O. Graudejus and B. G. Mueller, Ag²⁺ in trigonalbipyramidaler Umgebung: Neue Fluoride mit zweiwertigem Silber: Ag M(II)₃ M(IV)₃ F₂₀ (M(II) = Cd, Ca, Hg; M(IV) = Zr, Hf), Zeitschrift fuer Anorganische und Allgemeine Chemie (1950) (DE) 622, 1549–1556 (1996)

[37] T. Yamada, V. L. Deringer, R. Dronskowski, and H. Yamane, Synthesis, crystal structure, chemical bonding, and physical properties of the ternary Na/Mg stannide, Na₂MgSn, Inorg. Chem. 51(8), 4810 (2012)

[38] B. Peng, C. M. Yue, H. Zhang, Z. Fang, and H. M. Weng, Predicting Dirac semimetals based on sodium ternary compounds, npj Comput. Mater. 4, 68 (2018)

[39] H. Zentgraf, K. Claes, and R. Hoppe, Oxide eines neuen Formeltyps: Zur Kenntnis von K₃Ni₂O₄ und K₃Pt₂O₄, Zeitschrift fuer Anorganische und Allgemeine Chemie (1950) (DE) 462, 92–105 (1980)

[40] Z. Nong, J. Zhu, X. Yang, Y. Cao, Z. Lai, and Y. Liu, The mechanical, thermodynamic and electronic properties of Al₃Nb with DO₂₂ structure: A first-principles study, Physica B 407(17), 3555 (2012)

[41] H. He, C. Tyson, and S. Bobev, Eight-coordinated arsenic in the Zintl phases RbCd₄As₃ and RbZn₄As₃: Synthesis and structural characterization, Inorg. Chem. 50(17), 8375 (2011)

[42] R. W. Henning and J. D. Corbett, Cs₈Ga₁₁, a new isolated cluster in a binary gallium compound: A family of valence analogues A₈Tr₁₁X: A= Cs, Rb; Tr= Ga, In, Tl; X= Cl, Br, I, Inorg. Chem. 36(26), 6045 (1997)

[43] P. Blaha, K. Schwarz, G. Madsen, D. Kvasicka, and J. Luitz, WIEN2k: An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties, 2001

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

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature