Alkali-metal-induced topological nodal line semimetalin layered XN₂ (X= Cr, Mo, W)

Abstract

Based on first principles calculations and the K·p effective model, we propose that alkali metal deposition on the surface of hexagonal XN₂ (X= Cr, Mo, W) nanosheets induces topologically nontrivial phases in these systems. When spin orbit coupling (SOC) is disregarded, the electron-like conduction band from N-p_z orbitals can be considered to cross the hole-like valence band from X-d²_z orbitals, thereby giving rise to a topological nodal line state in lithium-functionalized XN₂ sheets (Li₂MoN₂ and Li₂WN₂). Such band crossing is protected by the existence of mirror reflection and time reversal symmetry. More interestingly, the bands cross exactly at the Fermi level, and the linear dispersion regions of such band crossings extend to as high as 0.9 eV above the crossing. For Li₂CrN₂, the results reveal the emergence of a Dirac cone at the Fermi level. Our calculations show that lattice compression decreases the thickness of a Li₂CrN₂ nanosheet, leading to phase transition to a nodal line semimetal. The evolution of the band gap of Li₂XN₂ at the Γ point indicates that the nontrivial topological character of Li₂XN₂ nanolayers is stable over a large strain range. When SOC is included, the band crossing point is gapped out giving rise to quantum spin Hall states in Li₂CrN₂ nanosheets, while for Li₂MoN₂, the SOC-induced gap at the crossing points is negligible.

Keywords

topological semimetal / nodal-line states / Dirac cone / band inversion

References

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

[2] K. He, Topological insulator: Both two- and threedimensional, Front. Phys. 7(2), 148 (2012)

[3] D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A topological Dirac insulator in a quantum spin Hall phase, Nature 452(7190), 970 (2008)

[4] Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface, Nat. Phys. 5(6), 398 (2009)

[5] S. Y. Xu, C. Liu, N. Alidoust, M. Neupane, D. Qian, I. Belopolski, J. D. Denlinger, Y. J. Wang, H. Lin, L. A. Wray, G. Landolt, B. Slomski, J. H. Dil, A. Marcinkova, E. Morosan, Q. Gibson, R. Sankar, F. C. Chou, R. J. Cava, A. Bansil, and M. Z. Hasan, Observation of a topological crystalline insulator phase and topological phase transition in Pb_1−xSn_xTe, Nat. Commun. 3(1), 1192 (2012)

[6] S. Y. Xu, C. Liu, S. K. Kushwaha, R. Sankar, J. W. Krizan, I. Belopolski, M. Neupane, G. Bian, N. Alidoust, T. R. Chang, H. T. Jeng, C. Y. Huang, W. F. Tsai, H. Lin, F. Chou, P. P. Shibayev, R. J. Cava, and M. Z. Hasan, Observation of Fermi arc surface states in a topological metal, Science 347(6219), 294 (2015)

[7] 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)

[8] B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X 5(3), 031013 (2015)

[9] C. K. Chiu and A. P. Schnyder, Classification of reflection-symmetry-protected topological semimetals and nodal superconductors, Phys. Rev. B 90(20), 205136 (2014)

[10] J. Behrends, J. W. Rhim, S. Liu, A. G. Grushin, and J. H. Bardarson, Nodal-line semimetals from Weyl superlattices, Phys. Rev. B 96(24), 245101 (2017)

[11] T. Bzdušek, Q. Wu, A. Ruegg, M. Sigrist, and A. A. Soluyanov, Nodal-chain metals, Nature 538(7623), 75 (2016)

[12] H. Weng, X. Dai, and Z. Fang, Topological semimetals predicted from first-principles calculations, J. Phys.: Condens. Matter 28(30), 303001 (2016)

[13] B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals, Science 353(6299), aaf5037 (2016)

[14] H. Weng, C. Fang, Z. Fang, and X. Dai, Coexistence of Weyl fermion and massless triply degenerate nodal points, Phys. Rev. B 94(16), 165201 (2016)

[15] G. T. Volovik, Momentum space topology of fermion zero modes brane, JETP Lett. 75(2), 55 (2002)

[16] 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)

[17] M. Dadsetani and A. Ebrahimian, Breaking inversion symmetry induces excitonic peak in optical absorption of topological semimetal, J. Phys. Chem. Solids 100, 161 (2017)

[18] M. Dadsetani and A. Ebrahimian, Optical distinctions between Weyl semimetal TaAs and Dirac semimetal Na₃Bi: An ab initio investigation,Journal of Elec., Materi. 45, 5867 (2016)

[19] 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)

[20] A. A. Burkov, Topological semimetals, Nat. Mater. 15(11), 1145 (2016)

[21] X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83(20), 205101 (2011)

[22] A. A. Burkov, M. D. Hook, and L. Balents, Topological nodal semimetals, Phys. Rev. B 84(23), 235126 (2011)

[23] M. Z. Hasan, S. Y. Xu, I. Belopolski, and S. M. Huang, Discovery of weyl fermion semimetals and topological fermi arc states, Annu. Rev. Condens. Matter Phys. 8(1), 289 (2017)

[24] C. Fang, Y. Chen, H. Y. Kee, and L. Fu, Topological nodal line semimetals with and without spin-orbital coupling, Phys. Rev. B 92(8), 081201 (2015)

[25] Y. X. Zhao, A. P. Schnyder, and Z. D. Wang, Unified theory of PT and CP invariant topological metals and nodal superconductors, Phys. Rev. Lett. 116(15), 156402 (2016)

[26] R. Yu, Z. Fang, X. Dai, and H. Weng, Topological nodal line semimetals predicted from first-principles calculations, Front. Phys. 12(3), 127202 (2017)

[27] H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Weyl semimetal phase in noncentro-symmetric transition-metal monophosphides, Phys. Rev. X 5(1), 011029 (2015)

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

[29] 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)

[30] S. Borisenko, Q. Gibson, D. Evtushinsky, V. Zabolotnyy, B. Büchner, and R. J. Cava, experimental realization of a three-dimensional Dirac semimetal, Phys. Rev. Lett. 113(2), 027603 (2014)

[31] 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)

[32] S. Y. Xu, C. Liu, S. K. Kushwaha, R. Sankar, J. W. Krizan, I. Belopolski, M. Neupane, G. Bian, N. Alidoust, T. R. Chang, H. T. Jeng, C. Y. Huang, W. F. Tsai, H. Lin, P. P. Shibayev, F. C. Chou, R. J. Cava, and M. Z. Hasan, Observation of Fermi arc surface states in a topological metal, Science 347(6219), 294 (2015)

[33] G. Bian, T. R. Chang, R. Sankar, S. Y. Xu, H. Zheng, T. Neupert, C. K. Chiu, S. M. Huang, G. Chang, I. Belopolski, D. S. Sanchez, M. Neupane, N. Alidoust, C. Liu, B. Wang, C. C. Lee, H. T. Jeng, C. Zhang, Z. Yuan, S. Jia, A. Bansil, F. Chou, H. Lin, and M. Z. Hasan, Topological nodal-line fermions in spin-orbit metal PbTaSe₂, Nat. Commun. 7, 10556 (2016)

[34] Y. Wu, L. L. Wang, E. Mun, D. D. Johnson, D. Mou, L. Huang, Y. Lee, S. L. Bud’ko, P. C. Canfield, and A. Kaminski, Dirac node arcs in PtSn₄, Nat. Phys. 12(7), 667 (2016)

[35] L. M. Schoop, M. N. Ali, C. Straßer, A. Topp, A. Varykhalov, D. Marchenko, V. Duppel, S. S. P. Parkin, B. V. Lotsch, and C. R. Ast, Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS, Nat. Commun. 7, 11696 (2016)

[36] M. Neupane, I. Belopolski, M. M. Hosen, D. S. Sanchez, R. Sankar, M. Szlawska, S. Y. Xu, K. Dimitri, N. Dhakal, P. Maldonado, P. M. Oppeneer, D. Kaczorowski, F. Chou, M. Z. Hasan, and T. Durakiewicz, Observation of topological nodal fermion semimetal phase in ZrSiS, Phys. Rev. B 93(20), 201104 (2016)

[37] T. Liang, Q. Gibson, M. N. Ali, M. Liu, R. J. Cava, and N. P. Ong, Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd₃As₂, Nat. Mater. 14(3), 280 (2015)

[38] Y. Zhao, H. Liu, C. Zhang, H. Wang, J. Wang, Z. Lin, Y. Xing, H. Lu, J. Liu, Y. Wang, S. M. Brombosz, Z. Xiao, S. Jia, X. C. Xie, and J. Wang, Anisotropic Fermi surface and quantum limit transport in high mobility three-dimensional Dirac semimetal Cd₃As₂, Phys. Rev. X 5(3), 031037 (2015)

[39] H. Wang, H. Wang, H. Liu, H. Lu, W. Yang, S. Jia, X.J. Liu, X. C. Xie, J. Wei, and J. Wang, Observation of superconductivity induced by a point contact on 3D Dirac semimetal Cd₃As₂ crystals, Nat. Mater. 15(1), 38 (2016)

[40] H. Weng, Y. Liang, Q. Xu, R. Yu, Z. Fang, X. Dai, and Y. Kawazoe, Topological node-line semimetal in threedimensional graphene networks, Phys. Rev. B 92(4), 045108 (2015)

[41] R. Yu, H. Weng, Z. Fang, X. Dai, and X. Hu, Topological node-line semimetal and Dirac semimetal state in antiperovskite Cu₃PdN, Phys. Rev. Lett. 115(3), 036807 (2015)

[42] Y. Kim, B. J. Wieder, C. L. Kane, and A. M. Rappe, Dirac line nodes in inversion-symmetric crystals, Phys. Rev. Lett. 115(3), 036806 (2015)

[43] J. Zhang, M. Gao, J. Zhang, X. Wang, X. Zhang, M. Zhang, W. Niu, R. Zhang, and Y. Xu, Transport evidence of 3D topological nodal-line semimetal phase in ZrSiS, Front. Phys. 13(1), 137201 (2018)

[44] L. M. Schoop, M. N. Ali, C. Straßer, A. Topp, A. Varykhalov, D. Marchenko, V. Duppel, S. S. P. Parkin, B. V. Lotsch, and C. R. Ast, Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS, Nat. Commun. 7, 11696 (2016)

[45] S. M. Young and C. L. Kane, Dirac semimetals in two dimensions, Phys. Rev. Lett. 115(12), 126803 (2015)

[46] C. Niu, P. M. Buhl, G. Bihlmayer, D. Wortmann, Y. Dai, S. Blügel, and Y. Mokrousov, Two-dimensional topological nodal line semimetal in layered X₂Y (X= Ca, Sr, and Ba; Y=As, Sb, and Bi), Phys. Rev. B 95(23), 235138 (2017)

[47] J. L. Lu, W. Luo, X. Y. Li, S. Q. Yang, J. X. Cao, X. G. Gong, and H. J. Xiang, Two-dimensional node-line semimetals in a honeycomb-Kagome lattice, Chin. Phys. Lett. 34(5), 057302 (2017)

[48] Y. J. Jin, R. Wang, J. Z. Zhao, Y. P. Du, C. D. Zheng, L. Y. Gan, J. F. Liu, H. Xu, and S. Y. Tong, The prediction of a family group of two-dimensional node-line semimetals, Nanoscale 9(35), 13112 (2017)

[49] B. Yang, X. Zhang, and M. Zhao, Dirac node lines in two-dimensional Lieb lattices, Nanoscale 9(25), 8740 (2017)

[50] A. Ebrahimian and M. Dadsetani, Dependence of topological and optical properties on surface-terminated groups in two-dimensional molybdenum dinitride and tungsten dinitride nanosheets, Phys. Chem. Chem. Phys. 19(45), 30301 (2017)

[51] B. Feng, B. Fu, S. Kasamatsu, S. Ito, P. Cheng, C. C. Liu, Y. Feng, S. Wu, S. K. Mahatha, P. Sheverdyaeva, P. Moras, M. Arita, O. Sugino, T. C. Chiang, K. Shimada, K. Miyamoto, T. Okuda, K. Wu, L. Chen, Y. Yao, and I. Matsuda, Experimental realization of twodimensional Dirac nodal line fermions in monolayer Cu₂Si, Nat. Commun. 8(1), 1007 (2017)

[52] N. B. Kopnin, T. T. Heikkila, and G. E. Volovik, High temperature surface superconductivity in topological flat-band systems, Phys. Rev. B 83(22), 220503 (2011)

[53] Z. Y. Zhu, Y. C. Cheng, and U. Schwingenschlögl, Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors, Phys. Rev. B 84(15), 153402 (2011)

[54] D. Xiao, G. B. Liu, W. Feng, X. Xu, and W. Yao, Coupled spin and valley physics in monolayers of MoS2 and other group-VI Dichalcogenides, Phys. Rev. Lett. 108(19), 196802 (2012)

[55] Y. Ma, L. Kou, X. Li, Y. Dai, and T. Heine, Twodimensional transition metal dichalcogenides with a hexagonal lattice: Room-temperature quantum spin Hall insulators, Phys. Rev. B 93(3), 035442 (2016)

[56] P. F. Liu, L. Zhou, T. Frauenheim, and L. M. Wu, New quantum spin Hall insulator in two-dimensional MoS₂, with periodically distributed pores, Nanoscale 8(9), 4915 (2016)

[57] P. F. Liu, L. Zhou, T. Frauenheim, and L. M. Wu, Two dimensional hydrogenated molybdenum and tungsten dinitrides MN₂H₂ (M= Mo, W) as novel quantum spin hall insulators with high stability, Nanoscale 9(3), 1007 (2017)

[58] N. Alidoust, G. Bian, S. Y. Xu, R. Sankar, M. Neupane, C. Liu, I. Belopolski, D. X. Qu, J. D. Denlinger, F. C. Chou, and M. Z. Hasan, Observation of monolayer valence band spin-orbit effect and induced quantum well states in MoX₂, Nat. Commun. 5(1), 4673 (2014)

[59] K. Dolui, I. Rungger, C. Das Pemmaraju, and S. Sanvito, Possible doping strategies for MoS₂ monolayers: An ab initio study, Phys. Rev. B 88(7), 075420 (2013)

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

[61] K. Hummer, J. Harl, and G. Kresse, Heyd-Scuseria- Ernzerhof hybrid functional for calculating the lattice dynamics of semiconductors, Phys. Rev. B 80(11), 115205 (2009)

[62] F. Tran and P. Blaha, Accurate band gaps of semiconductors and insulators with a semilocal exchangecorrelation potential, Phys. Rev. Lett. 102(22), 226401 (2009)

[63] P. Blaha, K. Schwarz, G. Madsen, D. Kvasicka, and J. Luitz, WIEN2k, An Augmented Plane Wave Plus Local OrbitalsProgram for Calculating Crystal Properties, TU Vienna, Vienna,2001

[64] V. Blum, R. Gehrke, F. Hanke, P. Havu, V. Havu, X. Ren, K. Reuter, and M. Scheffler, Ab initio molecular simulations with numeric atom-centered orbitals, Comput. Phys. Commun. 180(11), 2175 (2009)

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

[66] X. Zhang, X. F. Qiao, W. Shi, J. B. Wu, D. S. Jiang, and P. H. Tan, Phonon and Raman scattering of two-dimensional transition metal dichalcogenides from monolayer, multilayer to bulk material, Chem. Soc. Rev. 44(9), 2757 (2015)

[67] See the Supplemental Material.

[68] G. Bian, T. R. Chang, H. Zheng, S. Velury, S. Y. Xu, T. Neupert, C. K. Chiu, S. M. Huang, D. S. Sanchez, I. Belopolski, N. Alidoust, P. J. Chen, G. Chang, A. Bansil, H. T. Jeng, H. Lin, and M. Z. Hasan, Drumhead surface states and topological nodal-line fermions in TlTaSe₂, Phys. Rev. B 93(12), 121113 (2016)

[69] L. Fu, C. L. Kane, and E. J. Mele, Topological insulators in three dimensions, Phys. Rev. Lett. 98(10), 106803 (2007)

[70] L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B 76(4), 045302 (2007)

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