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Two-dimensional quadratic double Weyl semimetal

Xinlei Zhao1, Fengjie Ma1,*, Peng-Jie Guo2,†, and Zhong-Yi Lu3

  • 1Center for Advanced Quantum Studies and Department of Physics, Beijing Normal University, Beijing 100875, China
  • 2Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
  • 3Department of Physics, Renmin University of China, Beijing 100872, China

  • *fengjie.ma@bnu.edu.cn
  • †pjguo@iphy.ac.cn
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Phys. Rev. Research 4, 043183 – Published 12 December, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.043183

Abstract

Unconventional Weyl semimetals have attracted intensive research interest in condensed-matter physics and materials science, but they are very rare in two dimensions. In this work, based on symmetry analysis and first-principles electronic structure calculations, we predict that the Si/Bi van der Waals heterostructure is a two-dimensional unconventional quadratic double Weyl semimetal with strong spin-orbit coupling (SOC). Although unprotected by the C3v double group symmetry of the heterostructure, the two-dimensional quadratic double Weyl semimetal is stable for compressive strains up to 6.64%. The system transforms into a trivial semimetal with further increasing strain, where the phase boundary is a two-dimensional triply degenerate semimetal state. Furthermore, the Kane-Mele tight-binding model calculations show that the quadratic double Weyl phase is derived from the competition between the Rashba SOC and the proximity-effect-enhanced intrinsic SOC. On the other hand, by breaking mirror symmetry, the quadratic double Weyl semimetal transforms into a quantum spin Hall insulator as well as a quantum valley Hall insulator phase. Thus, the Si/Bi heterostructure is an excellent platform for studying the exotic physics of the two-dimensional double Weyl semimetal and other novel topological phases.

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References (45)

  1. 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, 205101 (2011).
  2. G. Xu, H. Weng, Z. Wang, X. Dai, and Z. Fang, Chern Semimetal and the Quantized Anomalous Hall Effect in HgCr2Se4, Phys. Rev. Lett. 107, 186806 (2011).
  3. H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal Monophosphides, Phys. Rev. X 5, 011029 (2015).
  4. H. Weng, X. Dai, and Z. Fang, Topological semimetals predicted from first-principles calculations, J. Phys.: Condens. Matter 28, 303001 (2016).
  5. S.-Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C.-C. Lee, S.-M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349, 613 (2015).
  6. X. Huang, L. Zhao, Y. Long, P. Wang, D. Chen, Z. Yang, H. Liang, M. Xue, H. Weng, Z. Fang, X. Dai, and G. Chen, Observation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAs, Phys. Rev. X 5, 031023 (2015).
  7. Q. Wang, Y. Xu, R. Lou, Z. Liu, M. Li, Y. Huang, D. Shen, H. Weng, S. Wang, and H. Lei, Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions, Nat. Commun. 9, 3681 (2018).
  8. E. Liu, Y. Sun, N. Kumar, L. Muechler, A. Sun, L. Jiao, S.-Y. Yang, D. Liu, A. Liang, Q. Xu, J. Kroder, V. Süß, H. Borrmann, C. Shekhar, Z. Wang, C. Xi, W. Wang, W. Schnelle, S. Wirth, Y. Chen, S. T. B. Goennenwein, and C. Felser, Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal, Nat. Phys. 14, 1125 (2018).
  9. Z. Song and X. Dai, Hear the Sound of Weyl Fermions, Phys. Rev. X 9, 021053 (2019).
  10. J. Xiang, S. Hu, Z. Song, M. Lv, J. Zhang, L. Zhao, W. Li, Z. Chen, S. Zhang, J.-T. Wang, Y.-f. Yang, X. Dai, F. Steglich, G. Chen, and P. Sun, Giant Magnetic Quantum Oscillations in the Thermal Conductivity of TaAs: Indications of Chiral Zero Sound, Phys. Rev. X 9, 031036 (2019).
  11. S.-M. Huang, S.-Y. Xu, I. Belopolski, C.-C. Lee, G. Chang, T.-R. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, D. Sanchez, H. Zheng, H.-T. Jeng, A. Bansil, T. Neupert, H. Lin, and M. Z. Hasan, New type of Weyl semimetal with quadratic double Weyl fermions, Proc. Natl. Acad. Sci. USA 113, 1180 (2016).
  12. W. Wu, Z.-M. Yu, X. Zhou, Y. X. Zhao, and S. A. Yang, Higher-order Dirac fermions in three dimensions, Phys. Rev. B 101, 205134 (2020).
  13. T. Zhang, R. Takahashi, C. Fang, and S. Murakami, Twofold quadruple Weyl nodes in chiral cubic crystals, Phys. Rev. B 102, 125148 (2020).
  14. W. Yao, S. A. Yang, and Q. Niu, Edge States in Graphene: From Gapped Flat-Band to Gapless Chiral Modes, Phys. Rev. Lett. 102, 096801 (2009).
  15. H. Pan, X. Li, F. Zhang, and S. A. Yang, Perfect valley filter in a topological domain wall, Phys. Rev. B 92, 041404(R) (2015).
  16. K. Sun and E. Fradkin, Time-reversal symmetry breaking and spontaneous anomalous Hall effect in Fermi fluids, Phys. Rev. B 78, 245122 (2008).
  17. K. Sun, H. Yao, E. Fradkin, and S. A. Kivelson, Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing, Phys. Rev. Lett. 103, 046811 (2009).
  18. H. Isobe and N. Nagaosa, Coulomb Interaction Effect in Weyl Fermions with Tilted Energy Dispersion in Two Dimensions, Phys. Rev. Lett. 116, 116803 (2016).
  19. L. Hao and C. S. Ting, Topological phase transitions and a two-dimensional Weyl superconductor in a half-metal/superconductor heterostructure, Phys. Rev. B 94, 134513 (2016).
  20. J.-Y. You, C. Chen, Z. Zhang, X.-L. Sheng, S. A. Yang, and G. Su, Two-dimensional Weyl half-semimetal and tunable quantum anomalous Hall effect, Phys. Rev. B 100, 064408 (2019).
  21. Y. Guo, Z. Lin, J. Q. Zhao, J. Lou, and Y. Chen, Two-dimensional tunable Dirac/Weyl semimetal in non-Abelian gauge field, Sci. Rep. 9, 18516 (2019).
  22. W. Meng, X. Zhang, Y. Liu, L. Wang, X. Dai, and G. Liu, Two-dimensional Weyl semimetal with coexisting fully spin-polarized type-I and type-II Weyl points, Appl. Surf. Sci. 540, 148318 (2021).
  23. T. He, X. Zhang, Y. Liu, X. Dai, G. Liu, Z.-M. Yu, and Y. Yao, Ferromagnetic hybrid nodal loop and switchable type-I and type-II Weyl fermions in two dimensions, Phys. Rev. B 102, 075133 (2020).
  24. D. Wu, Y. Huang, S. Sun, J. Gao, Z. Guo, H. Weng, Z. Fang, K. Jiang, and Z. Wang, Unprotected quadratic band crossing points and quantum anomalous Hall effect in FeB2 monolayer, Sci. China Phys. Mech. Astron. 65, 256811 (2022).
  25. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri et al., QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
  26. P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. D. Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio, Jr., A. Ferretti, A. Floris, G. Fratesi, G. Fugallo et al., Advanced capabilities for materials modelling with quantum ESPRESSO, J. Phys.: Condens. Matter 29, 465901 (2017).
  27. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).
  28. D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B 41, 7892(R) (1990).
  29. M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist, Van Der Waals Density Functional for General Geometries, Phys. Rev. Lett. 92, 246401 (2004).
  30. A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 178, 685 (2008).
  31. 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).
  32. A. Stpniak-Dybala, P. Dyniec, M. Kopciuszyski, R. Zdyb, M. Jałochowski, and M. Krawiec, Planar silicene: A new silicon allotrope epitaxially grown by segregation, Adv. Funct. Mater. 29, 1906053 (2019).
  33. T. Hirahara, N. Fukui, T. Shirasawa, M. Yamada, M. Aitani, H. Miyazaki, M. Matsunami, S. Kimura, T. Takahashi, S. Hasegawa, and K. Kobayashi, Atomic and Electronic Structure of Ultrathin Bi(111) Films Grown on Bi2Te3(111) Substrates: Evidence for a Strain-Induced Topological Phase Transition, Phys. Rev. Lett. 109, 227401 (2012).
  34. L. Miao, Z. F. Wang, W. Ming, M.-Y. Yao, M. Wang, F. Yang, Y. R. Song, F. Zhu, A. V. Fedorov, Z. Sun, C. L. Gao, C. Liu, Q.-K. Xue, C.-X. Liu, F. Liu, D. Qian, and J.-F. Jia, Quasiparticle dynamics in reshaped helical Dirac cone of topological insulators, Proc. Natl. Acad. Sci. USA 110, 2758 (2013).
  35. Z. F. Wang, M.-Y. Yao, W. Ming, L. Miao, F. Zhu, C. Liu, C. L. Gao, D. Qian, J.-F. Jia, and F. Liu, Creation of helical Dirac fermions by interfacing two gapped systems of ordinary fermions, Nat. Commun. 4, 1384 (2013).
  36. S. Murakami, Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling, Phys. Rev. Lett. 97, 236805 (2006).
  37. H. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice: (I). Proof by homotopy theory, Nucl. Phys. B 185, 20 (1981).
  38. H. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice: (II). Intuitive topological proof, Nucl. Phys. B 193, 173 (1981).
  39. P.-J. Guo, Y.-W. Wei, K. Liu, Z.-X. Liu, and Z.-Y. Lu, Eightfold Degenerate Fermions in Two Dimensions, Phys. Rev. Lett. 127, 176401 (2021).
  40. C. L. Kane and E. J. Mele, Z2 Topological Order and the Quantum Spin Hall Effect, Phys. Rev. Lett. 95, 146802 (2005).
  41. E. C. Marino, L. O. Nascimento, V. S. Alves, and C. M. Smith, Interaction Induced Quantum Valley Hall Effect in Graphene, Phys. Rev. X 5, 011040 (2015).
  42. D. Xiao, W. Yao, and Q. Niu, Valley-Contrasting Physics in Graphene: Magnetic Moment and Topological Transport, Phys. Rev. Lett. 99, 236809 (2007).
  43. J. Ding, Z. Qiao, W. Feng, Y. Yao, and Q. Niu, Engineering quantum anomalous/valley Hall states in graphene via metal-atom adsorption: An ab-initio study, Phys. Rev. B 84, 195444 (2011).
  44. P. Ghaemi, S. Ryu, and D.-H. Lee, Quantum valley Hall effect in proximity-induced superconducting graphene: An experimental window for deconfined quantum criticality, Phys. Rev. B 81, 081403(R) (2010).
  45. I. Watanabe, S. Souma, K. Nakayama, K. Sugawara, C. X. Trang, K. Segawa, K. Yamauchi, T. Oguchi, T. Takahashi, and T. Sato, Pb/Bi heterostructure as a versatile platform to realize topological superconductivity, Prog. Theor. Exp. Phys. 2022, 04A103 (2022).

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Phys. Rev. Research 4, 043183– Published 12 December, 2022
  • Received 18 February 2022
  • Accepted 8 November 2022
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