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Low-energy bands, optical properties, and spin/valley-Hall conductivity of silicene and germanene


In this work, we study systematically low-energy bands, optical absorbance and spin/valley-Hall conductivity of silicene and germanene in the presence of a perpendicular electric field. Our analytical calculations indicate that both silicene and germanene are semiconductors with a tiny energy gap and we can control their energy gap by the perpendicular electric field. Our calculations also demonstrate that the low-frequency optical absorbance of silicene is much greater than that of germanene and the external electric field plays an important role in determining the optical absorption peaks. When the Fermi level is in the forbidden band, the Hall conductivity is quantized, while spin/valley-Hall conductivities of both silicene and germanene depend strongly on the Fermi energy when the Fermi level is in the conduction band. Analytical results for spin/valley-Hall conductivities of silicene and germanene are presented in detail in this work.

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  1. 1

    Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA (2004) Electric field effect in atomically thin carbon films. Science 306:666–669

    CAS  Article  Google Scholar 

  2. 2

    Tao L, Cinquanta E, Chiappe D, Grazianetti C, Fanciulli M, Dubey M, Molle A, Akinwande D (2015) Silicene field-effect transistors operating at room temperature. Nat Nanotechnol 10:227–231

    CAS  Article  Google Scholar 

  3. 3

    Rachel S, Ezawa M (2014) Giant magnetoresistance and perfect spin filter in silicene, germanene, and stanene. Phys Rev B 89:195303

    Article  Google Scholar 

  4. 4

    Feng B, Ding Z, Meng S, Yao Y, He X, Cheng P, Chen L, Wu K (2012) Evidence of silicene in honeycomb structures of silicon on Ag (111). Nano Lett 12:3507–3511

    CAS  Article  Google Scholar 

  5. 5

    Dávila ME, Xian L, Cahangirov S, Rubio A, Le Lay G (2014) Germanene: a novel two-dimensional germanium allotrope akin to graphene and silicene. New J Phys 16:095002

    Article  Google Scholar 

  6. 6

    Liu CC, Feng W, Yao Y (2011) Quantum spin Hall effect in silicene and two-dimensional germanium. Phys Rev Lett 107:076802

    Article  Google Scholar 

  7. 7

    Liu CC, Jiang H, Yao Y (2011) Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin. Phys Rev B 84:195430

    Article  Google Scholar 

  8. 8

    Schwierz F (2010) Graphene transistors. Nat Nanotechnol 5:487–496

    CAS  Article  Google Scholar 

  9. 9

    Tabert CJ, Nicol EJ (2013) Valley-spin polarization in the magneto-optical response of silicene and other similar 2D crystals. Phys Rev Lett 110:197402

    CAS  Article  Google Scholar 

  10. 10

    Tabert CJ, Nicol EJ (2013) AC/DC spin and valley Hall effects in silicene and germanene. Phys Rev B 87:235426

    Article  Google Scholar 

  11. 11

    Matthes L, Pulci O, Bechstedt F (2013) Massive Dirac quasiparticles in the optical absorbance of graphene, silicene, germanene, and tinene. J Phys Condens Matter 25:395305

    Article  Google Scholar 

  12. 12

    Ni Z, Liu Q, Tang K, Zheng J, Zhou J, Qin R, Gao Z, Yu D, Lu J (2012) Tunable bandgap in silicene and germanene. Nano Lett 12:113–118

    CAS  Article  Google Scholar 

  13. 13

    Matthes L, Gori P, Pulci O, Bechstedt F (2013) Universal infrared absorbance of two-dimensional honeycomb group-IV crystals. Phys Rev B 87:035438

    Article  Google Scholar 

  14. 14

    Muoi D, Hieu NN, Nguyen CV, Hoi BD, Nguyen HV, Hien ND, Poklonski NA, Kubakaddi SS, Phuc HV (2020) Magneto-optical absorption in silicene and germanene induced by electric and Zeeman fields. Phys Rev B 101:205408

    Article  Google Scholar 

  15. 15

    Do TN, Gumbs G, Shih PH, Huang D, Lin MF (2019) Valley-and spin-dependent quantum Hall states in bilayer silicene. Phys Rev B 100:155403

    CAS  Article  Google Scholar 

  16. 16

    Tabert CJ, Nicol EJ (2013) Magneto-optical conductivity of silicene and other buckled honeycomb lattices. Phys Rev B 88:085434

    Article  Google Scholar 

  17. 17

    Shakouri K, Vasilopoulos P, Vargiamidis V, Peeters FM (2014) Spin-and valley-dependent magnetotransport in periodically modulated silicene. Phys Rev B 90:125444

    Article  Google Scholar 

  18. 18

    Bolotin KI, Ghahari F, Shulman MD, Stormer HL, Kim P (2009) Observation of the fractional quantum Hall effect in graphene. Nature 462:196–199

    CAS  Article  Google Scholar 

  19. 19

    Dean CR, Young AF, Cadden-Zimansky P, Wang L, Ren H, Watanabe K, Taniguchi T, Kim P, Hone J, Shepard KL (2011) Multicomponent fractional quantum Hall effect in graphene. Nat Phys 7:693–696

    CAS  Article  Google Scholar 

  20. 20

    Tahir M, Manchon A, Sabeeh K, Schwingenschlögl U (2013) Quantum spin/valley Hall effect and topological insulator phase transitions in silicene. Appl Phys Lett 102:162412

    Article  Google Scholar 

  21. 21

    Ezawa M (2012) Valley-polarized metals and quantum anomalous Hall effect in silicene. Phys Rev Lett 109:055502

    Article  Google Scholar 

  22. 22

    Ezawa M (2012) Spin-valley optical selection rule and strong circular dichroism in silicene. Phys Rev B 86:161407

    Article  Google Scholar 

  23. 23

    Ezawa M (2013) Spin valleytronics in silicene: Quantum spin Hall-quantum anomalous Hall insulators and single-valley semimetals. Phys Rev B 87:155415

    Article  Google Scholar 

  24. 24

    Hien ND, Nguyen CV, Hieu NN, Kubakaddi SS, Duque CA, Mora-Ramos ME, Dinh L, Bich TN, Phuc HV (2020) Magneto-optical transport properties of monolayer transition metal dichalcogenides. Phys Rev B 101:045424

    Article  Google Scholar 

  25. 25

    Bao H, Liao W, Zhang X, Yang H, Yang X, Zhao H (2017) Photoinduced quantum spin/valley Hall effect and its electrical manipulation in silicene. J Appl Phys 121:205106

    Article  Google Scholar 

  26. 26

    Vargiamidis V, Vasilopoulos P, Hai GQ (2014) Dc and ac transport in silicene. J Phys Condens Matter 26:345303

    CAS  Article  Google Scholar 

  27. 27

    Mahan GD (2010) Many-particle physics, 3rd edn. Plenum, New York

    Google Scholar 

  28. 28

    Kane CL, Mele EJ (2005) Quantum spin Hall effect in graphene. Phys Rev Lett 95:226801

    CAS  Article  Google Scholar 

  29. 29

    Li Z, Carbotte JP (2012) Longitudinal and spin-valley Hall optical conductivity in single layer MoS 2. Phys Rev B 86:205425

    Article  Google Scholar 

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This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 103.01-2017.309.

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Correspondence to Le T. Hoa or Nguyen N. Hieu.

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Huong, P.T., Muoi, D., Phuc, H.V. et al. Low-energy bands, optical properties, and spin/valley-Hall conductivity of silicene and germanene. J Mater Sci 55, 14848–14857 (2020).

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