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.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price includes VAT (USA)
Tax calculation will be finalised during checkout.
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
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
Rachel S, Ezawa M (2014) Giant magnetoresistance and perfect spin filter in silicene, germanene, and stanene. Phys Rev B 89:195303
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
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
Liu CC, Feng W, Yao Y (2011) Quantum spin Hall effect in silicene and two-dimensional germanium. Phys Rev Lett 107:076802
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
Schwierz F (2010) Graphene transistors. Nat Nanotechnol 5:487–496
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
Tabert CJ, Nicol EJ (2013) AC/DC spin and valley Hall effects in silicene and germanene. Phys Rev B 87:235426
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
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
Matthes L, Gori P, Pulci O, Bechstedt F (2013) Universal infrared absorbance of two-dimensional honeycomb group-IV crystals. Phys Rev B 87:035438
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
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
Tabert CJ, Nicol EJ (2013) Magneto-optical conductivity of silicene and other buckled honeycomb lattices. Phys Rev B 88:085434
Shakouri K, Vasilopoulos P, Vargiamidis V, Peeters FM (2014) Spin-and valley-dependent magnetotransport in periodically modulated silicene. Phys Rev B 90:125444
Bolotin KI, Ghahari F, Shulman MD, Stormer HL, Kim P (2009) Observation of the fractional quantum Hall effect in graphene. Nature 462:196–199
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
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
Ezawa M (2012) Valley-polarized metals and quantum anomalous Hall effect in silicene. Phys Rev Lett 109:055502
Ezawa M (2012) Spin-valley optical selection rule and strong circular dichroism in silicene. Phys Rev B 86:161407
Ezawa M (2013) Spin valleytronics in silicene: Quantum spin Hall-quantum anomalous Hall insulators and single-valley semimetals. Phys Rev B 87:155415
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
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
Vargiamidis V, Vasilopoulos P, Hai GQ (2014) Dc and ac transport in silicene. J Phys Condens Matter 26:345303
Mahan GD (2010) Many-particle physics, 3rd edn. Plenum, New York
Kane CL, Mele EJ (2005) Quantum spin Hall effect in graphene. Phys Rev Lett 95:226801
Li Z, Carbotte JP (2012) Longitudinal and spin-valley Hall optical conductivity in single layer MoS 2. Phys Rev B 86:205425
This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 103.01-2017.309.
Conflict of interest
The authors declare that they have no conflict of interest.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
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). https://doi.org/10.1007/s10853-020-05044-0