Advertisement

Valley Hall Effect and Magnetic Moment in Magnetized Silicene

  • Sake WangEmail author
  • Pengzhan Zhang
  • Chongdan Ren
  • Hongyu Tian
  • Juan Pang
  • Chi Song
  • Minglei SunEmail author
Original Paper
  • 53 Downloads

Abstract

We investigate the physical properties of silicene with both staggered sublattice potential and magnetization by using Kubo formalism, the latter arises from the magnetic proximity effect by depositing Fe atoms to silicene or depositing silicene on an appropriate ferromagnetic insulator. Based on the low-energy continuum model of the system where inversion symmetry is broken, we show that the system exhibits spin half metal state when staggered sublattice potential is in the same magnitude with mean and staggered magnetization. Besides, Hall conductivity and magnetic moment are all valley dependent, so we investigate the valley Hall effect of the system further by considering magnetization exclusively. This means carriers in different valleys turning into opposite directions transverse to an in-plane electric field. At last, we prove these results by investigating Berry curvature that characterizing Hall transport, which is also valley dependent. These effects can be used to generate valley-polarized currents solely by magnetization, forming the basis for the valley-based electronics applications.

Keywords

Silicene Valleytronics Magnetization Valley Hall effect Kubo formula Magnetic moment 

Notes

Funding Information

This study was funded by the National Natural Science Foundation of China (grant numbers 11704165, 11864047, and 21702082), the National Science Foundation for Post-doctoral Scientists of China (grant number 2017M621711), the Major Research Project for Innovative Group of Education Department of Guizhou Province (grant number KY[2018]028), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (grant number 17KJB140008), and the Science Foundation of Jinling Institute of Technology (grant numbers 40620062 and 40620064).

References

  1. 1.
    Lalmi, B., Oughaddou, H., Enriquez, H., Kara, A., Vizzini, S., Ealet, B., Aufray, B.: Epitaxial growth of a silicene sheet. Appl. Phys. Lett. 97(22), 223109 (2010).  https://doi.org/10.1063/1.3524215 ADSCrossRefGoogle Scholar
  2. 2.
    Vogt, P., Padova, P.D., Quaresima, C., Avila, J., Frantzeskakis, E., Asensio, M.C., Resta, A., Ealet, B., Le Lay, G.: Silicene: compelling experimental evidence for graphenelike two-dimensional silicon. Phys. Rev. Lett. 108(15), 155501 (2012).  https://doi.org/10.1103/PhysRevLett.108.155501 ADSCrossRefGoogle Scholar
  3. 3.
    Meng, L., Wang, Y., Zhang, L., Du, S., Wu, R., Li, L., Zhang, Y., Li, G., Zhou, H., Hofer, W.A., Gao, H.J.: Buckled silicene formation on Ir(111). Nano. Lett. 13(2), 685 (2013).  https://doi.org/10.1021/nl304347w ADSCrossRefGoogle Scholar
  4. 4.
    Fleurence, A., Friedlein, R., Ozaki, T., Kawai, H., Wang, Y., Yamada-Takamura, Y.: Experimental evidence for epitaxial silicene on diboride thin films. Phys. Rev. Lett. 108(24), 245501 (2012).  https://doi.org/10.1103/PhysRevLett.108.245501 ADSCrossRefGoogle Scholar
  5. 5.
    Yamakage, A., Ezawa, M., Tanaka, Y., Nagaosa, N.: Charge transport in pn and npn junctions of silicene. Phys. Rev. B 88(8), 085322 (2013).  https://doi.org/10.1103/PhysRevB.88.085322 ADSCrossRefGoogle Scholar
  6. 6.
    Fagan, S.B., Baierle, R.J., Mota, R., da Silva, A.J.R., Fazzio, A.: Ab initio calculations for a hypothetical material: silicon nanotubes. Phys. Rev. B 61(15), 9994 (2000).  https://doi.org/10.1103/PhysRevB.61.9994 ADSCrossRefGoogle Scholar
  7. 7.
    Liu, C.C., Feng, W., Yao, Y.: Quantum spin Hall effect in silicene and two-dimensional germanium. Phys. Rev. Lett. 107(7), 076802 (2011).  https://doi.org/10.1103/PhysRevLett.107.076802 ADSCrossRefGoogle Scholar
  8. 8.
    Wang, S., Yu, J.: Magnetic behaviors of 3d transition metal-doped silicane: a first-principle study. J. Supercond. Nov. Magn. 31(9), 2789 (2018).  https://doi.org/10.1007/s10948-017-4532-4 CrossRefGoogle Scholar
  9. 9.
    Wang, S., Yu, J.: Tuning electronic properties of silicane layers by tensile strain and external electric field: a first-principles study. Thin Solid Films 654, 107 (2018).  https://doi.org/10.1016/j.tsf.2018.03.061. http://www.sciencedirect.com/science/article/pii/S0040609018302050 ADSCrossRefGoogle Scholar
  10. 10.
    Ukhtary, M.S., Nugraha, A.R.T., Hasdeo, E.H., Saito, R.: Broadband transverse electric surface wave in silicene. Appl. Phys. Lett. 109(6), 063103 (2016).  https://doi.org/10.1063/1.4960531 ADSCrossRefGoogle Scholar
  11. 11.
    Ezawa, M., Le Lay, G.: Focus on silicene and other 2D materials. New J. Phys. 17(9), 090201 (2015). http://stacks.iop.org/1367-2630/17/i=9/a=090201 ADSCrossRefGoogle Scholar
  12. 12.
    Chen, L., Liu, C.C., Feng, B., He, X., Cheng, P., Ding, Z., Meng, S., Yao, Y., Wu, K.: Evidence for Dirac fermions in a honeycomb lattice based on silicon. Phys. Rev. Lett. 109(5), 056804 (2012).  https://doi.org/10.1103/PhysRevLett.109.056804 ADSCrossRefGoogle Scholar
  13. 13.
    Spencer, M.J., Morishita, T. (eds.): Silicene: structure, properties and applications. Springer International Publishing, Cham (2016)Google Scholar
  14. 14.
    Guzmán-Verri, G.G., Lew Yan Voon, L.C.: Electronic structure of silicon-based nanostructures. Phys. Rev. B 76(7), 075131 (2007).  https://doi.org/10.1103/PhysRevB.76.075131 ADSCrossRefGoogle Scholar
  15. 15.
    Liu, C.C., Jiang, H., Yao, Y.: Low-energy effective Hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin. Phys. Rev. B 84(19), 195430 (2011).  https://doi.org/10.1103/PhysRevB.84.195430 ADSCrossRefGoogle Scholar
  16. 16.
    Ezawa, M.: Valley-polarized metals and quantum anomalous Hall effect in silicene. Phys. Rev. Lett. 109(5), 055502 (2012).  https://doi.org/10.1103/PhysRevLett.109.055502 ADSCrossRefGoogle Scholar
  17. 17.
    Ezawa, M.: A topological insulator and helical zero mode in silicene under an inhomogeneous electric field. New J. Phys. 14(3), 033003 (2012). http://stacks.iop.org/1367-2630/14/i=3/a=033003 ADSCrossRefGoogle Scholar
  18. 18.
    Zhang, L.D., Yang, F., Yao, Y.: Possible electric-field-induced superconducting states in doped silicene. Sci. Rep. 5, 8203 (2015).  https://doi.org/10.1038/srep08203 CrossRefGoogle Scholar
  19. 19.
    Xiao, D., Yao, W., Niu, Q.: Valley-Contrasting physics in graphene: magnetic moment and topological transport. Phys. Rev. Lett. 99(23), 236809 (2007).  https://doi.org/10.1103/PhysRevLett.99.236809 ADSCrossRefGoogle Scholar
  20. 20.
    Swartz, A.G., Odenthal, P.M., Hao, Y., Ruoff, R.S., Kawakami, R.K.: Integration of the ferromagnetic insulator EuO onto graphene. ACS Nano 6(11), 10063 (2012).  https://doi.org/10.1021/nn303771f CrossRefGoogle Scholar
  21. 21.
    Haugen, H., Huertas-Hernando, D., Brataas, A.: Spin transport in proximity-induced ferromagnetic graphene. Phys. Rev. B 77(11), 115406 (2008).  https://doi.org/10.1103/PhysRevB.77.115406 ADSCrossRefGoogle Scholar
  22. 22.
    Semenov, Y.G., Kim, K.W., Zavada, J.M.: Spin field effect transistor with a graphene channel. Appl. Phys. Lett. 91(15), 153105 (2007).  https://doi.org/10.1063/1.2798596 ADSCrossRefGoogle Scholar
  23. 23.
    Ezawa, M.: Spin valleytronics in silicene: quantum spin Hall-quantum anomalous Hall insulators and single-valley semimetals. Phys. Rev. B 87(15), 155415 (2013).  https://doi.org/10.1103/PhysRevB.87.155415 ADSCrossRefGoogle Scholar
  24. 24.
    Wang, S.K., Tian, H.Y., Yang, Y.H., Wang, J.: Spin and valley half metal induced by staggered potential and magnetization in silicene. Chin. Phys. B 23(1), 017203 (2014). http://stacks.iop.org/1674-1056/23/i=1/a=017203 ADSCrossRefGoogle Scholar
  25. 25.
    Soodchomshom, B.: Perfect spin-valley filter controlled by electric field in ferromagnetic silicene. J. Appl. Phys. 115(2), 023706 (2014).  https://doi.org/10.1063/1.4861644 ADSCrossRefGoogle Scholar
  26. 26.
    Prarokijjak, W., Soodchomshom, B.: Large magnetoresistance dips and perfect spin-valley filter induced by topological phase transitions in silicene. J. Magn. Magn. Mater. 452, 407 (2018).  https://doi.org/10.1016/j.jmmm.2018.01.004. http://www.sciencedirect.com/science/article/pii/S0304885317322217 ADSCrossRefGoogle Scholar
  27. 27.
    Jatiyanon, K., Soodchomshom, B.: Spin-valley and layer polarizations induced by topological phase transitions in bilayer silicene. Superlattice. Microst. 120, 540 (2018).  https://doi.org/10.1016/j.spmi.2018.06.021 ADSCrossRefGoogle Scholar
  28. 28.
    Yarmohammadi, M.: The effect of Rashba spin–orbit coupling on the spin- and valley-dependent electronic heat capacity of silicene. RSC Adv. 7(18), 10650 (2017).  https://doi.org/10.1039/C6RA26339A CrossRefGoogle Scholar
  29. 29.
    Wei, P., Lee, S., Lemaitre, F., Pinel, L., Cutaia, D., Cha, W., Katmis, F., Zhu, Y., Heiman, D., Hone, J., Moodera, J.S., Chen, C.T.: Strong interfacial exchange field in the graphene/EuS heterostructure. Nat. Mat. 15, 711 (2016).  https://doi.org/10.1038/nmat4603 CrossRefGoogle Scholar
  30. 30.
    Qiao, Z., Yang, S.A., Feng, W., Tse, W.K., Ding, J., Yao, Y., Wang, J., Niu, Q.: Quantum anomalous Hall effect in graphene from Rashba and exchange effects. Phys. Rev. B 82(16), 161414 (2010).  https://doi.org/10.1103/PhysRevB.82.161414 ADSCrossRefGoogle Scholar
  31. 31.
    Tse, W.K., Qiao, Z., Yao, Y., MacDonald, A.H., Niu, Q.: Quantum anomalous Hall effect in single-layer and bilayer graphene. Phys. Rev. B 83(15), 155447 (2011).  https://doi.org/10.1103/PhysRevB.83.155447 ADSCrossRefGoogle Scholar
  32. 32.
    Uchida, K., Xiao, J., Adachi, H., Ohe, J., Takahashi, S., Ieda, J., Ota, T., Kajiwara, Y., Umezawa, H., Kawai, H., Bauer, G.E.W., Maekawa, S., Saitoh, E.: Spin seebeck insulator. Nat. Mat. 9, 894 (2010).  https://doi.org/10.1038/nmat2856 CrossRefGoogle Scholar
  33. 33.
    Wang, Y.Y., Quhe, R.G., Yu, D.P., Lü, J.: Silicene spintronics–a concise review. Chin. Phys. B 24 (8), 87201 (2015).  https://doi.org/10.1088/1674-1056/24/8/087201 CrossRefGoogle Scholar
  34. 34.
    Ezawa, M.: Quantum Hall effects in silicene. J. Phys. Soc. Jpn. 81(6), 064705 (2012).  https://doi.org/10.1143/JPSJ.81.064705 ADSCrossRefGoogle Scholar
  35. 35.
    Ezawa, M.: Photoinduced topological phase transition and a single Dirac-cone state in silicene. Phys. Rev. Lett. 110(2), 026603 (2013).  https://doi.org/10.1103/PhysRevLett.110.026603 ADSCrossRefGoogle Scholar
  36. 36.
    Rycerz, A., Tworzydlo, J., Beenakker, C.W.J.: Valley filter and valley valve in graphene. Nat. Phys. 3 (3), 172 (2007).  https://doi.org/10.1038/nphys547 CrossRefGoogle Scholar
  37. 37.
    Ghaemi, P., Cayssol, J., Sheng, D.N., Vishwanath, A.: Fractional topological phases and broken time-reversal symmetry in strained graphene. Phys. Rev. Lett. 108 (26), 266801 (2012).  https://doi.org/10.1103/PhysRevLett.108.266801 ADSCrossRefGoogle Scholar
  38. 38.
    Tatsumi, Y., Ghalamkari, K., Saito, R.: Laser energy dependence of valley polarization in transition-metal dichalcogenides. Phys. Rev. B 94(23), 235408 (2016).  https://doi.org/10.1103/PhysRevB.94.235408 ADSCrossRefGoogle Scholar
  39. 39.
    Beenakker, C.W.J., Gnezdilov, N.V., Dresselhaus, E., Ostroukh, V.P., Herasymenko, Y., Adagideli, I., Tworzydło, J.: Valley switch in a graphene superlattice due to pseudo-Andreev reflection. Phys. Rev. B 97 (24), 241403 (2018).  https://doi.org/10.1103/PhysRevB.97.241403 ADSCrossRefGoogle Scholar
  40. 40.
    Gorbachev, R.V., Song, J.C.W., Yu, G.L., Kretinin, A.V., Withers, F., Cao, Y., Mishchenko, A., Grigorieva, I.V., Novoselov, K.S., Levitov, L.S., Geim, A.K.: Detecting topological currents in graphene superlattices. Science 346(6208), 448 (2014).  https://doi.org/10.1126/science.1254966 ADSCrossRefGoogle Scholar
  41. 41.
    Wang, S.K., Wang, J., Chan, K.S.: Multiple topological interface states in silicene. New J. Phys. 16(4), 045015 (2014). http://stacks.iop.org/1367-2630/16/i=4/a=045015 ADSCrossRefGoogle Scholar
  42. 42.
    Lundeberg, M.B., Folk, J.A.: Harnessing chirality for valleytronics. Science 346(6208), 422 (2014).  https://doi.org/10.1126/science.1260989 ADSCrossRefGoogle Scholar
  43. 43.
    Wang, J.J., Liu, S., Wang, J., Liu, J.F.: Valley filter and valve effect by strong electrostatic potentials in graphene. Sci. Rep. 7(1), 10236 (2017).  https://doi.org/10.1038/s41598-017-10460-5 ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Gunlycke, D., White, C.T.: Graphene valley filter using a line defect. Phys. Rev. Lett. 106(13), 136806 (2011).  https://doi.org/10.1103/PhysRevLett.106.136806 ADSCrossRefGoogle Scholar
  45. 45.
    Ren, C., Zhou, B., Sun, M., Wang, S., Li, Y., Tian, H., Lu, W.: Chiral filtration-induced spin/valley polarization in silicene line defects. Appl. Phys. Express 11(6), 063006 (2018). http://stacks.iop.org/1882-0786/11/i=6/a=063006 ADSCrossRefGoogle Scholar
  46. 46.
    Wang, S., Ren, C., Li, Y., Tian, H., Lu, W., Sun, M.: Spin and valley filter across line defect in silicene. Appl. Phys. Express 11(5), 053004 (2018). http://stacks.iop.org/1882-0786/11/i=5/a=053004 ADSCrossRefGoogle Scholar
  47. 47.
    Wang, S.K., Wang, J.: Valley precession in graphene superlattices. Phys. Rev. B 92(7), 075419 (2015).  https://doi.org/10.1103/PhysRevB.92.075419 ADSCrossRefGoogle Scholar
  48. 48.
    Ando, T.: Theory of valley Hall conductivity in graphene with gap. J. Phys. Soc. Jpn. 84(11), 114705 (2015).  https://doi.org/10.7566/JPSJ.84.114705 ADSCrossRefGoogle Scholar
  49. 49.
    Sui, M., Chen, G., Ma, L., Shan, W.Y., Tian, D., Watanabe, K., Taniguchi, T., Jin, X., Yao, W., Xiao, D., Zhang, Y.: Gate-tunable topological valley transport in bilayer graphene. Nat. Phys. 11(12), 1027 (2015).  https://doi.org/10.1038/nphys3485 CrossRefGoogle Scholar
  50. 50.
    Shimazaki, Y., Yamamoto, M., Borzenets, I.V., Watanabe, K., Taniguchi, T., Tarucha, S.: Generation and detection of pure valley current by electrically induced Berry curvature in bilayer graphene. Nat. Phys. 11(12), 1032 (2015).  https://doi.org/10.1038/nphys3551 CrossRefGoogle Scholar
  51. 51.
    Ando, T.: Theory of valley Hall conductivity in bilayer graphene. J. Phys. Soc. Jpn. 84(11), 114704 (2015).  https://doi.org/10.7566/JPSJ.84.114704 ADSCrossRefGoogle Scholar
  52. 52.
    Ezawa, M.: Valleytronics on the surface of a topological crystalline insulator: elliptic dichroism and valley-selective optical pumping. Phys. Rev. B 89(19), 195413 (2014).  https://doi.org/10.1103/PhysRevB.89.195413 ADSCrossRefGoogle Scholar
  53. 53.
    Wang, S., Wang, J.: Spin and valley half-metal state in MoS2 monolayer. Physica B: Condens. Matter 458, 22 (2015).  https://doi.org/10.1016/j.physb.2014.10.026. http://www.sciencedirect.com/science/article/pii/S0921452614008230 ADSCrossRefGoogle Scholar
  54. 54.
    Fujita, T., Jalil, M.B.A., Tan, S.G.: Valley filter in strain engineered graphene. Appl. Phys. Lett. 97(4), 043508 (2010).  https://doi.org/10.1063/1.3473725 ADSCrossRefGoogle Scholar
  55. 55.
    Wang, S.K., Wang, J.: Spin and valley filter in strain engineered silicene. Chin. Phys. B 24(3), 037202 (2015). http://stacks.iop.org/1674-1056/24/i=3/a=037202 ADSCrossRefGoogle Scholar
  56. 56.
    Sasaki, K.I., Saito, R.: Pseudospin and deformation-induced gauge field in graphene. Prog. Theor. Phys. Suppl. 176, 253 (2008).  https://doi.org/10.1143/PTPS.176.253 ADSCrossRefzbMATHGoogle Scholar
  57. 57.
    Tian, H., Wang, J.: Spatial valley separation in strained graphene pn junction. J. Phys. Condens. Matter 29(38), 385401 (2017). http://stacks.iop.org/0953-8984/29/i=38/a=385401 CrossRefGoogle Scholar
  58. 58.
    Wang, J.J., Liu, S., Wang, J., Liu, J.F.: Valley-coupled transport in graphene with Y-shaped Kekulé structure. Phys. Rev. B 98(19), 195436 (2018).  https://doi.org/10.1103/PhysRevB.98.195436 ADSCrossRefGoogle Scholar
  59. 59.
    Golub, L.E., Tarasenko, S.A., Entin, M.V., Magarill, L.I.: Valley separation in graphene by polarized light. Phys. Rev. B 84(19), 195408 (2011).  https://doi.org/10.1103/PhysRevB.84.195408 ADSCrossRefGoogle Scholar
  60. 60.
    Qiao, Z., Yang, S.A., Wang, B., Yao, Y., Niu, Q.: Spin-polarized and valley helical edge modes in graphene nanoribbons. Phys. Rev. B 84(3), 035431 (2011).  https://doi.org/10.1103/PhysRevB.84.035431 ADSCrossRefGoogle Scholar
  61. 61.
    Garcia-Pomar, J.L., Cortijo, A., Nieto-Vesperinas, M.: Fully valley-polarized electron beams in graphene. Phys. Rev. Lett. 100(23), 236801 (2008).  https://doi.org/10.1103/PhysRevLett.100.236801 ADSCrossRefGoogle Scholar
  62. 62.
    Wang, J., Chan, K.S., Lin, Z.: Quantum pumping of valley current in strain engineered graphene. Appl. Phys. Lett. 104(1), 013105 (2014).  https://doi.org/10.1063/1.4861119 ADSCrossRefGoogle Scholar
  63. 63.
    Jiang, Y., Low, T., Chang, K., Katsnelson, M.I., Guinea, F.: Generation of pure bulk valley current in graphene. Phys. Rev. Lett. 110(4), 046601 (2013).  https://doi.org/10.1103/PhysRevLett.110.046601 ADSCrossRefGoogle Scholar
  64. 64.
    Marcellino, J.T.J., Wang, M.J., Wang, S.K.: Generation of valley pump currents in silicene. Chin. Phys. B 28(1), 17204 (2019).  https://doi.org/10.1088/1674-1056/28/1/017204 CrossRefGoogle Scholar
  65. 65.
    Luo, W., Sheng, L., Wang, B.G., Xing, D.Y.: Topological spin and valley pumping in silicene. Sci. Rep. 6, 31325 (2016).  https://doi.org/10.1038/srep31325 ADSCrossRefGoogle Scholar
  66. 66.
    Rozhkov, A.V., Rakhmanov, A.L., Sboychakov, A.O., Kugel, K.I., Nori, F.: Spin-valley half-metal as a prospective material for spin valleytronics. Phys. Rev. Lett. 119(10), 107601 (2017).  https://doi.org/10.1103/PhysRevLett.119.107601 ADSCrossRefGoogle Scholar
  67. 67.
    Rakhmanov, A.L., Sboychakov, A.O., Kugel, K.I., Rozhkov, A.V., Nori, F.: Spin-valley half-metal in systems with fermi surface nesting. Phys. Rev. B 98(15), 155141 (2018).  https://doi.org/10.1103/PhysRevB.98.155141 ADSCrossRefGoogle Scholar
  68. 68.
    Grujić, M.M., Tadić, M.ž., Peeters, F.M.: Spin-valley filtering in strained graphene structures with artificially induced carrier mass and spin-orbit coupling. Phys. Rev. Lett. 113(4), 046601 (2014).  https://doi.org/10.1103/PhysRevLett.113.046601 ADSCrossRefGoogle Scholar
  69. 69.
    Cresti, A., Nikolic, B.K., Garcıa, J.H., Roche, S.: Charge, spin and valley Hall effects in disordered graphene. Riv. Nuovo Cimento 39, 12 (2016)Google Scholar
  70. 70.
    Yang, Y., Xu, Z., Sheng, L., Wang, B., Xing, D.Y., Sheng, D.N.: Time-reversal-symmetry-broken quantum spin Hall effect. Phys. Rev. Lett. 107(6), 066602 (2011).  https://doi.org/10.1103/PhysRevLett.107.066602 ADSCrossRefGoogle Scholar
  71. 71.
    žutić, I., Fabian, J., Das Sarma, S.: Spintronics: fundamentals and applications. Rev. Mod. Phys. 76 (2), 323 (2004).  https://doi.org/10.1103/RevModPhys.76.323 ADSCrossRefGoogle Scholar
  72. 72.
    Ren, Y., Qiao, Z., Niu, Q.: Topological phases in two-dimensional materials: a review. Rep. Prog. Phys. 79(6), 066501 (2016). http://stacks.iop.org/0034-4885/79/i=6/a=066501 ADSCrossRefGoogle Scholar
  73. 73.
    Valenzuela, S.O., Tinkham, M.: Direct electronic measurement of the spin Hall effect. Nature 442(7099), 176 (2006).  https://doi.org/10.1038/nature04937 ADSCrossRefGoogle Scholar
  74. 74.
    Kimura, T., Otani, Y., Sato, T., Takahashi, S., Maekawa, S.: Room-temperature reversible spin Hall effect. Phys. Rev. Lett. 98(15), 156601 (2007).  https://doi.org/10.1103/PhysRevLett.98.156601 ADSCrossRefGoogle Scholar
  75. 75.
    Tian, H.Y., Wang, J.: Spin-polarized transport in a normal/ferromagnetic/normal zigzag graphene nanoribbon junction. Chin. Phys. B 21(1), 017203 (2012). http://stacks.iop.org/1674-1056/21/i=1/a=017203 ADSCrossRefGoogle Scholar
  76. 76.
    Tian, H., Wang, S., Hu, J., Wang, J.: The chirality dependent spin filter design in the graphene-like junction. J. Phys. Condens. Matter 27(12), 125005 (2015). http://stacks.iop.org/0953-8984/27/i=12/a=125005 ADSCrossRefGoogle Scholar
  77. 77.
    Marcellino, J.T.J., Wang, M.J., Wang, S.K., Wang, J.: Spin-current pump in silicene. Chin. Phys. B 27(5), 57801 (2018).  https://doi.org/10.1088/1674-1056/27/5/057801. http://stacks.iop.org/1674-1056/27/i=5/a=057801 CrossRefGoogle Scholar
  78. 78.
    Murakami, S., Nagaosa, N., Zhang, S.C.: Dissipationless quantum spin current at room temperature. Science 301(5638), 1348 (2003).  https://doi.org/10.1126/science.1087128 ADSCrossRefGoogle Scholar
  79. 79.
    Sinova, J., Culcer, D., Niu, Q., Sinitsyn, N.A., Jungwirth, T., MacDonald, A.H.: Universal intrinsic spin Hall effect. Phys. Rev. Lett. 92(12), 126603 (2004).  https://doi.org/10.1103/PhysRevLett.92.126603 ADSCrossRefGoogle Scholar
  80. 80.
    Cao, T., Wang, G., Han, W., Ye, H., Zhu, C., Shi, J., Niu, Q., Tan, P., Wang, E., Liu, B., Feng, J.: Valley-selective circular dichroism of monolayer molybdenum disulphide. Nat. Commun. 3, 887 (2012).  https://doi.org/10.1038/ncomms1882 ADSCrossRefGoogle Scholar
  81. 81.
    Mak, K.F., He, K., Shan, J., Heinz, T.F.: Control of valley polarization in monolayer MoS2 by optical helicity. Nat. Nanotechnol. 7(8), 494 (2012).  https://doi.org/10.1038/nnano.2012.96 ADSCrossRefGoogle Scholar
  82. 82.
    Li, P., Li, X., Zhao, W., Chen, H., Chen, M.X., Guo, Z.X., Feng, J., Gong, X.G., MacDonald, A.H.: Topological Dirac states beyond π-orbitals for silicene on SiC(0001) surface. Nano Lett. 17(10), 6195 (2017).  https://doi.org/10.1021/acs.nanolett.7b02855 ADSCrossRefGoogle Scholar
  83. 83.
    Qiao, Z., Jiang, H., Li, X., Yao, Y., Niu, Q.: Microscopic theory of quantum anomalous Hall effect in graphene. Phys. Rev. B 85(11), 115439 (2012).  https://doi.org/10.1103/PhysRevB.85.115439 ADSCrossRefGoogle Scholar
  84. 84.
    Ezawa, M.: High spin-Chern insulators with magnetic order. Sci. Rep. 3, 3435 (2013).  https://doi.org/10.1038/srep03435 ADSCrossRefGoogle Scholar
  85. 85.
    Ezawa, M: From graphene to silicene: a new 2D topological insulator. JPS Conf. Proc. 1, 012003 (2014).  https://doi.org/10.7566/JPSCP.1.012003 Google Scholar
  86. 86.
    Zhao, J., Liu, H., Yu, Z., Quhe, R., Zhou, S., Wang, Y., Liu, C.C., Zhong, H., Han, N., Lu, J., Yao, Y., Wu, K.: Rise of silicene: a competitive 2D material. Prog. Mater. Sci. 83, 24 (2016). 10.1016/j.pmatsci.2016.04.001. http://www.sciencedirect.com/science/article/pii/S0079642516300068 CrossRefGoogle Scholar
  87. 87.
    Wallace, P.R.: The band theory of graphite. Phys. Rev. 71(9), 622 (1947).  https://doi.org/10.1103/PhysRev.71.622 ADSCrossRefzbMATHGoogle Scholar
  88. 88.
    Castro Neto, A.H., Guinea, F., Peres, N.M.R., Novoselov, K.S., Geim, A.K.: The electronic properties of graphene. Rev. Mod. Phys. 81(1), 109 (2009).  https://doi.org/10.1103/RevModPhys.81.109 ADSCrossRefGoogle Scholar
  89. 89.
    Zhang, X.L., Liu, L.F., Liu, W.M.: Quantum anomalous Hall effect and tunable topological states in 3d transition metals doped silicene. Sci. Rep. 3, 2908 (2013).  https://doi.org/10.1038/srep02908 CrossRefGoogle Scholar
  90. 90.
    Zhang, X.L., Liu, L.F., Liu, W.M.: Erratum: Quantum anomalous Hall effect and tunable topological states in 3d transition metals doped silicene. Sci. Rep. 4, 3801 (2014).  https://doi.org/10.1038/srep03801 CrossRefGoogle Scholar
  91. 91.
    Bansil, A., Lin, H., Das, T.: Colloquium: topological band theory. Rev. Mod. Phys. 88(2), 021004 (2016).  https://doi.org/10.1103/RevModPhys.88.021004 ADSCrossRefGoogle Scholar
  92. 92.
    van Duppen, B., Vasilopoulos, P., Peeters, F.M.: Spin and valley polarization of plasmons in silicene due to external fields. Phys. Rev. B 90(3), 035142 (2014).  https://doi.org/10.1103/PhysRevB.90.035142 ADSCrossRefGoogle Scholar
  93. 93.
    Kubo, R.: Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 12(6), 570 (1957).  https://doi.org/10.1143/JPSJ.12.570 ADSMathSciNetCrossRefGoogle Scholar
  94. 94.
    Tian, H.Y., Ma, R., Chan, K.S., Wang, J.: Disorder effect on the integer quantum Hall effect in trilayer graphene. J. Phys. Condens. Matter 25(49), 495503 (2013). http://stacks.iop.org/0953-8984/25/i=49/a=495503 CrossRefGoogle Scholar
  95. 95.
    Sinitsyn, N.A., Hill, J.E., Min, H., Sinova, J., MacDonald, A.H.: Charge and spin Hall conductivity in metallic graphene. Phys. Rev. Lett. 97(10), 106804 (2006).  https://doi.org/10.1103/PhysRevLett.97.106804 ADSCrossRefGoogle Scholar
  96. 96.
    Oka, T., Aoki, H.: Photovoltaic Hall effect in graphene. Phys. Rev. B 79(8), 081406 (2009).  https://doi.org/10.1103/PhysRevB.79.081406 ADSCrossRefGoogle Scholar
  97. 97.
    Oka, T., Aoki, H.: Erratum: Photovoltaic Hall effect in graphene [Phys. Rev. B 79, 081406(R) (2009)]. Phys. Rev. B 79(16), 169901 (2009).  https://doi.org/10.1103/PhysRevB.79.169901 ADSCrossRefGoogle Scholar
  98. 98.
    Niu, Q., Thouless, D.J., Wu, Y.S.: Quantized Hall conductance as a topological invariant. Phys. Rev. B 31(6), 3372 (1985).  https://doi.org/10.1103/PhysRevB.31.3372 ADSMathSciNetCrossRefGoogle Scholar
  99. 99.
    Thouless, D.J., Kohmoto, M., Nightingale, M.P., den Nijs, M.: Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49(6), 405 (1982).  https://doi.org/10.1103/PhysRevLett.49.405 ADSCrossRefGoogle Scholar
  100. 100.
    Kohmoto, M.: Topological invariant and the quantization of the Hall conductance. Ann. Phys. (N. Y.) 160 (2), 343 (1985).  https://doi.org/10.1016/0003-4916(85)90148-4. http://www.sciencedirect.com/science/article/pii/0003491685901484 ADSMathSciNetCrossRefGoogle Scholar
  101. 101.
    Rezania, H., Satar, A.K.: Magnetic field effects on optical conductivity of doped armchair graphene nanoribbon. J. Supercond. Nov. Magn.  https://doi.org/10.1007/s10948-018-4727-3 (2018)
  102. 102.
    Tahir, M., Schwingenschlögl, U.: Valley polarized quantum Hall effect and topological insulator phase transitions in silicene. Sci. Rep. 3, 1075 (2013).  https://doi.org/10.1038/srep01075 ADSCrossRefGoogle Scholar
  103. 103.
    Marder, M.P.: Condensed Matter Physics. Wiley, New York (2010)CrossRefGoogle Scholar
  104. 104.
    Tahir, M., Manchon, A., Sabeeh, K., Schwingenschlögl, U.: Quantum spin/valley Hall effect and topological insulator phase transitions in silicene. Appl. Phys. Lett. 102(16), 162412 (2013).  https://doi.org/10.1063/1.4803084 ADSCrossRefGoogle Scholar
  105. 105.
    Schliemann, J., Loss, D.: Dissipation effects in spin-Hall transport of electrons and holes. Phys. Rev. B 69 (16), 165315 (2004).  https://doi.org/10.1103/PhysRevB.69.165315 ADSCrossRefGoogle Scholar
  106. 106.
    Sinova, J., Jungwirth, T., Kučera, J., MacDonald, A.H.: Infrared magnetooptical properties of (III,Mn)V ferromagetic semiconductors. Phys. Rev. B 67(23), 235203 (2003).  https://doi.org/10.1103/PhysRevB.67.235203 ADSCrossRefGoogle Scholar
  107. 107.
    Sinitsyn, N.A., Hankiewicz, E.M., Teizer, W., Sinova, J.: Spin Hall and spin-diagonal conductivity in the presence of Rashba and Dresselhaus spin-orbit coupling. Phys. Rev. B 70(8), 081312 (2004).  https://doi.org/10.1103/PhysRevB.70.081312 ADSCrossRefGoogle Scholar
  108. 108.
    Marino, E.C., Nascimento, L.O., Alves, V.S., Smith, C.M.: Interaction induced quantum valley Hall effect in graphene. Phys. Rev. X 5(1), 011040 (2015).  https://doi.org/10.1103/PhysRevX.5.011040 CrossRefGoogle Scholar
  109. 109.
    Yang, M., Wang, J.: Fabry-Pérot states mediated quantum valley–Hall conductance in a strained graphene system. New J. Phys. 16(11), 113060 (2014). http://stacks.iop.org/1367-2630/16/i=11/a=113060 ADSCrossRefGoogle Scholar
  110. 110.
    Mak, K.F., McGill, K.L., Park, J., McEuen, P.L.: The valley Hall effect in MoS2 transistors. Science 344(6191), 1489 (2014).  https://doi.org/10.1126/science.1250140 ADSCrossRefGoogle Scholar
  111. 111.
    Zhu, Z.G., Berakdar, J.: Berry-curvature-mediated valley-Hall and charge-Hall effects in graphene via strain engineering. Phys. Rev. B 84(19), 195460 (2011).  https://doi.org/10.1103/PhysRevB.84.195460 ADSCrossRefGoogle Scholar
  112. 112.
    Pan, H., Li, X., Jiang, H., Yao, Y., Yang, S.A.: Valley-polarized quantum anomalous Hall phase and disorder-induced valley-filtered chiral edge channels. Phys. Rev. B 91(4), 045404 (2015).  https://doi.org/10.1103/PhysRevB.91.045404 ADSCrossRefGoogle Scholar
  113. 113.
    Li, Z., Carbotte, J.P.: Longitudinal and spin-valley Hall optical conductivity in single layer MoS2. Phys. Rev. B 86(20), 205425 (2012).  https://doi.org/10.1103/PhysRevB.86.205425 ADSCrossRefGoogle Scholar
  114. 114.
    Tian, H.Y.: Spin-valley quantum Hall phases in graphene. Chin. Phys. B 24(12), 127301 (2015). http://stacks.iop.org/1674-1056/24/i=12/a=127301 ADSCrossRefGoogle Scholar
  115. 115.
    Tabert, C.J., Nicol, E.J.: AC/DC spin and valley Hall effects in silicene and germanene. Phys. Rev. B 87 (23), 235426 (2013).  https://doi.org/10.1103/PhysRevB.87.235426 ADSCrossRefGoogle Scholar
  116. 116.
    Chang, M.C., Niu, Q.: Berry phase, hyperorbits, and the Hofstadter spectrum: Semiclassical dynamics in magnetic Bloch bands. Phys. Rev. B 53(11), 7010 (1996).  https://doi.org/10.1103/PhysRevB.53.7010 ADSCrossRefGoogle Scholar
  117. 117.
    Qi, X.L., Zhang, S.C.: Topological insulators and superconductors. Rev. Mod. Phys. 83(4), 1057 (2011).  https://doi.org/10.1103/RevModPhys.83.1057 ADSCrossRefGoogle Scholar
  118. 118.
    Kitagawa, T., Oka, T., Brataas, A., Fu, L., Demler, E.: Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels. Phys. Rev. B 84(23), 235108 (2011).  https://doi.org/10.1103/PhysRevB.84.235108 ADSCrossRefGoogle Scholar
  119. 119.
    Thonhauser, T., Ceresoli, D., Vanderbilt, D., Resta, R.: Orbital magnetization in periodic insulators. Phys. Rev. Lett. 95(13), 137205 (2005).  https://doi.org/10.1103/PhysRevLett.95.137205 ADSCrossRefGoogle Scholar
  120. 120.
    Xiao, D., Shi, J., Niu, Q.: Berry phase correction to electron density of states in solids [Phys. Rev. Lett. 95, 137204 (2005)]. Phys. Rev. Lett. 95(16), 169903 (2005).  https://doi.org/10.1103/PhysRevLett.95.169903 ADSCrossRefGoogle Scholar
  121. 121.
    Yao, W., MacDonald, A.H., Niu, Q.: Optical control of topological quantum transport in semiconductors,. Phys. Rev. Lett. 99(4), 047401 (2007).  https://doi.org/10.1103/PhysRevLett.99.047401 ADSCrossRefGoogle Scholar
  122. 122.
    Ando, T., Nakanishi, T., Saito, R.: Berry’s phase and absence of back scattering in carbon nanotubes. J. Phys. Soc. Jpn. 67(8), 2857 (1998).  https://doi.org/10.1143/JPSJ.67.2857 ADSCrossRefGoogle Scholar
  123. 123.
    Berry, M.V.: Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. Lond. A: Math. Phys. Sci. 392(1802), 45 (1984).  https://doi.org/10.1098/rspa.1984.0023. http://rspa.royalsocietypublishing.org/content/392/1802/45 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  124. 124.
    Xiao, D., Chang, M.C., Niu, Q.: Berry phase effects on electronic properties. Rev. Mod. Phys. 82(3), 1959 (2010).  https://doi.org/10.1103/RevModPhys.82.1959 ADSMathSciNetCrossRefzbMATHGoogle Scholar
  125. 125.
    Kim, Y., Choi, K., Ihm, J., Jin, H.: Topological domain walls and quantum valley Hall effects in silicene. Phys. Rev. B 89(8), 085429 (2014).  https://doi.org/10.1103/PhysRevB.89.085429 ADSCrossRefGoogle Scholar
  126. 126.
    Pan, H., Li, Z., Liu, C.C., Zhu, G., Qiao, Z., Yao, Y.: Valley-polarized quantum anomalous Hall effect in silicene. Phys. Rev. Lett. 112(10), 106802 (2014).  https://doi.org/10.1103/PhysRevLett.112.106802 ADSCrossRefGoogle Scholar
  127. 127.
    Lü, X.L., Xie, Y., Xie, H.: Topological and magnetic phase transition in silicene-like zigzag nanoribbons. New J. Phys. 20(4), 043054 (2018).  https://doi.org/10.1088/1367-2630/aabc6e ADSCrossRefGoogle Scholar
  128. 128.
    Liang, Q.F., Wu, L.H., Hu, X.: Electrically tunable topological state in [111] perovskite materials with an antiferromagnetic exchange field. New J. Phys. 15(6), 063031 (2013).  https://doi.org/10.1088/1367-2630/15/6/063031 ADSCrossRefGoogle Scholar
  129. 129.
    Manzetti, S., Enrichi, F.: State-of-the-art developments in metal and carbon-based semiconducting nanomaterials: applications and functions in spintronics, nanophotonics, and nanomagnetics. Adv. Manuf. 5(2), 105 (2017).  https://doi.org/10.1007/s40436-017-0172-y CrossRefGoogle Scholar
  130. 130.
    Liu, B., Zhou, K.: Recent progress on graphene-analogous 2D nanomaterials: properties, modeling and applications. Prog. Mater. Sci. 100, 99 (2019).  https://doi.org/10.1016/j.pmatsci.2018.09.004. http://www.sciencedirect.com/science/article/pii/S0079642518300938 CrossRefGoogle Scholar
  131. 131.
    Feng, Y.P., Shen, L., Yang, M., Wang, A., Zeng, M., Wu, Q., Chintalapati, S., Chang, C.R.: Prospects of spintronics based on 2D materials. WIREs Comput. Mol. Sci. 7(5), 1313 (2017).  https://doi.org/10.1002/wcms.1313 CrossRefGoogle Scholar
  132. 132.
    Náfrádi, B., Choucair, M., Forró, L.: Electron spin dynamics of two-dimensional layered materials. Adv. Funct. Mater. 27(19), 1604040 (2017).  https://doi.org/10.1002/adfm.201604040 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of ScienceJinling Institute of TechnologyNanjingChina
  2. 2.College of Electronic and Information EngineeringJinling Institute of TechnologyNanjingChina
  3. 3.School of Physics and Electronic ScienceZunyi Normal UniversityZunyiChina
  4. 4.School of Physics and Electronic EngineeringLinyi UniversityLinyiChina
  5. 5.College of Material EngineeringJinling Institute of TechnologyNanjingChina
  6. 6.Physical Science and Engineering DivisionKing Abdullah University of Science and TechnologyThuwalSaudi Arabia

Personalised recommendations