Skip to main content
Log in

Valley Hall Effect and Magnetic Moment in Magnetized Silicene

  • Original Paper
  • Published:
Journal of Superconductivity and Novel Magnetism Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  13. Spencer, M.J., Morishita, T. (eds.): Silicene: structure, properties and applications. Springer International Publishing, Cham (2016)

    Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Google Scholar 

  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

    ADS  Google Scholar 

  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

    Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  Google Scholar 

  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

    Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Google Scholar 

  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

    Article  Google Scholar 

  34. Ezawa, M.: Quantum Hall effects in silicene. J. Phys. Soc. Jpn. 81(6), 064705 (2012). https://doi.org/10.1143/JPSJ.81.064705

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  42. Lundeberg, M.B., Folk, J.A.: Harnessing chirality for valleytronics. Science 346(6208), 422 (2014). https://doi.org/10.1126/science.1260989

    ADS  Google Scholar 

  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

    Article  ADS  MathSciNet  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Google Scholar 

  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

    Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  MATH  Google Scholar 

  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

    Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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. 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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  84. Ezawa, M.: High spin-Chern insulators with magnetic order. Sci. Rep. 3, 3435 (2013). https://doi.org/10.1038/srep03435

    ADS  Google Scholar 

  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. 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

    Article  Google Scholar 

  87. Wallace, P.R.: The band theory of graphite. Phys. Rev. 71(9), 622 (1947). https://doi.org/10.1103/PhysRev.71.622

    Article  ADS  MATH  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Google Scholar 

  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

    Google Scholar 

  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

    ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  MathSciNet  Google Scholar 

  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

    Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  MathSciNet  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  MathSciNet  Google Scholar 

  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)

    Google Scholar 

  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

    ADS  Google Scholar 

  103. Marder, M.P.: Condensed Matter Physics. Wiley, New York (2010)

    Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  ADS  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

Download references

Funding

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).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Sake Wang or Minglei Sun.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, S., Zhang, P., Ren, C. et al. Valley Hall Effect and Magnetic Moment in Magnetized Silicene. J Supercond Nov Magn 32, 2947–2957 (2019). https://doi.org/10.1007/s10948-019-5055-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10948-019-5055-y

Keywords

Navigation