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.
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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
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
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
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
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
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
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
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
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
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
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
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
Spencer, M.J., Morishita, T. (eds.): Silicene: structure, properties and applications. Springer International Publishing, Cham (2016)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Ezawa, M.: Quantum Hall effects in silicene. J. Phys. Soc. Jpn. 81(6), 064705 (2012). https://doi.org/10.1143/JPSJ.81.064705
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
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
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
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
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
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
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
Lundeberg, M.B., Folk, J.A.: Harnessing chirality for valleytronics. Science 346(6208), 422 (2014). https://doi.org/10.1126/science.1260989
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
Valenzuela, S.O., Tinkham, M.: Direct electronic measurement of the spin Hall effect. Nature 442(7099), 176 (2006). https://doi.org/10.1038/nature04937
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
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
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
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
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
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
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
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
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
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
Ezawa, M.: High spin-Chern insulators with magnetic order. Sci. Rep. 3, 3435 (2013). https://doi.org/10.1038/srep03435
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
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
Wallace, P.R.: The band theory of graphite. Phys. Rev. 71(9), 622 (1947). https://doi.org/10.1103/PhysRev.71.622
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
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
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
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
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
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
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
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
Oka, T., Aoki, H.: Photovoltaic Hall effect in graphene. Phys. Rev. B 79(8), 081406 (2009). https://doi.org/10.1103/PhysRevB.79.081406
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
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
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
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
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)
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
Marder, M.P.: Condensed Matter Physics. Wiley, New York (2010)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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).
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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
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DOI: https://doi.org/10.1007/s10948-019-5055-y