Phase transition of Quasi-topological insulator to band insulator in bilayer Germanene

Document Type : Full length research Paper

Authors

Department of Physics, Shahid Rajaee Teacher Training University, Lavizan, Tehran 16788-15811, Iran

Abstract

Bilayer germanene nanoribbons (bGNR), due to interlayer bonds and strong spin-orbit coupling, have more application in the design of nano-devices and spintronics. Quantum transport properties and topological phases transition of zigzag superlattice bGNR exposed to the vertical electric field and Rashba spin-orbit coupling (RSOC) are studied within the tight-binding based non-equilibrium Green's function approach. Results demonstrate that by applying the vertical external electric field, a gap opening and metal-semimetal phase transition occur in the system. Meanwhile, we found the topological phase transition of a quasi-topological insulator-band insulator by applying a vertical electric field in bGNR. Further, results reveal that by tuning the RSOC strength, we can control the spin current. This controllability of spin and quantum transport in GNR may contribute to potential applications in nano-devices and the development of spintronic.

Keywords

Main Subjects


[1] Y. Xu, G. Jin, Manipulating topological inner-edge states in hybrid silicene nanoribbons, Physical Review B 95 (2017) 155425. https://doi.org/10.1103/PhysRevB.95.155425.
[2] A. Hattori, S. Tanaya, K. Yada, M. Araidai, M. Sato, Y. Hatsugai, K. Shiraishi, Y. Tanaka, Edge states of hydrogen terminated monolayer materials: silicene, germanene and stanene ribbons, Journal of Physics: Condensed Matter 29 (2017) 11. DOI: 10.1088/1361-648x/aa57e0.
[3] Y. Ding, Y. Wang, Electronic structures of zigzag silicene nanoribbons with asymmetric  edges, Applied Physics Letters 102 (2013) 143115. https://doi.org/10.1063/1.4801948.
[4] D.Z. Jakovljevi, M.M. Gruji, M.Z. Tadi, F.M. Peeters, Helical edge states in silicene and germanene nanorings in perpendicular magnetic field, Journal of Physics: Condensed Matter 30 (2017) 3, https://doi.org/10.1088/1361-648X/aa9e67.
[5] M. Zare, F. Parhizgar, R. Asgari, Topological phase and edge states dependence of the RKKY interaction in zigzag silicene nanoribbon, Physical Review B 94 (2016) 045443. https://doi.org/10.1103/PhysRevB.94.045443.
[6] M. Tahir, Q.Y. Zhang, U. Schwingenschlögl, Floquet edge states in germanene nanoribbons, Scientific Reports 6 (2016) 31821. doi: 10.1038/srep31821.
[7] K. Takeda, K. Shiraishi, Theoretical possibility of stage corrugation in Si and Ge analogs of graphite, Physical Review B 50 (1994) 14916. https://doi.org/10.1103/PhysRevB.50.1491.
[8] G.G. Guzmán-Verri, L.C. Lew Yan Voon, Electronic structure of silicon-based nanostructures, Physical Review B 76 (2007) 075131. https://doi.org/10.1103/PhysRevB.76.075131.
[9] S. Cahangirov, M. Topsakal, E. Aktürk, H. Şahin, S. Ciraci, Two- and One-Dimensional Honeycomb Structures of Silicon and Germanium, Physical Review Letter 102 (2009) 236804. https://doi.org/10.1103/PhysRevLett.102.236804.
[10] A. Acun, L. Zhang, P. Bampoulis, M.V. Farmanbar, A. van Houselt, A.N. Rudenko, H.J. Zandvliet, Germanene: the Germanium Analogue of Graphene, Journal of Physics: Condensed Matter 27 44 (2015) 443002. doi:10.1088/0953-8984/27/44/443002.
[11] M. Ezawa, Monolayer Topological Insulators: Silicene, Germanene, and Stanene, Journal of the Physical Society of Japan 84 (2015) 121003. https://doi.org/10.7566/JPSJ.84.121003.
[12] L. Matthes, F. Bechstedt, Influence of edge and field effects on topological states of germanene nanoribbons from self-consistent calculations, Physical Review B 90 (2014) 165431. https://doi.org/10.1103/PhysRevB.90.165431.
[13] M.Z. Hasan, L.K. Charles, Colloquium: topological insulators, Reviews of Modern Physics 82 (2010) 3045. https://doi.org/10.1103/RevModPhys.82.3045.
[14] X.L. Qi, S.C. Zhang, Topological insulators and superconductors, Reviews of Modern Physics 83 (2011) 1057. https://doi.org/10.1103/RevModPhys.83.1057.
[15] M. Ezawa, Dirac Theory and Topological Phases of Silicon Nanotube, Europhysics Letters 98 (2012) 6. http://iopscience.iop.org/0295-5075/98/6/67001.
[16] C. Wu, B.A. Bernevig, S.C. Zhang, Helical Liquid and the Edge of Quantum Spin Hall Systems, Physical Review Letter 96 (2006) 106401. https://doi.org/10.1103/PhysRevLett.96.106401.
[17] C.L. Kane, E.J. Mele, Quantum Spin Hall Effect in Graphene, Physical Review Letter 95 (2005) 226801. https://doi.org/10.1103/PhysRevLett.95.226801.
[18] H. Min, J.E. Hill, N.A. Sinitsyn, B.R. Sahu, L. Kleinman, A.H. MacDonald, Intrinsic and Rashba spin-orbit interactions in graphene sheets, Physical Review B 74 (2006) 165310. https://doi.org/10.1103/PhysRevB.74.165310.
[19] Y. Yao. F. Ye. X. L. Qi. S. C. Zhang. Z. Fang. Spin-orbit gap of graphene: First-principles calculations, Physical Review B 75 (2007) 041401. https://doi.org/10.1103/PhysRevB.75.041401.
[20] C.C. Liu. H. Jiang. Y, Yao. Low-energy effective hamiltonian involving spin-orbit coupling in silicene and two-dimensional germanium and tin, Physical Review B 84 19 (2011) 195430. https://doi.org/10.1103/PhysRevB.84.195430.
[21] J. Zheng, F. Chi, Y. Guo, Spin-current diodes based on germanene and stanene subjected to local exchange fields, Applied Physics Letters 113 (2018) 112404. https://doi.org/10.1063/1.5041899.
[22] J. Zheng, F. Chi, Y. Guo, Thermal Spin Generator Based on a Germanene Nanoribbon Subjected to Local Noncollinear Exchange Fields, Physical Review Applied 9 (2018) 024012. https://doi.org/10.1103/PhysRevApplied.9.024012.
[23] S. Mohammadi, A. Phirouznia, M. Esmailpour, Topological phases in few-layer silicene nanoribbon induced by normally applied electric field and Rashba spin-orbit coupling, Physica E: Low-dimensional Systems and Nanostructures 133 (2021) 114803. https://doi.org/10.1016/j.physe.2021.114803.
[24] M. Ezawa, Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene, Physical Review Letter 109 (2012) 055502. https://doi.org/10.1103/PhysRevLett.109.055502.
[25] W.K. Tse, Z. Qiao, Y. Yao, A.H. MacDonald, Q. Niu. Quantum anomalous Hall effect in single-layer and bilayer graphene. Physical Review B 83 (2011) 155447. https://doi.org/10.1103/PhysRevB.83.155447.
[26] S. Yuan, H. De Raedt, M.I. Katsnelson, Electronic Transport in Disordered Bilayer and Trilayer Graphene. Physical Review B 82 (2010) 235409. https://doi.org/10.1103/PhysRevB.82.235409.
[27] C. Huang, J. Zhou, H. Wu, K. Deng, P. Jena, E. Kan, Quantum Phase Transition in Germanene and Stanene Bilayer: From Normal Metal to Topological Insulator, The Journal of Physical Chemistry Letters 7 (2016) 1919- 1924. https://doi.org/10.1021/acs.jpclett.6b00651.
[28] K. Shakouri, H. Simchi, M. Esmaeilzadeh, H. Mazidabadi, F.M. Peeters, Tunable spin and charge transport in silicene nanoribbons, Physical Review B 92 (2015) 035413. https://doi.org/10.1103/PhysRevB.92.035413.
[29] M.P.L. Sancho, J.M.L. Sancho, J. Rubio, Quick iterative scheme for the calculation of transfer matrices: application to Mo (100), Journal of Physics F: Metal Physics, 14 (1984) 1205. http://iopscience.iop.org/0305-4608/14/5/016.
[30] S. Mohammadi, F. Khoeini, M. Esmailpour, M. Khalkhali, Investigation of electrical properties in AB-Stacked bilayer Graphene-DNA nanostructures, Superlattices and Microstructures 130 (2019) 182. https://doi.org/10.1016/j.spmi.2019.04.029.
[31] T.C. Li, S.P. Lu, Quantum conductance of graphene nanoribbons with edge defects, Physical Review B 77 (2008) 085408. https://doi.org/10.1103/PhysRevB.77.085408.
[32] F. Khoeini, A.A. Shokri, F. Khoeini, Electronic transport through superlattice-graphene nanoribbons, The European Physical Journal B 75 (2010) 505. https://doi.org/10.1140/epjb/e2010-00159-5.
[33] S. Mohammadi, M. Esmailpour, F. Khoeini. Investigation of Graphene and Silicene-DNA nanostructures: DNA Sensing, Journal of Research on Many-body Systems 10 2 (2020) 1-12. doi:10.22055/jrmbs.2020.15567
[34] S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press. Cambridge (1997).
[35] S. Mohammadi, F. Khoeini, M. Esmailpour, A. Esmailpour, M. Akbari-Moghanjoughi, Tunable transport properties in graphene-DNA and silicene-DNA by controlling the thickness of nanopores. Chemical Physics 541 (2021) 111048. https://doi.org/10.1016/j.chemphys.2020.111048.
[36] S. Datta, Quantum Transport: Atom to Transistor. Cambridge University Press. England (2005).
[37] N.V. Grib, D.A. Ryndyk, R. Gutirrez, G. Cuniberti, Distance-dependent coherent charge transport in DNA: crossover from tunneling to free propagation. Journal of Biophysical Chemistry 1 (2010) 77. doi:10.4236/jbpc.2010.12010.
[38] K. Nakada, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Edge state in graphene ribbons: nanometer size effect and edge shape dependence, Physical Review B 54 (1996) 17954. https://doi.org/10.1103/PhysRevB.54.17954
[39] M. Ezawa, Quantized conductance and field-effect topological quantum transistor in silicene nanoribbons, Applied Physics Letters 102 (2013) 172103. https://doi.org/10.1063/1.4803010.
[40] M. Ezawa, Quasi-Topological Insulator and Trigonal Warping in Gated Bilayer Silicene, Journal of The Physical Society of Japan 81 (2012) 104713. https://doi.org/10.1143/JPSJ.81.104713.
[41] P.D. Padova, P. Vogt, A. Resta, J. Avila, I. Razado-Colambo, C. Quaresima, C. Ottaviani, B. Olivieri, T. Bruhn, T. Hirahara, T. Shirai, S. Hasegawa, M.C. Asensio, G.L. Lay, Evidence of Dirac fermions in multilayer silicone, Applied Physics Letters 102 (2013) 163106. https://doi.org/10.1063/1.4802782.
[42] Y.L. Song, Y. Zhang, J.M. Zhang, D.B. Lu, Effects of the edge shape and the width on the structural and electronic properties of silicene nanoribbons. Applied Surface Science 256 (2010) 6313-7. https://doi.org/10.1016/j.apsusc.2010.04.009.
[43] M. Fujita, K. Wakabayashi, K. Nakada, K. Kusakabe, Peculiar Localized State at Zigzag Graphite Edge, Journal of the Physical Society of Japan 65 (1996) 1920-3. https://doi.org/10.1143/jpsj.65.1920.
[44] Y. Miyamoto, K. Nakada, M. Fujita, First-principles study of edge states of H-terminated graphitic ribbons, Physical Review B 60 (1999) 16211. https://doi.org/10.1103/PhysRevB.59.985.
[45] M. Ezawa, N. Nagaosa, Interference of topologically protected edge states in silicene nanoribbons, Physical Review B 88 (2013) 121401(R). https://doi.org/10.1103/PhysRevB.88.121401.
[46] S. Chowdhury, D. Jana, A theoretical review on electronic, magnetic and optical properties of silicone, Reports on Progress in Physics 79 (2016) 126501. http://iopscience.iop.org/0034-4885/79/12/126501.
[47] M. Ezawa, Topological Phase Transition and Electrically Tunable Dia-magnetism in Silicene, The European Physical Journal B 85 (2012) 363. doi: 10.1140/epjb/e2012-30577-0.