A computational investigation of topological insulator Bi<sub>2</sub>Se<sub>3</sub> film

doi:10.1007/s11467-014-0441-1

Front. Phys.

2014, Vol. 9

Issue (6) : 760-767 https://doi.org/10.1007/s11467-014-0441-1

RESEARCH ARTICLE

A computational investigation of topological insulator Bi₂Se₃ film

Yi-Bin Hu¹(

), Yong-Hong Zhao², Xue-Feng Wang³

¹. Department of Physics, McGill University, 3600 rue University, Montréal, Québec, H3A 2T8, Canada
². College of Physics and Electronic Engineering, Institute of Solid State Physics, Sichuan Normal University, Chengdu 610068, China
³. Department of Physics, Soochow University, Suzhou 215006, China

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Abstract

Topological insulators have a bulk band gap like an ordinary insulator and conducting states on their edge or surface which are formed by spin–orbit coupling and protected by time-reversal symmetry. We report theoretical analyses of the electronic properties of three-dimensional topological insulator Bi₂Se₃ film on different energies. We choose five different energies (–123, –75, 0, 180, 350 meV) around the Dirac cone (–113 meV). When energy is close to the Dirac cone, the properties of wave function match the topological insulator’s hallmark perfectly. When energy is far way from the Dirac cone, the hallmark of topological insulator is broken and the helical states disappear. The electronic properties of helical states are dug out from the calculation results. The spin-momentum locking of the helical states are confirmed. A 3-fold symmetry of the helical states in Brillouin zone is also revealed. The penetration depth of the helical states is two quintuple layers which can be identified from layer projection. The charge contribution on each quintuple layer depends on the energy, and has completely different behavior along K and M direction in Brillouin zone. From orbital projection, we can find that the maximum charge contribution of the helical states is p_z orbit and the charge contribution on p_yand p_x orbits have 2-fold symmetry.

Keywords topological insulator spin–orbit coupling helical state

Corresponding Author(s): Yi-Bin Hu

Issue Date: 24 December 2014

Cite this article:

Yi-Bin Hu,Yong-Hong Zhao,Xue-Feng Wang. A computational investigation of topological insulator Bi₂Se₃ film[J]. Front. Phys. , 2014, 9(6): 760-767.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-014-0441-1
https://academic.hep.com.cn/fop/EN/Y2014/V9/I6/760

1	C. L. Kane and E. J. Mele, Z2 topological order and the quantum spin Hall effect, Phys. Rev. Lett., 2005, 95(14): 146802 https://doi.org/10.1103/PhysRevLett.95.146802
2	B. A. Bernevig, T. L. Hughes, and S. C. Zhang, Quantumu spin Hall effect and topological phase transition in HgTe quantum wells, Science, 2006, 314(5806): 1757 https://doi.org/10.1126/science.1133734
3	M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys., 2010, 82(4): 3045 https://doi.org/10.1103/RevModPhys.82.3045
4	X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys., 2011, 83(4): 1057 https://doi.org/10.1103/RevModPhys.83.1057
5	X. L. Qi and S. C. Zhang, The quantum spin Hall effect and topological insulators, Phys. Today, 2010, 63(1): 33 https://doi.org/10.1063/1.3293411
6	J. E. Moore, The birth of topological insulators, Nature, 2010, 464(7286): 194 https://doi.org/10.1038/nature08916
7	L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B, 2007, 76(4): 045302 https://doi.org/10.1103/PhysRevB.76.045302
8	X. L. Qi, T. L. Hughes, and S. C. Zhang, Topological field theory of time-reversal invariant insulators, Phys. Rev. B, 2008, 78(19): 195424 https://doi.org/10.1103/PhysRevB.78.195424
9	Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of a large-gap topological-insulator class with a single Dirac cone on the surface, Nat. Phys., 2009, 5(6): 398 https://doi.org/10.1038/nphys1274
10	H. J. Zhang, C. X. Liu, X. L. Qi, X. Dai, Z. Fang, and S. C. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface, Nat. Phys., 2009, 5(6): 438 https://doi.org/10.1038/nphys1270
11	D. Hsieh, Y. Xia, D. Qian, L. Wray, F. Meier, J. H. Dil, J. Osterwalder, L. Patthey, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Observation of time-reversal-protected single-Dirac-cone topologicalinsulator states in Bi2Te3 and Sb2Te3, Phys. Rev. Lett., 2009, 103(14): 146401 https://doi.org/10.1103/PhysRevLett.103.146401
12	K. He, Y. Zhang, K. He, C. Z. Chang, C. L. Song, L. L. Wang, X. Chen, J. F. Jia, Z. Fang, X. Dai, W. Y. Shan, S. Q. Shen, Q. Niu, X. L. Qi, S. C. Zhang, X. C. Ma, and Q. K. Xue, Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit, Nat. Phys., 2010, 6(8): 584 https://doi.org/10.1038/nphys1689
13	D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, A tunable topological insulator in the spin helical Dirac transport regime, Nature, 2009, 460(7259): 1101 https://doi.org/10.1038/nature08234
14	Y. S. Hor, A. Richardella, P. Roushan, Y. Xia, J. G. Checkelsky, A. Yazdani, M. Z. Hasan, N. P. Ong, and R. J. Cava, p-type Bi2Se3 for topological insulator and low-temperature thermoelectric applications, Phys. Rev. B, 2009, 79(19): 195208 https://doi.org/10.1103/PhysRevB.79.195208
15	S. R. Park, W. S. Jung, C. Kim, D. J. Song, C. Kim, S. Kimura, K. D. Lee, and N. Hur, Quasiparticle scattering and the protected nature of the topological states in a parent topological insulator Bi2Se3, Phys. Rev. B, 2010, 81: 041405(R) https://doi.org/10.1103/PhysRevB.81.041405
16	C. X. Liu, X. L. Qi, H. J. Zhang, X. Dai, Z. Fang, and S. C. Zhang, Model Hamiltonian for topological insulators, Phys. Rev. B, 2010, 82(4): 045122 https://doi.org/10.1103/PhysRevB.82.045122
17	W. Zhang, R. Yu, S. J. Zhang, X. Dai, and Z. Fang, Firstprinciples studies of the three-dimensional strong topological insulators Bi2Te3, Bi2Se3 and Sb2Te3, New J. Phys., 2010, 12(6): 065013 https://doi.org/10.1088/1367-2630/12/6/065013
18	Jeongwoo Kim, Jinwoong Kim, and Seung-Hoon Jhi, Prediction of topological insulating behavior in crystalline Ge-Sb-Te, Phys. Rev. B, 2010, 82: 201312(R) https://doi.org/10.1103/PhysRevB.82.201312
19	O. V. Yazyev, J. E. Moore, and S. G. Louie, Spin polarization and transport of surface states in the topological insulators Bi2Se3 and Bi2Te3 from first principles, Phys. Rev. Lett., 2010, 105(26): 266806 https://doi.org/10.1103/PhysRevLett.105.266806
20	Z. Alpichshev, J. G. Analytis, J.-H. Chu, I. R. Fisher, Y. L. Chen, Z. X. Shen, A. Fang, and A. Kapitulnik, STM imaging of electronic waves on the surface of Bi2Te3: Topologically protected surface states and hexagonal warping effects, Phys. Rev. Lett., 2010, 104(1): 016401 https://doi.org/10.1103/PhysRevLett.104.016401
21	Y. H. Zhao, Y. B. Hu, L. Liu, Y. Zhu, and H. Guo, Helical states of topological insulator Bi2Se3, Nano Lett., 2011, 11(5): 2088 https://doi.org/10.1021/nl200584f
22	R. Yu, W. Zhang, H. J. Zhang, S. C. Zhang, X. Dai, and Z. Fang, Quantized anomalous Hall effect in magnetic topological insulators, Science, 2010, 329(5987): 61 https://doi.org/10.1126/science.1187485
23	T. M. Schmidt, R. H. Miwa, and A. Fazzio, Spin texture and magnetic anisotropy of Co impurities in Bi2Se3 topological insulators, Phys. Rev. B, 2011, 84(24): 245418 https://doi.org/10.1103/PhysRevB.84.245418
24	P. Blaha, K. Schwarz, P. Sorantin, and S. B. Trickey, Fullpotential, linearized augmented plane wave programs for crystalline systems, Comput. Phys. Commun., 1990, 59(2): 399 https://doi.org/10.1016/0010-4655(90)90187-6
25	Nanodcal is developed by NanoAcademic Technologies Inc. Nanodcal is an LCAO implementation of density functional theory within the Keldysh nonequilibrium Greens function formalism. It is a general purpose tool for ab initio modeling of electronic structure, equilibrium and non-equilibrium quantum transport.
26	J. Taylor, H. Guo, and J. Wang, Ab initio modeling of quantum transport properties of molecular electronic devices, Phys. Rev. B, 2001, 63(24): 245407 https://doi.org/10.1103/PhysRevB.63.245407
27	L. Kleinman and D. M. Bylander, Efficacious form for model pseudopotentials, Phys. Rev. Lett., 1982, 48(20): 1425 https://doi.org/10.1103/PhysRevLett.48.1425
28	G. Theurich and N. A. Hill, Self-consistent treatment of spinorbit coupling in solids using relativistic fully separable ab initio pseudopotentials, Phys. Rev. B, 2001, 64(7): 073106 https://doi.org/10.1103/PhysRevB.64.073106
29	L. Fernández-Seivane, M. A. Oliveria, S. Sanvito, and J. Ferrer, On-site approximation for spin–orbit coupling in linear combination of atomic orbitals density functional methods, J. Phys.: Condens. Matter, 2006, 18(34): 7999 https://doi.org/10.1088/0953-8984/18/34/012
30	J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 1992, 45(23): 13244 https://doi.org/10.1103/PhysRevB.45.13244

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