First-principle study of new phase of layered Bi<sub>2</sub>Se<sub>3</sub>

Guo Yu; Zhou Si; Zhao Ji-Jun

doi:10.7498/aps.70.20201434

Abstract

Recently, the boom of graphene has aroused great interest in searching for other two-dimensional (2D) compound materials, which possess many intriguing physical and chemical properties. Interestingly, 2D allotropes of differing atomic structures show even more diverse properties. The Bi₂Se₃ has attracted much attention due to its unique physical properties, while its allotrope has not been investigated. Based on first-principle calculations, here in this work we predict a new phase of Bi₂Se₃ monolayer with outstanding dynamic and thermal stabilities, named as β-Bi₂Se₃. Notably, the β-Bi₂Se₃ monolayer is a semiconductor with a modest direct band gap of 2.40 eV and small effective mass down to 0.52m₀, large absorption coefficient of 10⁵ cm^–1 in the visible-light spectrum, suitable band edge positions for photocatalysis of water splitting. Moreover, the breaking of mirror symmetry in β-Bi₂Se₃ along the out-of-plane direction induces vertical dipolar polarization, yielding a remarkable out-of-plane piezoelectric coefficient of 0.58 pm/V. These exceptional physical properties render the layered Bi₂Se₃ a promising candidate for future high-speed electronics and optoelectronics.

Keywords:

Authors and contacts

Key Laboratory of Materials Modification by Laser, Ion, and Electron Beams, Ministry of Education, School of Physics, Dalian University of Technology, Dalian 116024, China

Corresponding author: Zhou Si, sizhou@dlut.edu.cn

Funds: Project supported by the China Postdoctoral Science Foundation (Grant Nos. BX20190052, 2020M670739), the National Natural Science Foundation of China (Grant No. 11974068), and the Fundamental Research Funds for the Central Universities of China (Grant No. DUT20LAB110)

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References

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图 1 (a) α-Bi₂Se₃的原子结构; (b)单层β-Bi₂Se₃结构的俯视图(上图)和侧视图(下图); (c)双层β-Bi₂Se₃结构的俯视图(上图)和侧视图(下图); (d)经过10 ps第一性原理分子动力学模拟, 得到了300 K时Bi₂Se₃单层的平衡结构; (e) β-Bi₂Se₃的声子谱; (f) β-Bi₂Se₃单层的电子局域函数

Figure 1. (a) Atomic structure of α-Bi₂Se₃; (b) the top and side views of monolayer β-Bi₂Se₃; (c) the top and side views of bilayer β-Bi₂Se₃; (d) snapshots of the equilibrium structures of the β-Bi₂Se₃ monolayer at 300 K after 10 ps ab initio molecular dynamic simulation; (e) phonon dispersion of monolayer β-Bi₂Se₃; (f) electron localization function for monolayer β-Bi₂Se₃.

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图 A1 CALYPSO搜索得到的几个较低能量的Bi₂Se₃单层结构(a)及对应的声子谱(b), 其中Bi₂Se₃-1, Bi₂Se₃-2, Bi₂Se₃-3的形成能分别为–0.15, –0.12, –0.09 eV/atom

Figure A1. Some typical low-energy structures (a) of freestanding Bi₂Se₃ monolayer predicted by the CALYPSO code and corresponding phonon dispersions (b). The formation energy of Bi₂Se₃-1, Bi₂Se₃-2, Bi₂Se₃-3 are –0.15, –0.12, –0.09 eV/atom respectively.

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图 A2 温度为300 K时β-Bi₂Se₃单层的能量-时间变化曲线

Figure A2. Variations of temperature and energy with the time of AIMD simulation for β-Bi₂Se₃ monolayer at 300 K.

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图 2 α-Bi₂Se₃和β-Bi₂Se₃体系表面自由能的化学势相图

Figure 2. Chemical potential phase diagram of surface free ener-gy for α-Bi₂Se₃ and β-Bi₂Se₃.

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图 3 (a)不考虑SOC和(b)考虑SOC时, 采用HSE06泛函计算得到的β-Bi₂Se₃的能带结构和LDOS

Figure 3. The electronic band structures (left panel) and LDOS (right panel) (a) without and (b) with SOC effect for monolayer β-Bi₂Se₃ using HSE06 functional, respectively.

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图 4 (a)采用HSE06泛函并且考虑SOC效应的双层(左图)和块体(右图)β-Bi₂Se₃的能带结构; (b)单层β-Bi₂Se₃带隙随双轴应变的变化

Figure 4. (a) The electronic band structures for bilayer (left panel) and bulk (right panel) β-Bi₂Se₃ based on HSE06 level with SOC effect; (d) effect of biaxial strain on band gap of monolayer β-Bi₂Se₃.

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图 A3 不同堆叠方式的双层β-Bi₂Se₃　(a)能量最低的β-Bi₂Se₃双层结构, 将它的能量设定为0 eV; (b)相对能量为0.32 eV;(c)相对能量为0.55 eV

Figure A3. β-Bi₂Se₃ bilayer with different stacking types and their relative energies: (a) the atomic structure of β-Bi₂Se₃ bilayer with the lowest energy, and its energy is set to 0 eV; the bilayer structures with relative energies of 0.32 eV (b) and 0.55 eV (c), respectively.

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图 5 (a)单层β-Bi₂Se₃的VBM和CBM对比pH = 7和pH = 0的氧化还原电势; (b)单层β-Bi₂Se₃的光吸收系数, λ是波长, 虚线中间区域表示可见光区

Figure 5. (a) The location of VBM and CBM relative to vacuum energy of monolayer β-Bi₂Se₃ at pH = 0 and 7; (b) optical absorption coefficient for monolayer β-Bi₂Se₃. λ is the wave length, and the area between the red and the purple represents the visible range

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表 1 单层、双层和块体β-Bi₂Se₃相对真空能级的价带顶VBM和导带底CBM, 空穴和电子沿着x和y方向的有效质量(m_xh, m_yh, m_xe, m_ye). 载流子有效质量以自由电子的静止质量m₀为单位

Table 1. The VBM and CBM related to vacuum level for monolayer, bilayer and bulk β-Bi₂Se₃, and the corresponding carrier effective mass. m₀ is the electron rest mass.

β-Bi₂Se₃ VBM/eV CBM/eV m_xh m_xe m_yh m_ye

Monolayer –5.82 –3.43 7.88 0.70 5.69 0.66
Bilayer –5.00 –4.24 2.55 0.52 2.36 0.52
Bulk — — 0.65 0.63 0.65 0.67

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[1]	Zhang H, Liu C X, Qi X L, Dai X, Fang Z, Zhang S C 2009 Nat. Phys. 5 438 Google Scholar
[2]	Kong D, Chen Y, Cha J J, Zhang Q, Analytis J G, Lai K, Liu Z, Hong S S, Koski K J, Mo S K 2011 Nat. Nanotechnol. 6 705 Google Scholar
[3]	Brom J E, Ke Y, Du R, Won D, Weng X, Andre K, Gagnon J C, Mohney S E, Li Q, Chen K 2012 Appl. Phys. Lett. 100 162110 Google Scholar
[4]	Alegria L D, Schroer M D, Chatterjee A, Poirier G R, Pretko M, Patel S K, Petta J R 2012 Nano Lett. 12 4711 Google Scholar
[5]	Alegria L D, Petta J R 2012 Nanotechnology 23 435601 Google Scholar
[6]	Le P H, Wu K H, Luo C W, Leu J 2013 Thin Solid Films 534 659 Google Scholar
[7]	Hirahara T, Sakamoto Y, Takeichi Y, Miyazaki H, Kimura S, Matsuda I, Kakizaki A, Hasegawa S 2010 Phys. Rev. B 82 155309 Google Scholar
[8]	Yu X, He L, Lang M, Jiang W, Xiu F, Liao Z, Wang Y, Kou X, Zhang P, Tang J 2012 Nanotechnology 24 015705 Google Scholar
[9]	Li Y Y, Wang G, Zhu X G, Liu M H, Ye C, Chen X, Wang Y Y, He K, Wang L L, Ma X C 2010 Adv. Mater. 22 4002 Google Scholar
[10]	Xia Y, Qian D, Hsieh D, Wray L, Pal A, Lin H, Bansil A, Grauer D, Hor Y S, Cava R J 2009 Nat. Phys. 5 398 Google Scholar
[11]	Bansal N, Koirala N, Brahlek M, Han M G, Zhu Y, Cao Y, Waugh J, Dessau D S, Oh S 2014 Appl. Phys. Lett. 104 241606 Google Scholar
[12]	Chen S, Zhao C, Li Y, Huang H, Lu S, Zhang H, Wen S 2014 Opt. Mater. Express 4 587 Google Scholar
[13]	Sun Y, Cheng H, Gao S, Liu Q, Sun Z, Xiao C, Wu C, Wei S, Xie Y 2012 J. Am. Chem. Soc. 134 20294 Google Scholar
[14]	Min Y, Park G, Kim B, Giri A, Zeng J, Roh J W, Kim S I, Lee K H, Jeong U 2015 ACS Nano 9 6843 Google Scholar
[15]	Xu H, Chen G, Jin R, Chen D, Wang Y, Pei J, Zhang Y, Yan C, Qiu Z 2014 Crystengcomm 16 3965 Google Scholar
[16]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666 Google Scholar
[17]	Li Y, Xu L, Liu H, Li Y 2014 Chem. Soc. Rev. 43 2572 Google Scholar
[18]	Li L, Yu Y, Ye G J, Ge Q, Ou X, Wu H, Feng D, Chen X H, Zhang Y 2014 Nat. Nanotechnol. 9 372 Google Scholar
[19]	Qiao J, Kong X, Hu Z X, Yang F, Ji W 2014 Nat. Commun. 5 4475 Google Scholar
[20]	Ghosh B, Nahas S, Bhowmick S, Agarwal A 2015 Phys. Rev. B 91 115433 Google Scholar
[21]	Mogulkoc Y, Modarresi M, Mogulkoc A, Ciftci Y O 2016 Comput. Mater. Sci. 124 23 Google Scholar
[22]	Kresse G, Furthmüller J 1996 Phys. Rev. B 54 11169 Google Scholar
[23]	Kresse G, Joubert D 1999 Phys. Rev. B 59 1758 Google Scholar
[24]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[25]	Grimme S 2006 J. Comput. Chem. 27 1787 Google Scholar
[26]	Grimme S, Antony J, Ehrlich S, Krieg H 2010 J. Chem. Phys. 132 154104 Google Scholar
[27]	Togo A, Oba F, Tanaka I 2008 Phys. Rev. B 78 134106 Google Scholar
[28]	Baroni S, De Gironcoli S, Dal Corso A, Giannozzi P 2001 Rev. Mod. Phys. 73 515 Google Scholar
[29]	Barnett R N, Landman U 1993 Phys. Rev. B 48 2081 Google Scholar
[30]	Martyna G J, Klein M L, Tuckerman M 1992 J. Chem. Phys. 97 2635 Google Scholar
[31]	Wang Y, Lv J, Zhu L, Ma Y 2010 Phys. Rev. B 82 094116 Google Scholar
[32]	Wang Y, Miao M, Lv J, Zhu L, Yin K, Liu H, Ma Y 2012 J. Chem. Phys. 137 224108 Google Scholar
[33]	Han N, Liu H, Zhou S, Zhao J 2016 J. Phys. Chem. C 120 14699 Google Scholar
[34]	Zhan L B, Yang C L, Wang M S, Ma X G 2020 Physica E 124 114272 Google Scholar
[35]	Zhang Y, He K, Chang C Z, Song C L, Wang L L, Chen X, Jia J F, Fang Z, Dai X, Shan W Y, Shen S Q, Niu Q, Qi X L, Zhang S C, Ma X C, Xue Q K 2010 Nat. Phys. 6 584 Google Scholar
[36]	Graziano G, Klimeš J, Fernandez Alonso F, Michaelides A 2012 J. Phys.-Condes. Matter 24 424216 Google Scholar
[37]	Cai Y, Zhang G, Zhang Y W 2014 Sci. Rep. 4 6677 Google Scholar
[38]	Chakrapani V, Angus J C, Anderson A B, Wolter S D, Stoner B R, Sumanasekera G U 2007 Science 318 1424 Google Scholar
[39]	Zhuang H L, Hennig R G 2013 Chem. Mater. 25 3232 Google Scholar
[40]	Ma Z, Zhuang J, Zhang X, Zhou Z 2018 Front. Phys. 13 138104 Google Scholar
[41]	Zhang X, Zhang Z, Wu D, Zhang X, Zhao X, Zhou Z 2018 Small Methods 2 1700359 Google Scholar
[42]	Beal A R, Hughes H P 1979 Solid State Phys. 12 881 Google Scholar
[43]	Duerloo K N, Ong M T, Reed E J 2012 J. Phys. Chem. Lett. 3 2871 Google Scholar
[44]	King Smith R D, Vanderbilt D 1993 Phys. Rev. B 47 1651 Google Scholar
[45]	Hangleiter A, Hitzel F, Lahmann S, Rossow U 2003 Appl. Phys. Lett. 83 1169 Google Scholar
[46]	Shimada K 2006 Jpn. J. Appl. Phys. 45 L358 Google Scholar
[47]	Guo Y, Zhou S, Bai Y, Zhao J 2017 Appl. Phys. Lett. 110 163102 Google Scholar

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First-principle study of new phase of layered Bi₂Se₃

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β-Bi₂Se₃	VBM/eV	CBM/eV	m_xh	m_xe	m_yh	m_ye
Monolayer	–5.82	–3.43	7.88	0.70	5.69	0.66
Bilayer	–5.00	–4.24	2.55	0.52	2.36	0.52
Bulk	—	—	0.65	0.63	0.65	0.67

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First-principle study of new phase of layered Bi2Se3

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Corresponding author: Zhou Si, sizhou@dlut.edu.cn

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First-principle study of new phase of layered Bi₂Se₃