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近年来, 在石墨烯研究热潮的推动下, 众多种类丰富、性能各异的二维化合物材料相继被发现, 其中一些二维材料具有多种同素异构体, 进而呈现出更丰富的性质. 层状Bi2Se3由于其独特的物理性质, 受到人们广泛的关注, 而它的同素异构体尚未有人研究. 本文采用基于密度泛函理论的结构搜索方法, 预测了一个稳定的β-Bi2Se3新相, 它具有良好的动力学和热力学稳定性, 并在低Bi2Se3源化学势条件下容易形成. 单层β-Bi2Se3是一个直接带隙为2.44 eV的二维半导体, 其电子载流子有效质量低至0.52m0, 在可见光范围内具有高达105 cm–1的光吸收系数, 并且能带边缘位置适中, 可用于光催化水分解制氢气. 此外, 由于β-Bi2Se3在垂直层面方向的镜面对称性破缺, 能够产生面外极化强度, 具有0.58 pm/V的面外压电系数. 鉴于其新颖的电子特性, 二维β-Bi2Se3在未来的电子器件中可能发挥重要的作用.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.
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Keywords:
- semiconductor /
- Bi2Se3 /
- allotrope /
- electronic structures /
- layered material
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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
Fig. 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.
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
Fig. 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.
图 A2 温度为300 K时β-Bi2Se3单层的能量-时间变化 曲线
Fig. A2. Variations of temperature and energy with the time of AIMD simulation for β-Bi2Se3 monolayer at 300 K.
图 2 α-Bi2Se3和β-Bi2Se3体系表面自由能的化学势相图
Fig. 2. Chemical potential phase diagram of surface free ener-gy for α-Bi2Se3 and β-Bi2Se3.
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
Fig. 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.
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
Fig. 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.
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
Fig. 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.
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
Fig. 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
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(mxh, myh, mxe, mye). 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 mxh mxe myh mye 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
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[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
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[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
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[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
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[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
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[15] Xu H, Chen G, Jin R, Chen D, Wang Y, Pei J, Zhang Y, Yan C, Qiu Z 2014 Crystengcomm 16 3965
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[47] Guo Y, Zhou S, Bai Y, Zhao J 2017 Appl. Phys. Lett. 110 163102
Google Scholar
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