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摘要

黑磷烯具有各向异性且独特的光电性能被广泛研究. 应变、电压等常用来调制能带结构, 进而调制其光电特性. 本文采用紧束缚近似哈密顿量, 考虑施加垂直磁场、电场、面内面外应变条件下的黑磷烯能带结构, 进一步利用Kubo公式研究了黑磷烯光电导率在多个调制因子下的特征, 并从能带结构进行了机理分析. 垂直磁场使能带劈裂, 产生多通道带间跃迁, 光电导率表现出多个峰. 随着面内拉伸应变增加能隙增加, 光电导峰位依赖于能隙. 而面外拉伸应变对能隙的调制区别于面内应变, 能隙表现出非单调变化. 电场通过带隙的变化, 调制光电导率峰值位置. 综合不同的调制因子, 能带和光电导表现出丰富的调制效果, 为研究基于黑磷烯光电器件的应用提供理论支持.

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Abstract

Black phosphorene (BP) has been widely investigated for its anisotropic and unique photoelectric properties. Strain, voltage and so on are commonly used to modulate the energy band structure and accordingly its photoelectric characteristics. In this study, we consider the energy band structure of BP in the vertical magnetic field, electric field, and in-plane/out-of-plane strains by using the tight-binding approximate Hamiltonian. The anisotropic frequency-dependent interband optical conductivity (IOC) of BP is investigated by using the Kubo formula in these modulation factors. Inherent asymmetry in band dispersion along the armchair (AC) direction and the zigzag (ZZ) direction leads to anisotropic IOC. The introduction of a vertical magnetic field induces band splitting, thereby generating multiple interband transition channels. In this case, the IOC along both the AC direction and the ZZ direction exhibits three peaks around the original peak position, and the magnitudes of the peaks are also modulated. With the increase of in-plane strain (from –20% to 20%), the band gap increases monotonically, and both the position and magnitude of the peaks vary with band gap changing. However, the band gap of BP undergoes a non-monotonic change under out-of-plane strain (from –20% to 20%), which is different from the change under in-plane strain. The band gap reaches a minimum value when a tensile strain of 12% is applied. Along the AC direction, the modulation of the IOC by in-plane strain is opposite to the modulation of out-of-plane strain ( ε _z< 12%), indicating a competitive effect when triaxial strains are applied. Along the ZZ direction, in-plane strain primarily modulates the peak magnitude, while out-of-plane strain effectively modulates not only the peak position but also the peak magnitude obviously. The modulation of the IOC by forward and reverse electric fields are symmetrical. The coefficient for the peak position shift due to the vertical electric field is 1/2 in the AC direction and 1/10 in the ZZ direction. By integrating various modulation factors, we achieve versatile control over the energy band and IOC of BP, providing theoretical support for the application of BP in optoelectronic devices.

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通信作者:杨翠红,chyang@nuist.edu.cn

基金项目:国家自然科学基金(批准号: 11547030)资助的课题.

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Corresponding author:Yang Cui-Hong,chyang@nuist.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 11547030).

文章全文: translate this paragraph

参考文献

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施引文献

下载: 全尺寸图片幻灯片

t_i	具体数值/eV	a_i	具体数值/Å
t₁	–1.22	a₁	1.41763
t₂	3.665	a₂	0.79732
t₃	–0.205	a₃	3.01227
t₄	–0.105	a₄	2.21468
t₅	–0.055	a₅	3.63258

下载: 导出CSV

γ	$ \alpha _{1}^\gamma $	$ \alpha _{2}^\gamma $	$ \alpha _{3}^\gamma $	$ \alpha _{4}^\gamma $	$ \alpha _{5}^\gamma $
x	0.4460	0.0992	0.7505	0.3976	0.7530
y	0.5571	0	0.2461	0.2280	0
z	0	0.9052	0	0.3722	0.2538

下载: 导出CSV

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