Liu Pu, Zhou Xiaoying, Xiao Xianbo, Zhou Benliang, Zhou Guanghui
Department of Physics and Key Laboratory for Low-Dimensional Structures and Quantum Manipulation (Ministry of Education), Hunan Normal University, Changsha 410081, People's Republic of China.
J Phys Condens Matter. 2020 Jul 1;32(28):285301. doi: 10.1088/1361-648X/ab7df4.
We theoretically investigate the electronic structure and optical absorption spectrum of armchair-edged black phosphorene nanoribbons (APNRs) with and without uniaxial strain based on the tight-binding Hamiltonian and Kubo formula. We analytically obtain the energy spectrum and wavefunction, and reveal the band gap scaling law as 1/(N + 1) for APNRs in the presence and absence of uniaxial strain, where N is the number of armchair dimer across the ribbon. We find the band gap of APNRs linearly increases (decreases) with increasing in-plane uniaxial tensile (compressive) strain ɛ , but shows contrary dependence on the out-of-plane uniaxial strain ɛ . The effective mass versus strain exhibits the same behavior to that of band gap but with nonlinear dependence. Under an incident light linearly-polarized along the ribbon, we demonstrate that the inter-band optical transitions obey the selection rule Δn = n - n' = 0, but the intra-band transitions are forbidden for both pristine and strained APNRs originating from the orthogonality between the transverse wavefunctions of the sublattices belonging to different subbands. Importantly, the transverse electric field or impurities can release the optical selection rules by breaking the wavefunction orthogonality, which results in that the optical transitions between any subbands are all possible. Our findings provide further understanding on the electronic and optical properties of APNRs, which may pave the way for designing optoelectronic devices based on phosphorene.
我们基于紧束缚哈密顿量和久保公式，从理论上研究了有、无单轴应变的扶手椅型边缘黑磷纳米带（APNRs）的电子结构和光吸收光谱。我们通过解析得到了能谱和波函数，并揭示了在有、无单轴应变情况下，APNRs的带隙标度律为1/(N + 1)，其中N是纳米带中扶手椅二聚体的数量。我们发现，APNRs的带隙随着面内单轴拉伸（压缩）应变ɛ的增加而线性增加（减小），但对面外单轴应变ɛ呈现相反的依赖关系。有效质量与应变的关系与带隙相同，但具有非线性依赖。在沿纳米带方向线性偏振的入射光下，我们证明带间光跃迁遵循选择规则Δn = n - n' = 0，但对于原始和应变的APNRs，带内跃迁均被禁止，这源于属于不同子带的子晶格横向波函数之间的正交性。重要的是，横向电场或杂质可以通过打破波函数正交性来释放光学选择规则，这使得任何子带之间的光学跃迁都成为可能。我们的研究结果为进一步理解APNRs的电子和光学性质提供了帮助，这可能为基于磷烯的光电器件设计铺平道路。
