Even-odd-dependent optical transitions of zigzag monolayer black phosphorus nanoribbons
Even-odd-dependent optical transitions of zigzag monolayer black phosphorus nanoribbons
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之字形单层黑磷纳米带的奇偶相关光学跃迁
DOI：
10.1007/s11433-020-1599-2
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Kai Chang
中科院分区：
文献类型：
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作者：
P. Liu;X. Z. Zhu;X. Y. Zhou;G. H. Zhou;Kai Chang
利用紧密结合的哈密顿公式和Kubo公式分析了锯齿边磷纳米带（ZPNRs）的电子结构和光学性质。通过直接求解离散薛定谔方程，我们得到了n - zpnr的能谱和波函数（其中TV为横向之字形原子链的个数），并根据晶格对称性对特征态进行了分类。然后，在对称性分析和光跃迁矩阵元素解析表达式的基础上，得到了zpnr的光跃迁选择规则。在沿带状线偏振的入射光下，我们确定了偶数和奇数nis的n- zpnr的光学跃迁选择规则不同。具体来说，对于偶数- nzpnr，带间（带内）选择规则为An =奇（偶），因为由于c2x对称的存在，导（价）带中对应的波函数的奇偶性为（-1）n[(-1)(n+1)]。然而，由于没有c2xsymmetry，任何子带之间的光学跃迁都是可能的。我们的研究结果进一步揭示了ZPNR的电子态和光学性质，有助于解释ZPNR样品的光学实验数据。
We analytically study the electronic structure and optical properties of zigzag-edged phosphorene nanoribbons (ZPNRs) using the tight-binding Hamiltonian and Kubo formula. By directly solving the discrete Schrodinger equation, we obtain the energy spectra and wavefunctions forN-ZPNR (where TV is the number of transverse zigzag atomic chains) and classify the eigenstates according to the lattice symmetry. Then, we obtain the optical transition selection rule of ZPNRs on the basis of symmetry analysis and analytical expressions of optical transition matrix elements. Under incident light that is linearly polarized along the ribbon, we determine that the optical transition selection rule forN-ZPNR with even- or odd-Nis qualitatively different. Specifically, for even-NZPNRs, the inter- (intra-) band selection rule is An =odd (even) because the parity of the wavefunction corresponding to then-th subband in the conduction (valence) band is (-1)n[(-1)(n+1)] owing to the presence ofC2xsymmetry. However, the optical transitions between any subbands are possible owing to the absence ofC2xsymmetry. Our results provide a further understanding on the electronic states and optical properties of ZPNRs, which are useful for explaining the optical experiment data on ZPNR samples.