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 e...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 for N-ZPNR(where N 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 for N-ZPNR with even-or odd-N is qualitatively different. Specifically, for even-N ZPNRs, the inter-(intra-) band selection rule is ?n =odd(even) because the parity of the wavefunction corresponding to the n-th subband in the conduction(valence) band is(-1)~n[(-1)~((n+1))] owing to the presence of C(2x) symmetry. However, the optical transitions between any subbands are possible owing to the absence of C(2x) symmetry. 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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11804092,11774085,61674145,and 69876039)the Project Funded by China Postdoctoral Science Foundation(Grant Nos.BX20180097,and 2019M652777)the Hunan Provincial Natural Science Foundation of China(Grant No.2019JJ40187)。
文摘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 for N-ZPNR(where N 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 for N-ZPNR with even-or odd-N is qualitatively different. Specifically, for even-N ZPNRs, the inter-(intra-) band selection rule is ?n =odd(even) because the parity of the wavefunction corresponding to the n-th subband in the conduction(valence) band is(-1)~n[(-1)~((n+1))] owing to the presence of C(2x) symmetry. However, the optical transitions between any subbands are possible owing to the absence of C(2x) symmetry. 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.
