We study theoretically the optical response for perfect zigzag-edge silicene nanoribbons with N silicon atoms of the A and B sublattices（N-ZSiNRs） under the irradiation of an external electromagnetic field at low te...We study theoretically the optical response for perfect zigzag-edge silicene nanoribbons with N silicon atoms of the A and B sublattices（N-ZSiNRs） under the irradiation of an external electromagnetic field at low temperatures.The 8- and 16-ZSiNRs are demonstrated to exhibit a broad energy regime of absorption coefficient, refractive index, extinction coefficient, and reflectivity from infrared to ultraviolet, utilizing the dipole-transition theorem for semiconductors. The optical spectra for 8- and 16-ZSiNRs may be classified into two types of the transitions,one between valence and conduction subbands with the same parity, and the other among the edge state and bulk state subbands. With the increase of the ribbon width, the optical spectra for ZSiNRs are proved to exhibit red shift and blue shift at the lower and higher energy regimes, respectively. The obtained novel features are believed to be of significance in designs of silicene-based optoelectronic devices.展开更多
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 under Grant Nos 11664010 and 11264013the Hunan Provincial Natural Science Foundation of China under Grant Nos 2017JJ2217 and 12JJ4003+3 种基金the Scientific Research Fund of Hunan Provincial Education Department of China under Grant No 14B148the Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Provincethe Innovation Project for Postgraduate of Hunan Province under Grant No CX2015B549the Research Program of Jishou University under Grant Nos 15JDY026 and Jdy16021
文摘We study theoretically the optical response for perfect zigzag-edge silicene nanoribbons with N silicon atoms of the A and B sublattices（N-ZSiNRs） under the irradiation of an external electromagnetic field at low temperatures.The 8- and 16-ZSiNRs are demonstrated to exhibit a broad energy regime of absorption coefficient, refractive index, extinction coefficient, and reflectivity from infrared to ultraviolet, utilizing the dipole-transition theorem for semiconductors. The optical spectra for 8- and 16-ZSiNRs may be classified into two types of the transitions,one between valence and conduction subbands with the same parity, and the other among the edge state and bulk state subbands. With the increase of the ribbon width, the optical spectra for ZSiNRs are proved to exhibit red shift and blue shift at the lower and higher energy regimes, respectively. The obtained novel features are believed to be of significance in designs of silicene-based optoelectronic devices.
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.
