Theoretical Studies On Electronic States And Two-Photon Absorption In Black Phosphorus Nanoribbons

In recent years,the research on the two-dimensional layered structure of black phosphorus and transition metal sulfide has been gradually rising.As the most stable black phosphorus among the three allotropes of phosphorus,the atomic arrangement presents a single-layer corrugated structure,which is a typical direct bandgap semiconductor material.The gap width of black phosphorus can be adjusted from0.3eV to 2eV,so it has a good nonlinear optical response in the visible light band,which just fills the gap between graphene with zero band gap and transition metal sulfide with wider band gap.At present,there have been many reports on experimentalstudiesonnonlinearopticalpropertiesandresponsesof low-dimensional materials related to black phosphorus,but the theoretical research on nonlinear optics is still lackingThis paper is based on the tight binding model,using the long-wave approximation method to study the band structure and electronic states of single-layer black phosphorus nanoribbons.On this basis,the expression of the two-photon absorption coefficient of single armchair black phosphorus nanoribbons is derived by using the second-order perturbation theory,and the transition selection rule of electrons are obtained.The electronic states of the black phosphorus nanoribbons with different boundary structures and the two-photon absorption spectra of the armchair black phosphorus nanoribbons are calculated and simulated by Matlab R2010b software.The effects of the width and boundary of the nanoribbon width on the electron energy states of the black phosphorus nanoribbon width and the influence of the parameters such as the width of the nanoribbon width and the relaxation energy of the electron excited state on the two-photon absorption coefficient of the handrail type black phosphorus nanoribbon width are analyzed.The results show that:?1?the electronic band structure of single-layer black phosphorus nanoribbons has a parabolic continuous state in one direction and a discrete state with the quantum number in the other direction.With the increase of nanoribbon width,the curvature of electron energy spectrum is increased,the interval between energy levels is decreased,the energy density of carrier increases,and the band gap narrow down.No matter what kind of boundary structure,the valence band energy level and conduction band energy level have different degrees of symmetry;For the electron energy states of the zigzag boundary structure,there is an edge state energy level.?2?In the various transitions of the single armchair black phosphorus nanoribbons two-photon absorption phenomenon,the in-band transitions are dominant;The single armchair black phosphorus nanoribbons has a large two-photon absorption coefficient in the visible region of 10^-6m/W,which is four orders of magnitude larger than the two-photon absorption coefficient of traditional semiconductor quantum dots.The single armchair black phosphorus nanoribbons has a huge two-photon absorption coefficient in the infrared band,which can reach10^-1m/W.The width and relaxation of nanoribbons play an important role in adjusting the two-photon absorption coefficient of single armchair black phosphorus nanoribbons.The research results in this paper provide a theoretical reference for the experimental work of black phosphorus and a guiding significance for the practical application of nonlinear optics and photoelectric devices.