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Research 3 55 5 X 4X Y 3 2 1 0 –1 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0 4 8 Energy (eV) 16 20 0 4 8 12 16 Energy (eV) Y 20 𝜀𝜀1 𝜀𝜀2 12 X Y X (a) 4 4 3 2 1 0 –1 2.8 2.4 2.0 1.6 1.2 0.8 0.4 Y Loss function Dielectric function Loss function Dielectric function 0.0 0 4 8 12 16 20 0 4 8 12 16 20 at point K. The real part ε1 ðωÞ of the dielectric tensor is obtained from the Kramers-Cronin relation: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ε1ðωÞ + iε2ðωÞ − 1 ð αβ αβ 2 ∞ ε2 ω′ ω′ ε1 ðωÞ=1+πP 2 2 dω′: 0 ω′ −ω +iη ð2Þ ε1ðωÞ + iεðωÞ + 1 By calculating the dielectric equation and the electron energy loss equation of the incident radiation after the polarity of the electric field vector E in the directions of a and b, it can be seen that the crystal structure of boro- phene is anisotropic, resulting in the anisotropy in its optical properties. In Figure 2(a), the virtual section of the dielectric medium model function quickly decreases at small frequen- cies close to the area of free electron. Direction of light polar- ization X, ε2ðωÞ, increases fast at 2.41 eV and then up to the peak at 3.52 eV. Interband transitions from many occupied K states under electromotive force appear at the consistent energy, resulting in a powerful spike for direction of light The absorption constant αðωÞ and RðωÞ can be calculated from functions (4) and (5) according to the above-mentioned optical characteristics of borophene such as dielectric func- tion and energy loss spectrum LðωÞ. ð3Þ 1 ε2ðωÞ LðωÞ=Im −εðωÞ = ε2ðωÞ+ε2ðωÞ, 12 Energy (eV) Energy (eV) Figure 2: The optical response of polarized light on the X and Y axes to the illumination of 2D borophene cells, as illustrated in (a) and (b). Reprinted with permission from Ref. [35]. Copyright 2016 Royal Society of Chemistry. ε0 is the dielectric constant of the vacuum, ω is for vol- ume, v and c explicit the Ev and Ec, ω express the energy of the object phonon, u · r stands for momentum symbol, and Ψck and Ψvk express the conduction band and valence band αβ pffiffi 2ω ε21ðωÞ + ε2ðωÞ 1/2 − ε1ðωÞg1/2, c (b) ð4Þ RðωÞ = pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ð5Þ αðωÞ =PDF Image | Two-Dimensional Borophene
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