An analytic expression for π and π＊ electronic structure of graphene is derived within the tight-binding approximation. Including up to fifth-nearest neighbors, the tight-binding description of electronic dispersio...An analytic expression for π and π＊ electronic structure of graphene is derived within the tight-binding approximation. Including up to fifth-nearest neighbors, the tight-binding description of electronic dispersion quite accurately reproduces the first-principle calculation result over the entire Brillouin zone. The maximal deviation of the fifth-nearest tight-binding result from the first-principle result is only 6 meV for π band, and 25 meV for π＊ band. This 25 meV deviation is only one-tenth of the maximal deviation of the third-nearest tight-binding result. It is more important that the fitted parameters exponentially approach to zero as the distance between interacting atoms increases.展开更多
Up to now,at least 806 carbon allotropes have been proposed theoretically.Three interesting carbon allotropes(named Pbam-32,P6/mmm,and I43d)were recently uncovered based on a random sampling strategy combined with spa...Up to now,at least 806 carbon allotropes have been proposed theoretically.Three interesting carbon allotropes(named Pbam-32,P6/mmm,and I43d)were recently uncovered based on a random sampling strategy combined with space group and graph theory.The calculation results show that they are superhard and remarkably stable compared with previously proposed metastable phases.This indicates that they are likely to be synthesized in experiment.We use the factor group analysis method to analyze theirΓ-point vibrational modes.Owing to their large number of atoms in primitive unit cells(32 atoms in Pbam-32,36 atoms in P6/mmm,and 94 atoms in I43d),they have many Raman-and infrared-active modes.There are 48 Raman-active modes and 37 infrared-active modes in Pbam-32,24 Raman-active modes and 14 infrared-active modes in P6/mmm,and 34 Raman-active modes and 35 Raman-and infrared-active modes in I43d.Their calculated Raman spectra can be divided into middle frequency range from 600 cm-1 to 1150 cm-1 and high frequency range above 1150 cm-1.Their largest infrared intensities are 0.82,0.77,and 0.70(D/Å)2/amu for Pbam,P6/mmm,and I43d,respectively.Our calculated results provide an insight into the lattice vibrational spectra of these sp3 carbon allotropes and suggest that the middle frequency Raman shift and infrared spectrum may play a key role in identifying newly proposed carbon allotropes.展开更多
基金Supported from the Scientific Research Foundation of Henan University of Science and Technology under Grant Nos.2008ZY036Student Research Training Program 2009178, and 2009183
文摘An analytic expression for π and π＊ electronic structure of graphene is derived within the tight-binding approximation. Including up to fifth-nearest neighbors, the tight-binding description of electronic dispersion quite accurately reproduces the first-principle calculation result over the entire Brillouin zone. The maximal deviation of the fifth-nearest tight-binding result from the first-principle result is only 6 meV for π band, and 25 meV for π＊ band. This 25 meV deviation is only one-tenth of the maximal deviation of the third-nearest tight-binding result. It is more important that the fitted parameters exponentially approach to zero as the distance between interacting atoms increases.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.U1404111,11504089,61874160,61675064,and 11404098)the Fund for Young Key Teacher of Henan Province,China(Grant No.2016GGJS-059)the Henan Provincial Major Scientific and Technological Projects,China(Grant No.182102210289).
文摘Up to now,at least 806 carbon allotropes have been proposed theoretically.Three interesting carbon allotropes(named Pbam-32,P6/mmm,and I43d)were recently uncovered based on a random sampling strategy combined with space group and graph theory.The calculation results show that they are superhard and remarkably stable compared with previously proposed metastable phases.This indicates that they are likely to be synthesized in experiment.We use the factor group analysis method to analyze theirΓ-point vibrational modes.Owing to their large number of atoms in primitive unit cells(32 atoms in Pbam-32,36 atoms in P6/mmm,and 94 atoms in I43d),they have many Raman-and infrared-active modes.There are 48 Raman-active modes and 37 infrared-active modes in Pbam-32,24 Raman-active modes and 14 infrared-active modes in P6/mmm,and 34 Raman-active modes and 35 Raman-and infrared-active modes in I43d.Their calculated Raman spectra can be divided into middle frequency range from 600 cm-1 to 1150 cm-1 and high frequency range above 1150 cm-1.Their largest infrared intensities are 0.82,0.77,and 0.70(D/Å)2/amu for Pbam,P6/mmm,and I43d,respectively.Our calculated results provide an insight into the lattice vibrational spectra of these sp3 carbon allotropes and suggest that the middle frequency Raman shift and infrared spectrum may play a key role in identifying newly proposed carbon allotropes.
