不变本征算符方法求解含不同在位势的一维双原子链的色散关系

摘要

本文运用全量子化的不变本征算符方法，求解了含有不同简谐在位势的一维双原子链模型，得到其色散关系并讨论了不同在位势系数之比和力常数对于色散关系高频支和低频支的影响，分析发现在位势的存在使得低频支和高频支的频谱都有一定程度的抬高；在一定的条件下，布里渊区边界的高频支与低频支存在交点，意味着在某些在位势下，高频支与低频支的频隙为零。%The dispersion law of a one-dimensional diatomic lattice with on-site potential cross on its dispersion relation is solved under the harmonic approximation with quantized invariant eigen-operator method (IEO) and the influences of on-site potential and force constant are discussed. It is shown that due to the existence of on-site potential the lattice vibration spectra induced are shifted. Under certain conditions, the point of intersection exist between optical branch and acoustic branch in the boundary of Brillioun zone, which means the frequency gap between optical branch and acoustic branch is zero.