N重旋转对称的二维准晶电子态与声子态的简并性

DEGENERACIES OF THE ELECTRONIC AND PHONON STATES OF THE TWO-DIMENSIONAL QUASICRYSTALS WITH N-FOLD ROTATIONAL SYMMETRY

通过相似变化矩阵,对具有N重旋转对称的二维准晶系统的哈密顿量和动力学矩阵进行对角约化。当N为偶数时,电子态与声子态中有(N-2)/(N+2)是双重简并,而4/(N+2)是非简并;当N为奇数时,电子态与声子态中有(N-1)/(N+1)是双重简并,而2/(N+1)是非简并。利用群论方法得到相同的结论。

The similarity transformation is introduced which reduce the hamiltonian and the dynamical matrix of the two-dimensional quasicrystals with A/-fold rotational symmetry. For the degeneracy, when N is even number, N-2 out of N+ 2 of electronic and phonon states are doubly degenerate and 4 out of N+ 2 are non-degenerate, and as N is odd number, N-1 out of N + 1 of electronic and phonon states are doubly degenerate and 2 out of N + 1 are nondegene-rate. We use group theory +o study the degeneracies of twodimensional quasicrystals and obtain the same conclusion.