二维双原子正方晶格振动的色散关系

Dispersion Relations of Two-dimensional Diatomic Square Lattice Vibration

利用晶格动力学理论推导了二维双原子正方晶格振动的色散关系表达式,得到第一布里渊区中沿Γ-X、Γ-M和X-M 3种对称方向的声子色散曲线,每一对称方向有四支格波,即两支声学波和两支光学波.讨论了原子质量和次近邻原子间作用对色散关系的影响,结果表明:当两原子质量相等时,3个对称方向的声学波与光学波间无频隙;当两原子质量不等时,声学波与光学波间出现频隙.计及次近邻原子间作用,对Γ点声子频率的大小和简并不影响,两声学模频率为零、两光学模频率简并;对X点声子频率的简并也无影响,但相应频率增大;使M点声子频率的简并度降低,高频声学和光学声子的频率增大,而低频声学和光学声子的频率不变;沿Γ-X方向四支格波仍是非简并的,对应的频率增大,但都表现出色散性;沿Γ-M和X-M方向简并格波的简并度消失,除Γ-M方向低频声学支和光学支频率不变之外,其他格波声子的频率都增大,并且四支格波都表现出色散性.

Based on lattice dynamics,the expressions of dispersion relations were derived for two-dimensional diatomic square lattice,the curves of phonon dispersion alongΓ-X,Γ-M and X-M three symmetry directions were obtained in the First Brillouin Zone. There are four pieces of lattice waves in each direction,where two branches are acoustic waves and other two are optical waves. The effects of two atom masses and secondary neighbor coupling to the dispersion relations were discussed. The results show that,when two masses in the basis are same,there is no the frequency gap between acoustic branches and optical branches along three directions. As two masses are unequal, the frequency gap exists between acoustic branches and optical branches. In presence of secondary neighbor coupling,there are not effects to the value and degeneracy of the phonon frequencies atΓpoint,where both acoustic and optical modes are degenerate. Also,there are no effects to degeneracy of the phonon frequencies at X point, but the phonon frequencies are increased. The degree of degeneracy of the phonon frequencies is reduced at M point,and the frequencies of high frequency acoustic and optical phonon are increased,but the frequencies of low frequency acoustic and optical phonon keep unchanged. Four branches are still non-degenerate alongΓ-X direction, and the phonon frequencies are increased,but they display distinctly dispersion. The degree of degenerate branches is disappeared along Γ-M and X-M directions,except that the frequencies of low frequency acoustic and optical branches retain unchanged alongΓ-M,the others are increased,and four branches are show dispersion. The above＆amp;nbsp;results indicate that the dispersion relations are remarkably affected by the atom masses and secondary neighbor coupling.