Dispersion Relations of Two-dimensional Equilateral Hexagonal Lattice Vibration

Abstract

Abstract:

Based on lattice dynamics, the dispersion relations of two-dimensional equilateral hexagonal lattice were derived, and the expressions of the dispersion relations along -M、M-Kand -K 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 the nearest neighbor and secondary neighbor coupling to the dispersion relations were discussed. The results show that, in only nearest neighbor coupling, the eigen frequencies of two acoustic modes are zero and other two non-zero values which correspond to optical modes are degenerate at point. One high frequency acoustic branch and one low frequency optical branch are degenerate at K point, and all four branches are nondegenerate at M point. One of the acoustic branches has totally zero frequencies and one optical branch is dispersionless over the entire symmetry directions. There is a frequency gap between acoustic branches and optical branches along -M direction, and no frequency gap in other directions. With the enhancement of the secondary neighbor coupling, the phonon frequencies are increased, and all four branches are displaied distinct dispersion along three directions, and the frequency gap is narrowed along -M direction. The above results indicate that the dispersion relations are remarkably affected by the secondary neighbor coupling. But the phonon frequencies are still degenerate at and points, further they remain unchanged at point.

Key words: optoelectronics, dispersion relation, lattice dynamics, equilateral hexagonal Lattice, secondary neighbor coupling

CLC Number:

O731

Chen Zhi-yuan, Wu Tao, Zhou Wen-liang. Dispersion Relations of Two-dimensional Equilateral Hexagonal Lattice Vibration[J]. J4, 2015, 32(6): 740-750.

References

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