A simple model for the vibrational modes in honeycomb lattices

Details A simple model for the vibrational modes in honeycomb lattices A simple model for the vibrational modes in honeycomb lattices

2003-07-24

arxiv.org/abs/cond-mat/0307616v2

European Journal of Physics 25, 723-736 (2004)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

9 pages, 12 figures, submitted to American Journal of Physics

Scientific paper

10.1088/0143-0807/25/6/004

The classical lattice dynamics of honeycomb lattices is studied in the harmonic approximation. Interactions between nearest neighbors are represented by springs connecting them. A short and necessary introduction of the lattice structure is presented. The dynamical matrix of the vibrational modes is then derived, and its eigenvalue problem is solved analytically. The solution may provide deeper insight into the nature of the vibrational modes. Numerical results for the vibrational frequencies are presented. To show that how effective our method used for the case of honeycomb lattice is, we also apply it to triangular and square lattice structures. A few suggested problems are listed in the concluding section.

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