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note
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As for the transverse mode calculation, the selected wave vector k is determined by following Eq. (20), so that the wave number k of selected wave vectors k is larger than one of the longitudinal modes. However, this selected wave vector k essentially indicates the same point as the wave vector for calculating the longitudinal mode spectra because of the periodicity of the reciprocal lattice vectors. In fact, the observed spectra in Fig. 5 are evidently TA and TO modes at the same wave vector point in the first Brillouin zone, and these excitation energies are in good agreement with experimental data. This coincidence of the phonon energies seen in Fig. 5 gives us support for the present computation.
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