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Unstable acoustic mode around Gamma point
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The same group published another paper "Monolayer honeycomb structures of group-IV elements and III-V binary compounds:First-principles calculations" PRB 80, 155453 2009.
It says:In our earlier paper(PRL 102, 236804, 2009) we found that ZA mode of 2D periodic Ge honeycomb gets imaginary frequencies near point of BZ. This situation has been interpreted as the instability against long-wavelength transversal waves. This instability can be removed by the defects, such as ripples which do not allow these waves by limiting the size of Ge sheets. Finite size Ge honeycomb sheets can also be stabilized since long-wavelength transversal waves do not occur. Long wavelength defects in honeycomb structures have been treated earlier. An extensive analysis of phonon modes in the present study revealed that the extent of the region of imaginary frequencies around the point also depends on the mesh size used in the calculations.Decreasing the mesh(I guess it is k-mesh, not q-mesh) size may lead to the decreasing of their particular zone. Therefore, a tedious analysis of the right mesh size is required to determine whether or not the imaginary frequency zone of ZA mode is an artifact of the mesh size. We performed this analysis of mesh size for Ge-LB structure and found an optimum fine mesh size where imaginary frequencies of ZA mode disappeared(opposite to the previous PRL result). We also note that since the interatomic forces related with ZA modes decay rapidly, the numerical inaccuracy in calculating forces due to the transversal displacement of distant atoms may give rise to difficulties in the treatment of ZA modes. Briefly, caution has to be exercised in deciding whether the imaginary frequencies of ZA modes is an artifact of numerical calculations.
In "Vibrational properties of silicene and germanene,Nano Research 2013, 6(1): 19–28", it says: The k-point mesh was set to 4 × 4 × 1 during the structural relaxation of the silicene unit cell, while a 25 × 25 × 1 Monkhorst–Pack grid was used for the phonon calculations.
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