A. Crystal structures
Among the two-dimensional group-IVA materials, the crystal structures of silicene, germanene, and stanene considered here have honeycomb lattice, as illustrated in top view of Fig. 1(a). In side view of Fig. 1(b), two atomic sites in a unit cell are located in two atomic layers of different heights along the z axis, exhibiting a buckled structure. The buckled honeycomb structure has a crystalline point group of D 3d , in contrast to flat graphene monolayer with D 6h group 33 . We computed lattice constant, a, and height difference, ∆, of buckled atomic layers for three monolayers in the absence of electric field, which are listed in Fig. 1 and agree with previous calculation results [21][22][23][24][25] . From silicene to stanene, the bigger is the atomic number, the larger is the lattice constant and the height difference. It is also seen that buckling degree gradually becomes larger with increasing ratio of ∆ to a, i.e. 0.12, 0.17, and 0.18 for three monolayers. For graphene with sp 2 bonds, the ratio is zero, while sp 3 hybridization leads to a ratio of 0.20. Therefore, the bonds of these three monolayers are regarded as a mix of sp 2 and sp 3 hybridizations 22,23 . We also computed the fully relaxed geometric structures of three monolayers, under vertical electric fields up to 0.2 V/Å . Compared with pristine monolayers, the deviations of the lattice constant and the height differences are less than 1‰ and 3%, respectively. Therefore, it is found that the influence of electric fields on geometric structures is tiny.

### Language ###
English

### Assessment ###
Information about structural differences between atomic materials could lead to a question about their relative buckling ratios.

### Query ###
What is the buckling ratio of stanene compared to silicene?
What is the buckling ratio of stanene compared to silicene?