Comparative study on the nonlinear properties of bilayer graphene and silicene under tension

• There is Van der Waals interaction between two layers of BLG.
• There is covalent bond interaction between two layers of BLS.
• Stiffnesses of BLG and BLS become slightly larger.
• Second-and third-order elastic constants of BLG and BLS have been obtained.

Atomic structures and nonlinear properties of single layer graphene (SLG), bilayer graphene (BLG), single layer silicene (SLS), and bilayer silicene (BLS) under equiaxial tension and uniaxial tensions along armchair and zigzag directions have been investigated comparatively using first-principles calculations. First, we have calculated the dependences of atomic structures (bond length, interlayer distance, and buckling height) of BLG and BLS on strain under three types of tensions. There exists the weak Van der Waals interaction between two layers of BLG and the interlayer distance is not variable with strain for three types of tensions. However, the interlayer of BLS is the covalent bond interaction, and the distance decreases with the increasing strain for three types of tensions. The continuum description of elastic response is formulated by expanding the elastic strain energy density in a Taylor series in strain truncated after the third-order term. The in-plane second- and third-order elastic constants of BLG and BLS have been obtained by fitting to the strain energy density versus Lagrangian strain relationships. The results show the in-plane stiffnesses of BLG and BLS become slightly larger than those of their single layer counterparts. In spite of the interlayer Si–Si covalent bond between two layers of BLS, its stiffness is still much less than BLG and SLG. Poisson’s ratios of BLG and BLS basically maintain unchanged compared to their single layer counterparts.