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Interlayer interaction controlling the properties of AB- and AA-stacked bilayer graphene-like BC$_{14}$N and Si$_{2}$C$_{14}$

We model bilayer graphene-like materials with Si$_2$C$_{14}$ and BC$_{14}$N stoichiometry, where the interlayer interactions play important roles shaping the physical properties of the systems. We find the interlayer interaction in Si$_2$C$_{14}$ to be repulsive due to the interaction of Si-Si atoms, and in BC$_{14}$N it is attractive due to B and N atoms for both the AA- and the AB-stacking. The repulsive interlayer interaction opens up a bandgap in Si$_2$C$_{14}$ while the attractive interlayer interaction in BC$_{14}$N induces a small indirect bandgap or overlaping of the valence conduction bands. Furthermore, the repulsive interaction decreases the Young modulus while the attractive interaction does not influence the Young modulus much. The stress-strain curves of both the AA- and the AB-stackings are suppressed compared to pure graphine bilayers. The optical response of Si$_2$C$_{14}$ is very sensitive to an applied electric field and an enrichment in the optical spectra is found at low energy. The enrichment is attributed to the bandgap opening and increased energy spacing between the $π{\text -}π^*$ bands. In BC$_{14}$N, the optical spectra are reduced due to the indirect bandgap or the overlapping of the $π{\text -}π^* $ bands. Last, a high Seebeck coefficient is observed due to the presence of a direct bandgap in Si$_2$C$_{14}$, while it is not much enhanced in BC$_{14}$N.