Interlayer Binding of Bilayer Low-dimensional $sp$,$sp^2$- Hybridized Carbon Networks : Quantum Monte Carlo Study

We have performed the quantum Monte Carlo(QMC) method to study interlayer binding of a bilayer $\alpha$-graphyne. A $sp$,$sp^2$-hybridized $\alpha$-graphyne have been received a great deal of attention due to its unique electronic properties compared with that of graphene. However, since the most stable mode in the DFT framework was varied along applied vdW-corrected correlation functionals, the most favored mode for a bilayer $\alpha$-graphyne was not confirmed.[1] Our QMC calculations confirmed the most favored mode for a bilayer $\alpha$-graphyne and revealed that vdW-corrected DFT binding energies significantly underestimate interlayer bindings of $sp$,$sp^2$-hybridized carbon network systems while overestimations within corresponding DFT functionals were observed in a graphene in recent QMC studies.[2] Among vdW-corrected DFT functionals, the rVV10 functional described the most consistent interlayer geometries with QMC ones for low-dimensional carbon allotropes, however, completely misestimated charge density distribution within the rVV10 yields significant quantitative discrepancy of interlayer binding energies between QMC ones. [1] O. Leenaerts {\it et al.}, Appl. Phys. Lett. {\bf 103}, 013105 (2013). [2] E. Mostaani {\it et al.}, Phys. Rev. Lett. {\bf 115}, 115501 (2015).