The Nature of Interlayer Binding and Stacking of $sp$-$sp^{2}$ Hybridized Carbon Layers: A Quantum Monte Carlo Study

TL;DR

This study uses quantum Monte Carlo simulations to accurately determine the interlayer binding energies of bilayer $ ext{alpha}$-graphyne, revealing nearly degenerate stability of two stacking configurations and highlighting limitations of DFT in modeling van der Waals interactions.

Contribution

First quantum Monte Carlo analysis of interlayer binding in $ ext{alpha}$-graphyne, showing near degeneracy of stacking modes and limitations of DFT for van der Waals interactions.

Findings

Interlayer binding energies are underestimated by DFT.

Two stacking modes are nearly energetically degenerate.

Both stacking configurations are equally probable at room temperature.

Abstract

$\alpha$-graphyne is a two-dimensional sheet of $sp$-$sp^2$ hybridized carbon atoms in a honeycomb lattice. While the geometrical structure is similar to that of graphene, the hybridized triple bonds give rise to electronic structure that is different from that of graphene. Similar to graphene, $\alpha$-graphyne can be stacked in bilayers with two stable configurations, but the different stackings have very different electronic structures: one is predicted to have gapless parabolic bands and the other a tunable band gap which is attractive for applications. In order to realize applications, it is crucial to understand which stacking is more stable. This is difficult to model, as the stability is a result of weak interlayer van der Waals interactions which are not well captured by density functional theory (DFT). We have used quantum Monte Carlo simulations that accurately include van der Waals interactions to calculate the interlayer binding energy of bilayer graphyne and to determine its most stable stacking mode. Our results show that interlayer bindings of $sp$- and $sp^{2}$-bonded carbon networks are significantly underestimated in a Kohn-Sham DFT approach, even with an exchange-correlation potential corrected to include, in some approximation, van der Waals interactions. Finally, our quantum Monte Carlo calculations reveal that the interlayer binding energy difference between the two stacking modes is only 0.9(4) meV/atom. From this we conclude that the two stable stacking modes of bilayer $\alpha$-graphyne are almost degenerate with each other, and both will occur with about the same probability at room temperature unless there is a synthesis path that prefers one stacking over the other.