The Nature of Interlayer Binding and Stacking of spsp-sp2sp^{2} Hybridized Carbon Layers: A Quantum Monte Carlo Study

$\alpha$-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.Comment: 25 pages, 6 figure

Layer-dependent optically-induced spin polarization in InSe

Optical control of spin in semiconductors has been pioneered using nanostructures of III-V and II-VI semiconductors, but the emergence of two-dimensional van der Waals materials offers an alternative low-dimensional platform for spintronic phenomena. Indium selenide (InSe), a group-III monochalcogenide van der Waals material, has shown promise for opto-electronics due to its high electron mobility, tunable direct bandgap, and quantum transport. There are predictions of spin-dependent optical selection rules suggesting potential for all-optical excitation and control of spin in a two-dimensional layered material. Despite these predictions, layer-dependent optical spin phenomena in InSe have yet to be explored. Here, we present measurements of layer-dependent optical spin dynamics in few-layer and bulk InSe. Polarized photoluminescence reveals layer-dependent optical orientation of spin, thereby demonstrating the optical selection rules in few-layer InSe. Spin dynamics are also studied in many-layer InSe using time-resolved Kerr rotation spectroscopy. By applying out-of-plane and in-plane static magnetic fields for polarized emission measurements and Kerr measurements, respectively, the $g$-factor for InSe was extracted. Further investigations are done by calculating precession values using a $\textbf{k} \cdot \textbf{p}$ model, which is supported by \textit{ab-initio} density functional theory. Comparison of predicted precession rates with experimental measurements highlights the importance of excitonic effects in InSe for understanding spin dynamics. Optical orientation of spin is an important prerequisite for opto-spintronic phenomena and devices, and these first demonstrations of layer-dependent optical excitation of spins in InSe lay the foundation for combining layer-dependent spin properties with advantageous electronic properties found in this material.Comment: 11 pages, 6 figures, supplemental materia