Stacking and Registry Effects in Layered Materials: The Case of Hexagonal Boron Nitride

Abstract

The interlayer sliding energy landscape of hexagonal boron nitride (h-BN) is investigated via a van der Waals corrected density functional theory approach. It is found that the main role of the van der Waals forces is to "anchor" the layers at a fixed distance, whereas the electrostatic forces dictate the optimal stacking mode and the interlayer sliding energy. A nearly free-sliding path is identified, along which bandgap modulations of ∼ 0.6 eV are obtained. We propose a simple geometrical model that quantifies the registry matching between the layers and captures the essence of the corrugated h-BN interlayer energy landscape. The simplicity of this phenomenological model opens the way to the modeling of complex layered structures, such as carbon and boron nitride nanotubes.The interlayer potential landscape in layered materials is essential for understanding their mechanical and electromechanical behavior. For example, nanoelectromechanical systems (NEMS) based on low dimensional structures of such materials often rely on mechanical deformations such as twisting [1][2][3] and bending [4][5][6]. These processes involve relative sliding of the layers, which exhibits a corrugated energy landscape even in atomically flat systems, such as graphite and hexagonal boron nitride (h-BN). This corrugation arises from the non-uniform charge density distribution around the atomic positions within each layer [7][8][9]. It is well accepted that the most important factors that govern corrugation in such system are electrostatic and dispersion interactions. However, a clear picture of how the complex interplay between these factors determines the corrugated energy landscape and its manifestation in unique material properties has not emerged yet.Previous efforts towards the understanding of these phenomena have utilized density functional theory (DFT) with (semi-)local approximations [9][10][11][12]. However, these methods do not provide an appropriate description of dispersive interactions. Several approaches within DFT have been developed to overcome this problem, demonstrating successful treatment of dispersion effects in graphite [13][14][15] and h-BN [13,14,16]. However, to the best of our knowledge, such studies have not addressed the question of corrugation.In this letter, we present a theoretical study of the intricate interplay between dispersion and electrostatic interactions in layered materials. As an illustrative example we choose the case of h-BN, where both types of interactions are expected to have a considerable influence on the landscape of the interlayer potential. Using a first-principles van der Waals (vdW) corrected DFT approach, we show that dispersion interactions play the role of fixing the interlayer distance, while the electrostatic forces determine the optimal stacking mode and the interlayer sliding corrugation. In addition, we predict the existence of a nearly free-sliding path along which considerable bandgap modulations are obtained. Finally, we propose a simple geometrical model that quantifies ...

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