Dimensionality of excitons in stacked van der Waals materials: The example of hexagonal boron nitride

Abstract

With the example of hexagonal boron nitride, we demonstrate how the character of electron-hole (e-h) pairs in van der Waals bound low-dimensional systems is driven by layer stacking. Four types of excitons appear, with either a two-or three-dimensional spatial extension. Electron and hole distributions are either overlapping or exhibit a charge-transfer nature. We discuss under which structural and symmetry conditions they appear and they are either dark or bright. This analysis provides the key elements to identify, predict, and possibly tailor the character of e-h pairs in van der Waals materials.Two-dimensional (2D) systems and layered weaklybound structures thereof are considered the materials of the 21st century. Their wealth of intriguing properties is widely explored from a fundamental scientific point of view but also in view of a plethora of possible applications [1,2]. Hexagonal boron nitride (h-BN) is one of these materials, consisting of covalently bound sheets that are held together by van der Waals (vdW) forces [3]. h-BN is a wide-gap semiconductor, exhibiting pronounced excitonic effects in its optical excitations that are present irrespective of the material's dimensionality [4][5][6][7][8][9][10][11]. Owing to the flat geometry of its in-plane hexagonal lattice, h-BN is often chosen as a building block in vdW heterostructures [12][13][14][15]. Combining different 2D systems, quantum confinement effects allow for tailoring their opto-electronic properties [16][17][18]. This not only concerns level alignment at the interface [19][20][21][22][23][24][25][26] but also the way the system interacts with light, i.e., quantum efficiency, as well as the character and spatial distribution of electron-hole (e-h) pairs [14,15,[27][28][29][30][31][32].In this Rapid Communication, we show that the nature and dimensionality of excitons can also be governed in a single vdW-bound bulk material, taking h-BN as an example. This seems surprising at a first glance as e-h pairs in this material have been found to exhibit basically the same character and extension in bulk [6][7][8], monolayers [10], as well as in interfaces with graphene [14]. Here we demonstrate how strongly stacking impacts the optical excitations of a vdW crystal at the absorption onset and beyond. By varying the arrangement of individual h-BN layers, we find in total four types of electron-hole pairs, of a two-dimensional, three-dimensional (3D), and charge-transfer character, and discuss their appearance by symmetry considerations. We focus on the five structures that are obtained by including four inequivalent atoms in the unit cell, allowing only a rigid translation by one bond length and/or exchanged positions between the two atomic species. We employ density-functional theory [33-37] and many-body perturbation theory (MBPT, including G 0 W 0 [38,39] and the Bethe-Salpeter equation [40][41][42][43]), implemented in the all-electron framework of the exciting code [44][45][46].Prototypes of the four kinds of excitations that can appear in h-BN ar...

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