Dielectric Genome of van der Waals Heterostructures

Abstract

Vertical stacking of two-dimensional (2D) crystals, such as graphene and hexagonal boron nitride, has recently lead to a new class of materials known as van der Waals heterostructures (vdWHs) with unique and highly tunable electronic properties. Ab-initio calculations should in principle provide a powerful tool for modeling and guiding the design of vdWHs, but in their traditional, form such calculations are only feasible for commensurable structures with a few layers. Here we show that the dielectric properties of realistic, incommensurable vdWHs comprising hundreds of layers can be calculated with ab-initio accuracy using a multi-scale approach where the dielectric functions of the individual layers (the dielectric building blocks) are coupled simply via their long-range Coulomb interaction. We use the method to illustrate the 2D-3D dielectric transition in multi-layer MoS2 crystals, the hybridization of quantum plasmons in large graphene/hBN heterostructures, and to demonstrate the intricate effect of substrate screening on the non-Rydberg exciton series in supported WS2.The class of 2D materials which started with graphene is rapidly expanding and now includes metallic and semiconducting transition metal dichalcogenides [1] in addition to group III-V semi-metals, semiconductors and insulators [2]. These atomically thin materials exhibit unique opto-electronic properties with high technological potential [3][4][5][6][7]. However, the 2D materials only form the basis of a new and much larger class of materials consisting of vertically stacked 2D crystals held together by weak van der Waals forces. In contrast to conventional heterostructures which require complex and expensive crystal-growth techniques to epitaxially grow the single-crystalline semiconductor layers, vdWHs can be stacked in ambient conditions with no requirements of lattice matching. The latter implies a weaker constraint, if any, on the choice of materials that can be combined into vdWHs.The weak inter-layer binding suggests that the individual layers of a vdWH largely preserve their original 2D properties modified only by the long range Coulomb interaction with the surrounding layers. Turning this argument around, it should be possible to predict the overall properties of a vdWH from the properties of the individual layers. In this Letter we show that this can indeed be achieved for the dielectric properties. Conceptually, this extends the Lego brick picture used by Geim and Grigorieva [8] for the atomic structure of a vdWH, to its dielectric properties. Specifically, we develop a semi-classical model which takes as input the dielectric functions of the individual isolated layers computed fully quantum mechanically and condensed into the simplest * kiran@fysik.dtu.dk † thygesen@fysik.dtu.dk possible representation, and couple them together via the Coulomb interaction, see Figure 1. Despite the complete neglect of interlayer hybridization, the model provides an excellent account of both the spatial and dynamical dielectric properties of vdWHs....

Excitons in van der Waals heterostructures: The important role of dielectric screening

“…We mention in passing that the dielectric functions of a large collection of 2D materials are available in the Computational Materials Repository [26]; see Refs. [27] and [22].…”

“…This can be obtained using the quantum-electrostatic heterostructure (QEH) model that we introduced recently [22]. In brief, the underlying procedure in the calculation of the dielectric function can be divided in two parts.…”

“…In Ref. [22] we showed, based on the comparison with full ab initio calculations, that the monopole/dipole basis is sufficient to obtain an accurate description of the dielectric and plasmonic properties of different layered heterostructures. We mention that in literature [35,36] the effect of environmental screening has been already investigated using a classical approach, proposed by Keldysh [37], based on the formation of image charges.…”

“…However, in the case of 2D layers supported by semi-infinite substrates or for thicker, i.e., few-layer, 2D materials, we find it important to account for the finite thickness and include the full nonlinear q dependence of the dielectric function. In a recent paper we introduced a method for calculating the dielectric function of general layered materials (so-called van der Waals heterostructures [19][20][21]) where the dielectric functions of the individual layers are computed ab initio and subsequently coupled together electrostatically [22]. In the present work we use this method to compute the screened electron-hole interaction and solve the resulting quasi-2D Mott-Wannier model for various types of heterostructures.…”

Interplay of screening and superconductivity in low-dimensional materials

“…In the long-wavelength limit, ε 1 (q) is fully determined by the dielectric background: ε 1 (q → 0) = ε sub . In the opposite limit (q 1Å −1 ), screening in the undoped case is solely due to the microscopic inter-band polarizability of the MoS 2 layer itself, ε 1 (q) ≈ 9.3 ≡ ε ∞ , but unaffected by the dielectric environment 33,34 .…”