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....

We study the collective electronic excitations in metallic single-and bilayer transition metal dichalcogenides (TMDCs) using time dependent density functional theory in the random phase approximation. For very small momentum transfers (below q ≈ 0.02 Å−1 ) the plasmon dispersion follows the √ q behavior expected for free electrons in two dimensions. For larger momentum transfer the plasmon energy is significantly red shifted due to screening by interband transitions. At around q ≈ 0.1 Å−1 the plasmon enters the dissipative electron-hole continuum and the plasmon dispersions flatten out at an energy around 0.6-1.1 eV, depending on the material. Using bilayer NbSe2 as example, we show that the plasmon modes of a bilayer structure take the form of symmetric and anti-symmetric hybrids of the single-layer modes. The spatially anti-symmetric mode is rather weak with a linear dispersion tending to zero for q = 0 while the energy of the symmetric mode follows the single-layer mode dispersion with a slight blue shift.

Electron energy loss spectroscopy (EELS) can be used to probe plasmon excitations in nanostructured materials with atomic-scale spatial resolution. For structures smaller than a few nanometers, quantum effects are expected to be important, limiting the validity of widely used semiclassical response models. Here we present a method to identify and compute spatially resolved plasmon modes from first-principles based on a spectral analysis of the dynamical dielectric function. As an example we calculate the plasmon modes of 0.5 to 4 nm thick Na films and find that they can be classified as (conventional) surface modes, subsurface modes, and a discrete set of bulk modes resembling standing waves across the film. We find clear effects of both quantum confinement and nonlocal response. The quantum plasmon modes provide an intuitive picture of collective excitations of confined electron systems and offer a clear interpretation of spatially resolved EELS spectra.

We present full quantum mechanical calculations of the hybridized plasmon modes of two nanowires at small separation, providing real space visualization of the modes in the transition from the classical to the quantum tunneling regime. The plasmon modes are obtained as certain eigenfunctions of the dynamical dielectric function which is computed using time dependent density functional theory (TDDFT). For freestanding wires, the energy of both surface and bulk plasmon modes deviate from the classical result for low wire radii and high momentum transfer due to effects of electron spill-out, non-local response, and coupling to single-particle transitions. For the wire dimer the shape of the hybridized plasmon modes are continuously altered with decreasing separation, and below 6 Å the energy dispersion of the modes deviate from classical results due to the onset of weak tunneling. Below 2-3 Å separation this mode is replaced by a charge-transfer plasmon which blue shifts with decreasing separation in agreement with experiment, and marks the onset of the strong tunneling regime.

No abstract