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

The existence of strongly bound excitons is one of the hallmarks of the newly discovered atomically thin semi-conductors. While it is understood that the large binding energy is mainly due to the weak dielectric screening in two dimensions (2D), a systematic investigation of the role of screening on 2D excitons is still lacking. Here we provide a critical assessment of a widely used 2D hydrogenic exciton model which assumes a dielectric function of the form {\epsilon}(q) = 1 + 2{\pi}{\alpha}q, and we develop a quasi-2D model with a much broader applicability. Within the quasi-2D picture, electrons and holes are described as in-plane point charges with a finite extension in the perpendicular direction and their interaction is screened by a dielectric function with a non-linear q-dependence which is computed ab-initio. The screened interaction is used in a generalized Mott-Wannier model to calculate exciton binding energies in both isolated and supported 2D materials. For isolated 2D materials, the quasi-2D treatment yields results almost identical to those of the strict 2D model and both are in good agreement with ab-initio many-body calculations. On the other hand, for more complex structures such as supported layers or layers embedded in a van der Waals heterostructure, the size of the exciton in reciprocal space extends well beyond the linear regime of the dielectric function and a quasi-2D description has to replace the 2D one. Our methodology has the merit of providing a seamless connection between the strict 2D limit of isolated monolayer materials and the more bulk-like screening characteristics of supported 2D materials or van der Waals heterostructures.

Dielectric Genome of van der Waals Heterostructures

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 efficiently calculated using a multiscale approach where the dielectric functions of the individual layers (the dielectric building blocks) are computed ab initio and coupled together via the long-range Coulomb interaction. We use the method to illustrate the 2D-3D transition of the dielectric function of multilayer MoS2 crystals, the hybridization of quantum plasmons in thick graphene/hBN heterostructures, and to demonstrate the intricate effect of substrate screening on the non-Rydberg exciton series in supported WS2. The dielectric building blocks for a variety of 2D crystals are available in an open database together with the software for solving the coupled electrodynamic equations.

Simple Screened Hydrogen Model of Excitons in Two-Dimensional Materials

We present a generalized hydrogen model for the binding energies (E_{B}) and radii of excitons in two-dimensional (2D) materials that sheds light on the fundamental differences between excitons in two and three dimensions. In contrast to the well-known hydrogen model of three-dimensional (3D) excitons, the description of 2D excitons is complicated by the fact that the screening cannot be assumed to be local. We show that one can consistently define an effective 2D dielectric constant by averaging the screening over the extend of the exciton. For an ideal 2D semiconductor this leads to a simple expression for E_{B} that only depends on the excitonic mass and the 2D polarizability α. The model is shown to produce accurate results for 51 transition metal dichalcogenides. Remarkably, over a wide range of polarizabilities the binding energy becomes independent of the mass and we obtain E_{B}^{2D}≈3/(4πα), which explains the recently observed linear scaling of exciton binding energies with band gap. It is also shown that the model accurately reproduces the nonhydrogenic Rydberg series in WS_{2} and can account for screening from the environment.

Interlayer Excitons and Band Alignment in MoS2/hBN/WSe2 van der Waals Heterostructures

van der Waals heterostructures (vdWH) are ideal systems for exploring light-matter interactions at the atomic scale. In particular, structures with a type-II band alignment can yield detailed insight into carrier-photon conversion processes, which are central to, for example, solar cells and light-emitting diodes. An important first step in describing such processes is to obtain the energies of the interlayer exciton states existing at the interface. Here we present a general first-principles method to compute the electronic quasi-particle (QP) band structure and excitonic binding energies of incommensurate vdWHs. The method combines our quantum electrostatic heterostructure (QEH) model for obtaining the dielectric function with the many-body GW approximation and a generalized 2D Mott-Wannier exciton model. We calculate the level alignment together with intra- and interlayer exciton binding energies of bilayer MoS2/WSe2 with and without intercalated hBN layers, finding excellent agreement with experimental photoluminescence spectra. A comparison to density functional theory calculations demonstrates the crucial role of self-energy and electron-hole interaction effects.

Exciton ionization in multilayer transition-metal dichalcogenides

Photodetectors and solar cells based on materials with strongly bound excitons rely crucially on field-assisted exciton ionization. We study the ionization process in multilayer transition-metal dichalcogenides (TMDs) within the Mott-Wannier model incorporating fully the pronounced anisotropy of these materials. Using complex scaling, we show that the field-dependence of the ionization process is strongly dependent on orientation. Also, we find that direct and indirect excitons behave qualitatively differently as a result of opposite effective anisotropy of these states. Based on first-principles material parameters, an analysis of several important TMDs reveals WSe2 and MoSe2 to be superior for applications relying on ionization of direct and indirect excitons, respectively.

Dissociation of two-dimensional excitons in monolayer WSe2

Two-dimensional (2D) semiconducting materials are promising building blocks for optoelectronic applications, many of which require efficient dissociation of excitons into free electrons and holes. However, the strongly bound excitons arising from the enhanced Coulomb interaction in these monolayers suppresses the creation of free carriers. Here, we identify the main exciton dissociation mechanism through time and spectrally resolved photocurrent measurements in a monolayer WSe2p–n junction. We find that under static in-plane electric field, excitons dissociate at a rate corresponding to the one predicted for tunnel ionization of 2D Wannier–Mott excitons. This study is essential for understanding the photoresponse of 2D semiconductors and offers design rules for the realization of efficient photodetectors, valley dependent optoelectronics, and novel quantum coherent phases.In two-dimensional semiconductors excitons are strongly bound, suppressing the creation of free carriers. Here, the authors investigate the main exciton dissociation pathway in p-n junctions of monolayer WSe2 by means of time and spectrally resolved photocurrent measurements.