The Dielectric Impact of Layer Distances on Exciton and Trion Binding Energies in van der Waals Heterostructures

Abstract

The electronic and optical properties of monolayer transition-metal dichalcogenides (TMDs) and van der Waals heterostructures are strongly subject to their dielectric environment. In each layer, the field lines of the Coulomb interaction are screened by the adjacent material, which reduces the single-particle band gap as well as exciton and trion binding energies. By combining an electrostatic model for a dielectric heteromultilayered environment with semiconductor many-particle methods, we demonstrate that the electronic and optical properties are sensitive to the interlayer distances on the atomic scale. An analytic treatment is used to provide further insight into how the interlayer gap influences different excitonic transitions. Spectroscopical measurements in combination with a direct solution of a three-particle Schrödinger equation reveal trion binding energies that correctly predict recently measured interlayer distances and shed light on the effect of temperature annealing.

Prospects and Limitations of Transition Metal Dichalcogenide Laser Gain Materials

“…As discussed in Ref. 51, TMD layers do not form perfect interfaces with surrounding dielectric layers in a van der Waals heterostructure but are separated by inter-layer gaps on the sub-nm scale. We assume here that the TMD monolayers are placed on a SiO 2 crystal with dielectric constant ε = 3.9 and an inter-layer gap of 0.3 nm, which has been found to be a reasonable value, see Ref.…”

“…We assume here that the TMD monolayers are placed on a SiO 2 crystal with dielectric constant ε = 3.9 and an inter-layer gap of 0.3 nm, which has been found to be a reasonable value, see Ref. 51 and the references therein. Besides the screening of Coulomb interaction between excited carriers inside the TMD layer, dielectric screening due to the environment modifies the TMD band structure.…”

“…Besides the screening of Coulomb interaction between excited carriers inside the TMD layer, dielectric screening due to the environment modifies the TMD band structure. We calculate the correction of the freestanding G 0 W 0 -band structure using a static GW self-energy with an interaction screened by the difference of a dielectric function with and without the environment [51]. The SBE (A1) are solved numerically by matrix inversion for each frequency to obtain the frequency-dependent microscopic polarization and, thereby, the optical susceptibility using Eq.…”

Dynamical screening effects of substrate phonons on two-dimensional excitons

“…Higher exciton states are less affected due to their larger Bohr radius, as discussed in Ref. 21. On the other hand, the interaction with hBN phonons systematically reduces exciton binding energies since the polaron shift is larger for the band gap than for bound states.…”

“…Key to these applications is the compatibility with different substrates or other two-dimensional (2d) materials in functional van der Waals heterostructures (vdW-HS). [13] Fascinating prospects arise from the possibility to engineer electronic and optical properties by manipulation of the Coulomb interaction in atomically thin materials via its dielectric environment [14][15][16][17][18][19][20][21][22]. It has also become customary to improve TMD sample qualities by means of encapsulation in hexagonal boron nitride (hBN).…”