Interlayer Excitons with Large Optical Amplitudes in Layered van der Waals Materials

Abstract

Vertically stacked two-dimensional materials form an ideal platform for controlling and exploiting light-matter interactions at the nanoscale. As a unique feature, these materials host electronic excitations of both intra- and interlayer type with distinctly different properties. In this Letter, using first-principles many-body calculations, we provide a detailed picture of the most prominent excitons in bilayer MoS, a prototypical van der Waals material. By applying an electric field perpendicular to the bilayer, we explore the evolution of the excitonic states as the band alignment is varied from perfect line-up to staggered (Type II) alignment. For moderate field strengths, the lowest exciton has intralayer character and is almost independent of the electric field. However, we find higher lying excitons that have interlayer character. They can be described as linear combinations of the intralayer B exciton and optically dark charge transfer excitons, and interestingly, these mixed interlayer excitons have strong optical amplitude and can be easily tuned by the electric field. The first-principles results can be accurately reproduced by a simple excitonic model Hamiltonian that can be straightforwardly generalized to more complex van der Waals materials.

Biaxial strain tuning of interlayer excitons in bilayer MoS2

“…A similar tunability of the interlayer van der Waals interaction upon biaxial strain has been recently reported in black phosphorus by Huang and co-workers [36]. The strain tunable interlayer distance could explain the large gauge factor observed for bilayer MoS 2 upon biaxial strain as Deilmann and Thygesen demonstrated through density functional theory calculations that the interlayer exciton position strongly depends on the interlayer distance [24]. In previous uniaxial strain works, on the other hand, because of the Poisson's ratio of the polycarbonate substrate (ν=0.37) when the flake is uniaxially stretched in one direction it is compressed in the perpendicular direction (within the basal plane) [37] counteracting most of the Poisson's effect induced upon uniaxial tension [16].…”

“…That peak can be also observed in trilayer and even multilayer MoS 2 but it cannot be as easily resolved as in the case of bilayer MoS 2 . This feature in the reflectance spectra have been recently demonstrated (through temperature dependent optical spectroscopy studies, magneto-optical measurements and density functional theory calculations) to be originated by the generation of interlayer (IL) excitons [14,15,24]. These excitons are, similarly to the A and B excitons, due to direct transitions at the K point but unlike them the electron and hole are spatially separated in the different MoS 2 layers (see the cartoon in figure 1(b)).…”

Light–matter interaction in van der Waals hetero-structures

“…(a) In a heterojunction (type II) interlayer excitons can have a lower excitation energy even though the exciton binding energy is reduced and become the excitonic ground state. (b) By varying the hybridization of neighbouring layers the interlayer states can strongly hybridize and gain large oscillator strength (marked as red color)[100,130].…”

Biaxial Strain Tuning of Interlayer Excitons in Bilayer MoS₂

“…This feature in the reflectance spectra have been recently demonstrated (through temperature dependent optical spectroscopy studies, magneto-optical measurements and density functional theory calculations) to be originated by the generation of interlayer (IL) excitons. 14,15,24 These excitons are, similarly to the A and B excitons, due to direct transitions at the K point but unlike them the electron and hole are spatially separated in the different MoS2 layers (see the cartoon in Figure 1 In order to biaxially strain the MoS2 bilayers we exploit the large thermal expansion mismatch between the PP substrate (~130×10 -6 K -1 ) and MoS2 (1.9×10 -6 K -1 ) 25 . PP has also a relatively high Young's modulus (1.5-2 GPa) for a polymer, which is essential to guarantee an optimal strain transfer from substrate to flake.…”

“…34 The strain tunable interlayer distance could explain the large gauge factor observed for bilayer MoS2 upon biaxial strain as Deilmann and Thygesen demonstrated though density functional theory calculations that the interlayer exciton position strongly depends on the interlayer distance. 24 In Figure 3 we test the reproducibility of the biaxial strain tuning exploiting the thermal expansion of the substrate. We modulated the temperature of the substrate between ~30ºC and ~40ºC (see the registered temperature vs. time in the top panel of The intensity of the differential reflectance spectra is displayed in the color axis of the colormap.…”