Magnification of Plasmon Resonances in Monolayer MoS$_{2}$ via Conjugated Molecular Adsorbates

The adsorption of carbon-conjugated molecules represents an established route to tune the electronic and optical properties of transition metal dichalcogenide (TMDC) monolayers. Here, we demonstrate from first principles that such a functionalization with prototypical compounds pyrene and tetracene can also enhance the magnitude of selected plasmon resonances in a MoS$_2$ single sheet, without significantly altering their energy and dispersion. Our proof-of-principle results indicate that such a magnification can be achieved by proper alignment of the molecules with respect to the direction of the transferred momentum. The distinct signatures in the loss function of the interface compared to those of its constituents suggest not only the presence of non-negligible interactions between them but also the possibility of using electron energy loss spectroscopy to detect the presence and the orientation of molecular adsorbates on TMDCs.


Introduction
5][6] From a fundamental perspective, TMDCs are characterized by distinct excitonic and plasmonic features. 7,80][11] These systems present two primary plasmon resonances, identified as π and π + σ due to the character of the electronic states ruling the corresponding electronic transitions, namely π → π * and σ → σ * : 12 π-resonances are typically found in the near ultraviolet region, between 5 and 10 eV, while σ-resonances are energetically higher, above 10 eV.Recent studies based on electron energy loss spectroscopy (EELS) have contributed to shed light on the details of these excitations in TMDCs.Among the most relevant ones, Moynihan et.al. studied the plasmon modes on a pristine single layer of MoS 2 , 13 Nerl et.al. explored both excitons and plasmons on a few layers of MoS 2 by means of EELS, 14 and Yue and coworkers focused on the q-dispersion of plasmons resonances in this material. 157][18][19] The deposition of organic layers on top of these materials gives rise to hybrid interfaces with tunable level alignment, [20][21][22] work function, 23,24 and spectral response 25,26 depending on the choice of the constituents.
1][42] Likewise, the study of the optical absorption properties of such hybrid interfaces, including excitons, [43][44][45][46][47][48] has contributed to a deeper understanding of these materials and opened new avenues to tune the exceptional optical properties of TMDCs.On the other hand, the electron energy loss of such systems is still largely unexplored.The main reason lies in the technical issues of corresponding measurements which would likely destroy the sample before delivering meaningful data.Until a viable solution to this problem is found, first-principles calculations can provide useful references for future experiments and, most importantly, new insight into the fundamental properties of TMDC/molecule interfaces.
In this work, we present a first-principles study of EELS spectra of two prototypical hybrid materials formed by monolayer MoS 2 decorated with physisorbed pyrene and tetracene molecules.The goal of this study is to understand, in a proof-of-principle fashion, whether and how the loss-function resonances of MoS 2 are modified by the presence of physisorbed conjugated molecules.0][51][52][53] By exploring different configurations in which the moieties are systematically rotated with respect to the direction of the transferred momentum q, we analyze the energy, intensity, and dispersion of the plasmon resonances arising in these hybrid interfaces.We find significant magnification induced by the molecular adsorbates of selected maxima in the loss function of MoS 2 , which is accompanied by minor variations in terms of energy and q-dependent dispersion.By comparing the results obtained for the interfaces with those of their individual constituents, we discuss the conditions under which the above-mentioned effects occur.These results provide insight into the interactions between TMDCs and their adsorbates complementary to the existing knowledge mainly based on electronic and optical spectroscopy.Moreover, the identified enhancement of the plasmon resonances of the TDMC suggests using the loss function as a meaningful observable to detect the presence of physisorbed molecules thereon.

Pyrene and Tetracene Physisorbed on Monolayer MoS 2
In this study, we consider two prototypical hybrid inorganic/organic interfaces formed by monolayer MoS 2 decorated with either pyrene or tetracene molecules adsorbed on its basal plane.The choice of these two compounds is suggested on their similar composition (both include only C and H atoms arranged in four phenyl rings), identical symmetry (D 2h point group), but different shapes.Tetracene is a member of the oligoacene family and is characterized by an anisotropic geometry.7,52,53 These compounds exhibit a weak coupling with MoS 2 as extensively discussed in previous work specifically dedicated to this aspect.38 In particular, the band structure and the density of states of the TMDC are negligibly affected by the presence of the physisorbed molecule and, apart from hybridization effects that are ruled by specific conditions, 37 the electronic structure of the interface is essentially a superposition of the features of its constituents.[37][38][39]45,54 For this reason, in optical absorption, specific transitions within the molecular frontier orbitals can be targeted, e.g., by a laser pulse.39 In order to explore the impact of the molecular orientation on the loss function of the corresponding interfaces with MoS 2 , we consider the four different configurations shown in Figure 1. Rotations wth steps of 30 • are considered, ranging from 0 • , corresponding to the short molecular axis parallel to the x-direction marked by a red arrow in Figure 1, to the orthogonal configuration 90 • , in which the long molecular axis is aligned with x.Due to the symmetry of both molecules and of the underlying TMDC, rotations of 120 • , 150 • , and 180 • are equivalent to the geometries at 60 • , 30 • , and 0 • , respectively.
To accommodate pyrene and tetracene on top of a single MoS 2 layer, we simulated the TMDC in a 4 × 4 hexagonal supercell with lattice parameter a = 4 × 3.18 Å = 12.72 Å.A vacuum layer of 20 Å is included in the out-of-plane direction z to decouple MoS 2 from its replicas.In the relaxed geometries, the vertical distance between pyrene (tetracene) and the underlying TMDC is 3.3 Å (3.4 Å), in agreement with previous studies on the same or on similar systems. 34,37,38,45In the resulting configurations, both molecules form a dense monolayer structure on top of the semiconductor with the spacing between the molecules and their in-plane neighbors depending on their orientation.In the case of pyrene, the separation from its nearest replica along x and y ranges from 5.9 Å and 5.For tetracene, differences among the various orientations are more pronounced due to the anisotropy of this compound.When the molecule is aligned with its short axis parallel to x (0 • ), the distance from its closest replicas in the x and y directions are 7.7 Å and 3.0 Å, respectively.On the other hand, in the perpendicular configuration (90 • ), the relaxed molecules do not lie perfectly flat on the substrate but their opposite ends slightly overlap with each other due to their very short separation (2.1 Å) along their long axes; along the short axes, instead, the distance between nearest replicas is 6.2 Å.We checked that increasing the spacing among tetracene molecules on MoS 2 such that they lay flat on the substrate does not change the results presented below.For an angle of 30 • , the separation along x (y) is equal to 7.2 Å (2.2 Å).At 60 • , the distance from the neighboring replica is 3.0 Å in both x and y directions.
It is worth stressing that the systems modeled with the procedure described above are not meant to represent realistic interfaces.First of all, to the best of our knowledge, there is no evidence that small molecules such as pyrene and tetracene can be adsorbed on TMDCs in a stable manner: only larger acenes like pentacene and extended rylenes such as terrylene have been demonstrated to form stable interfaces with TMDCs. 46,53,55Second, in realistic samples, intrinsic effects such as the density of the molecules on the substrate, the morphology of their clusters, and the thickness of their layers, as well as extrinsic factors such as temperature, pressure, and surface roughness play a decisive role in determining the characteristics of the interface.All these aspects should be carefully addressed for a reliable comparison with experiments but they go beyond the scope of the present work.

Computational Methods
The results presented in this work are obtained in the framework of density functional theory 56 and its time-dependent extension. 57Ground-state properties are calculated by solving the Kohn-Sham (KS) equations, 58 while EELS spectra are computed in linear response using the Lanczos algorithm. 59This approach is widely established in the community and has been applied to various classes of materials including elemental crystals, 60 binary compounds, 61 and interfaces. 62The key output quantity of these calculations is the loss function, defined as L(q, ω) = −Im ε −1 (q, ω), where ε is the macroscopic dielectric function of the material evaluated from its polarizability χ.The latter quantity represents the charge-density response function calculated from the solutions of the KS equations including the adopted approximation for the exchange-correlation functional.For further details on this approach, we redirect interested readers to a specialized review. 63The dispersion of the loss function is simulated considering non-zero values of transferred momentum q in the in-plane direction Γ-M, where M corresponds to the mid-point at the edge of the two-dimensional hexagonal Brillouin zone according to the usual convention. 64Assuming the direction of momentum transfer along the x-axis, only the corresponding component of the vector q (q x ) is varied.Four values of q ranging from 0.04 (2π/a), approaching the optical limit at q → 0, to 0.52 (2π/a) are considered.This range of momentum transfer was chosen based on preliminary results on an isolated MoS 2 monolayer, indicating that above q = 0.52 (2π/a) the features of the loss function in this material are strongly smeared and, hence, hardly recognizable.
All calculations are performed with Quantum ESPRESSO 65 adopting the SG15 Optimized Norm-Conserving Vanderbilt pseudopotentials 66 and a plane-wave basis set with kinetic energy and charge-density cutoff of 60 Ry and 300 Ry, respectively.The Perdew-Burke-Ernzerhof 67 functional is employed to approximate the exchange-correlation potential supplemented by the Tkatchenko-Scheffler scheme 68 to account for pairwise vdW interactions between molecules and substrate.The Brillouin zone of the hybrid interface and of the isolated TMDC simulated in the same supercell shown in Figure 1 is sampled by a 2 × 2 × 1 k-mesh.The loss function of the freestanding molecules is calculated for consistency in the same 4 × 4 supercell and with the moieties in the same arrangement formed in each heterostructure according to the rotation angle with respect to x.In these calculations, a denser 6 × 6 × 1 k-grid is adopted to better resolve the spectral features of the molecules.The considered hybrid interfaces are optimized with the quasi-Newtonian Broyden-Fletcher-Goldfarb-Shanno algorithm [69][70][71][72] with force and energy thresholds of 10 −3 Ry/bohr and 10 −4 Ry, respectively.The convergence of the EELS spectra is obtained with 500 Lanczos coefficients in the underlying algorithm, which are effectively extrapolated up to 40000 in post-processing.

Results and Discussion
Loss Function of Pyrene@MoS 2 We start our analysis from the loss functions of the hybrid interface pyrene@MoS 2 , see Fig- ure 2. For comparison, we examine in parallel the results obtained for the freestanding molecular layer in the same arrangement as in the heterostructures (Figure 2a) and the pristine TMDC without adsorbates (Figure 2b, dashed curves).This strategy is most appropriate for the analysis of the following results, given the broad energy range spanned by the calculated EELS spectra and the non-negligible influence of momentum transfer, which cannot be appropriately captured by standard electronic-structure calculations.
The EELS spectrum of pyrene is characterized by two main peaks at about 7 eV and 17 eV, labeled P 1 and P 2 , respectively.Energy and relative intensity of these maxima are in agreement with experimental data collected for pyrene in vapor phase, 73,74 which ascribe the former to the manifold of π-π * transitions 75,76 and the latter to σ-σ * transitions. 76The characteristics of the peaks do not vary significantly either with increasing values of q or upon rotation of the molecules.However, examining the results in more detail, one notices that the lowest-energy maximum becomes sharper and slightly red-shifted as the short molecular axis forms an angle of 90 • with respect to the x direction (see Figure 2a).This is due to the fact that depending on the orientation of the molecule, excitations with orthogonal polarization contribute to the peaks in the EELS.The results obtained at 0 • and 90 • can be compared with polarization-resolved EELS measurements performed on gaseous pyrene. 77ke our findings, the experimental data show a slight increase in the relative intensity of the first resonance when the molecule has its long axis aligned with x.
In the EELS of the pyrene@MoS 2 interface (solid curves in Figure 2b), we identify the π-resonance of MoS 2 around 8 eV 13,14 (dashed curves in Figure 2b), which is clearly visible also for the interface.At 14 eV, another sharp peak appears in the loss function of the TMDC monolayer followed by a shoulder at approximately 16 eV: these features belong to the π + σ band. 13Upon increasing momentum transfer, the main variation in the spectrum of MoS 2 is the intensity redistribution between these two maxima.For q = 0.36 (2π/a), the two features have almost equivalent strength while for larger values of q the higherenergy one becomes more intense (see dashed curves in Figure 2b).The effects of pyrene physisorption manifest themselves mostly in the region 12-20 eV, which is highlighted in gray in Figure 2b.The π-resonance is negligibly influenced by the presence of the molecule Figure 2: Electron energy loss spectra at different values of transferred momentum q of a) freestanding pyrene, b) pristine MoS 2 (dashed curves), and pyrene@MoS 2 (solid curves).The gray area in panel b) highlights the energy range in which the most significant changes to the loss function of MoS 2 occur due to molecular physisorption.The spectra computed at increasing values of q are offset for better visibility.regardless of its orientation.On the other hand, the π+σ band is largely affected by adsorbed pyrene.At q → 0, the relative spectral weight of the two maxima is reversed compared to the result obtained for the isolated TMDC (compare solid and dashed curves in Figure 2b).
A blue shift of ∼1-2 eV is additionally noticed for both maxima, as expected in light of their plasmonic nature. 14The second peak in the π + σ band remains more intense than the first one even at increasing transferred momentum, such that the loss function computed for the hybrid interface at q = 0.52 (2π/a) resembles quite closely the one obtained for MoS 2 with the same momentum transfer.The only visible difference is again the blue shift of the second resonance anticipating the dispersion discussed in detail below.The impact of pyrene orientation on the EELS is very moderate, consisting essentially of a slight, relative increase in the strength of the peak at 19 eV as the molecule approaches an angle of 90 • with respect to the x axis (see Figure 2b).

Loss Function of Tetracene@MoS 2
We now turn to the analysis of the loss function calculated for the tetracene@MoS 2 interface, see Figure 3.Following the same pattern adopted above for pyrene@MoS 2 , we inspect the spectra of the isolated components as a basis to understand the behavior obtained for the hybrid system.The q → 0 EELS spectrum of the freestanding tetracene layer at 0 • (short molecular axis parallel to x, see Figure 1b) is characterized by two maxima at about 8 eV (P ′ 1 ) and 17 eV (P ′ 2 ), see Figure 3a.P ′ 1 corresponds to an optical excitation polarized along the short axis of tetracene that is visible also in its absorption cross section. 76Notice that this is not the lowest-energy excitation of the tetracene molecule, which is also polarized along the short axis but appears at lower energy, around 2 eV. 78,79The overall similarity with the loss functions of pyrene (Figure 2a) is due to the common features exhibited by all carbon-based networks 80,81 including graphene. 12However, in contrast to pyrene and as a consequence of its more pronounced structural anisotropy, the EELS of tetracene is very sensitive to the orientation of the molecule with respect to the direction of transferred momentum.When the molecule is oriented with its long axis parallel to x, the loss function is dominated by a very sharp resonance at about 5 eV and by a broader but still pronounced maximum at ∼16 eV.The former corresponds to the second bright excitation in the spectrum of tetracene polarized along its long molecular axis. 79As mentioned, this is not the lowestenergy transition in this molecule, which is instead polarized along the short axis, as in all oligoacenes. 82,83At intermediate orientations of tetracene, the q → 0 EELS contains a combination of the signatures dominating the signals at 0 • and 90 • .At 60 • , the sharp resonance close to 5 eV is still clearly evident, although less intense than at 90 • , while the second maximum is broader and red-shifted.Finally, at 30 • , the two peaks are significantly smeared out but the maxima are energetically very close to P ′ 1 and P ′ 2 at 0 • .Notably, the sharp resonance at ∼5 eV dominating the EELS of tetracene oriented with its long axis parallel to x is detectable experimentally 73 like the weaker peak above 15 eV.The main features in the loss function of tetracene in all considered orientations are generally preserved in energy and intensity independently of q (see Figure 3a).The only visible exception is at 90 • and to a lesser extent at 60 • , where the strength of the first resonance decreases with increasing momentum transfer.Examining now the EELS spectrum of the tetracene@MoS 2 interface (Figure 3b), we notice an overall similarity with the loss function of pyrene@MoS 2 .The orientation of the molecule and the magnitude of q have little influence on the main spectral features.The lowenergy part of the EELS is dominated by the π resonance of MoS 2 .Even when the long axis of the molecule is aligned along x (90 • ), the relative intensity of the first peak increases only slightly with respect to the π resonance in the isolated TMDC.Only a very careful inspection of Figure 3b and Figure 2b reveals that this enhancement is larger in the presence of tetracene than of pyrene.On the other hand, the variations induced by the adsorbed molecule on the π + σ resonance are even more dramatic than in the spectrum of pyrene@MoS 2 , especially for 60 • and 90 • .In these cases, the relative intensity of the peak at ∼19 eV is considerably magnified compared to the corresponding feature in the EELS of isolated MoS 2 .Notably, the higher intensity of this maximum in the loss function of the hybrid interface is clearly visible also at large values of q, such that the resemblance with the spectrum of the pristine monolayer is much less pronounced than in EELS of tetracene@MoS 2 in the region 15-20 eV highlighted in gray in Figure 3b.

Energy Dispersion of the Loss Function
We conclude our analysis by discussing the energy dispersion of the loss function, which can be carried out most conveniently by plotting the EELS as a function of energy and momentum simultaneously.The graphs reported in Figure 4 contain the same information shown in Figures 2 and 3 but they offer a clearer visualization of the EELS dispersion in the hybrid heterostructures compared to their freestanding constituents.The π resonance dominating the loss function of the isolated MoS 2 is clearly visible in Figure 4a, where the decreasing intensity of this feature at increasing momentum transfer is apparent.In contrast, the π + σ band, which is extended over an energy range of about 8 eV, exhibits a positive dispersion, especially at its boundaries at 12 and 20 eV in the spectrum at q → 0 (cyan curves in Figure 4a).Remarkably, other stronger maxima that are visible at 12 and 20 eV in the optical limit, are dispersive, too (light green in Figure 4a).However, their increase in energy as a function of q is not as steep as for the above-mentioned lateral peaks.A similar trend is exhibited also by the intense feature centered at 17 eV.On the other hand, the strongest maximum at 14 eV is almost non-dispersive: at increasing q, only its intensity decreases, as discussed above, while its energy remains almost constant.
Finally, we inspect the EELS dispersion, which can be best appreciated in the color plots shown in Figure 4. We start from the freestanding molecular layers, see Figure 4b and d for pyrene and tetracene, respectively.In the case of pyrene, the two maxima, P 1 and P 2 , appear as dispersionless features, independent of the orientation of the moieties.The intensity of both spectral features is only moderately changing with respect to the rotation angle: the strongest signal is obtained when the long molecular axis is parallel to x (90 • ), due to the larger oscillator strength of the corresponding electronic excitations along that direction. 75,84Accordingly, the maximum at 90 • is slightly below in energy compared to the one at 0 • , as discussed with reference to Figure 2a.The situation is rather different in the case of tetracene, see Figure 4d, where the high anisotropy of this molecule leads to significantly different signals depending on its orientation with respect to the transferred momentum.For tetracene aligned with the short axis parallel to x (0 • ), two dispersionless features are seen at about 8 eV and 17 eV.A higher-energy maximum above 20 eV, which is visible as a shoulder in Figure 3b, can be noticed, too.At 30 • , only the resonance around 17 eV is visible, while the lower-energy one is too weak to be detected with the adopted color scale.At 60 • and 90 • , the sharp maximum at about 4.5 eV gives rise to an intense signal in the color plot, which is strongest when the long molecular axis is aligned along x (see Figure 4d, middle panels).Due to the localized character of this electronic excitation, the corresponding maximum in the loss function is dispersionless.Conversely, the feature at 17 eV exhibits a hint of a positive dispersion, which is most evident at 90 • but visible also at 60 • .We speculate that this behavior is due to the one-dimensional, carbon-conjugated lattice effectively generated by the molecule and its close-by replicas, where the electronic charge can delocalize itself.The displayed feature is compatible with the plasmonic behavior of a bilayer structure, 13,85 suggesting that the molecular layer effectively increases the thickness of the system compared to MoS 2 alone.
With the understanding gained of the q-dependent loss function of the individual building blocks, we finally analyze the results obtained for the hybrid interfaces.The EELS of pyrene@MoS 2 as a function of q is dominated by two main features (Figure 4c).The one centered at approximately 8 eV corresponds to the π resonance, which is dispersionless and exhibits a decreasing intensity at increasing values of q as in the isolated TMDC.However, the intensity of the π band at q → 0 is lower in the hybrid system compared to MoS 2 alone (compare Figure 4a and c).We speculate that the presence of physisorbed pyrene, which features a maximum in the EELS in the close vicinity of the π resonance of the TMDC (Figure 4b) partially suppresses the intensity of this resonance.The fact that the strength of the π band in the interface with the molecules at 90 • is slightly larger toward low values of q compared to the system at 0 • reinforces this hypothesis, given the corresponding increase in intensity of P 1 seen in the corresponding EELS plots (in Figure 4b).
The π + σ band is even more dramatically affected by the presence of the organic adsorbates.The influence of the molecules manifests itself in two ways.On the one hand, the relative intensity of the two main maxima at 14 and 19 eV is reverted and this effect is more pronounced when the molecules are aligned with their long axes parallel to the direction of the transferred momentum (90 • ).Notably, both features remain essentially dispersionless as in the spectrum of MoS 2 alone (see Figure 4a).On the other hand, there is a slight blue shift accompanied by a broadening of the entire π + σ resonance, especially toward higher energies.This behavior can be interpreted again as a consequence of the effective bilayer nature of the system 13,85 owing to the presence of the molecular monolayer on top of MoS 2 .
The dispersion relation of the loss function of the tetracene@MoS 2 interface (Figure 4e) exhibits similar features as those of pyrene@MoS 2 : The π resonance is dispersionless and undergoes a significant decrease in intensity at increasing values of q, while the π + σ band, dominated by two intense maxima at 14 and 19 eV, exhibit a clear positive dispersion, especially at its extrema.This being said some noteworthy differences emerge due to the more pronounced molecular anisotropy of tetracene.The increase in the intensity of the second resonance in the π + σ band (at ∼19 eV) is significantly more pronounced than in the hybrid interface between MoS 2 and pyrene.We can relate this behavior to the substantial magnitude gain of P ′ 2 when the molecule is at 90 • rather than at 0 • (Figure 4d).On the other hand, the very strong maximum exhibited by the EELS of tetracene at 90 • at about 4 eV does not participate in the EELS of the hybrid interface: there is no signal at that energy in Figure 4e.

Conclusions
In summary, we have investigated the q-dependent loss function of two prototypical hybrid interfaces formed by the carbon-conjugated molecules pyrene and tetracene physisorbed on single-layer MoS 2 .To assess the role of the molecular orientation with respect to the momentum transfer, we have considered four different configurations with the organic components rotated in steps of 30 • .The loss function of the hybrid systems is dominated by the π and π + σ resonances characterizing the response of the isolated TMDC monolayer.While the π band, around 7-8 eV in both systems, is almost unaffected by the presence of the molecule, the intensity and the energy of the π + σ resonance are largely influenced by the adsorbates.
In particular, we see a magnification of the sub-peaks in the latter in comparison to the spectrum of the pristine TMDC.This effect is more evident at low values of transferred momentum, although they are visible also at high q.The larger anisotropy of tetracene compared to pyrene further enhances this behavior when the molecule is aligned with its long axis parallel to the incoming momentum.The dispersion of the loss function provides additional information about the nature of identified features.While the π resonance is dispersionless and its strength decays with increasing q, in agreement with the result obtained for the isolated MoS 2 monolayer, the π + σ band is characterized by a more complex behavior.The weaker maxima at its extrema exhibit a positive dispersion resembling the trend of multilayer structures. 85Moreover, the increasing intensity of these features in the presence of the molecule is a signature of the coupling between the organic and inorganic constituents of the interface.
In conclusion, our results reveal in a proof-of-principle fashion that the physisorption of conjugated molecules enhances selected resonances in the q-dependent loss function of TMDCs, due to the energetic proximity of corresponding maxima in the isolated compounds.This magnification is a signal of the electronic interactions between the constituents which can be exploited to detect the presence of organic adsorbates on the inorganic substrate.
The dependence on the orientation of the molecules with respect to the direction of the transferred momentum can be further used to identify the structural arrangement of the adsorbates.Future EELS experiments on such systems will be very helpful to confirm our results or to stimulate new theoretical investigations.In this case, a detailed analysis of the morphology of the sample and of the effects of temperature will be necessary to ensure a reliable comparison with the experimental data.

Figure 1 :
Figure 1: Top view of the optimized geometries of a) pyrene and b) tetracene adsorbed on a 4 × 4 supercell of MoS 2 monolayer with different orientations.The x-axis, marked by the red arrow, corresponds to the direction of transferred momentum.

Figure 3 :
Figure 3: Electron energy loss spectra at different values of transferred momentum q of a) freestanding tetracene, b) isolated MoS 2 (dashed curves), and tetracene@MoS 2 (solid curves).The gray area in panel b) highlights the energy range in which the most significant changes to the loss function of MoS 2 occur due to the physisorbed molecules.The spectra computed at increasing values of q are offset for better visibility.

Figure 4 :
Figure 4: Energy dispersion of the loss function (LF) of a) the isolated MoS 2 monolayer, b) freestanding pyrene, c) pyrene@MoS 2 , d) freestanding tetracene, and e) tetracene@MoS 2 .The molecular orientations indicated in panels b) and d) hold also for panels c) and e).