Modulation of New Excitons in Transition Metal Dichalcogenide‐Perovskite Oxide System

Abstract The exciton, a quasi‐particle that creates a bound state of an electron and a hole, is typically found in semiconductors. It has attracted major attention in the context of both fundamental science and practical applications. Transition metal dichalcogenides (TMDs) are a new class of 2D materials that include direct band‐gap semiconductors with strong spin–orbit coupling and many‐body interactions. Manipulating new excitons in semiconducting TMDs could generate a novel means of application in nanodevices. Here, the observation of high‐energy excitonic peaks in the monolayer‐MoS2 on a SrTiO3 heterointerface generated by a new complex mechanism is reported, based on a comprehensive study that comprises temperature‐dependent optical spectroscopies and first‐principles calculations. The appearance of these excitons is attributed to the change in many‐body interactions that occurs alongside the interfacial orbital hybridization and spin–orbit coupling brought about by the excitonic effect propagated from the substrate. This has further led to the formation of a Fermi‐surface feature at the interface. The results provide an atomic‐scale understanding of the heterointerface between monolayer‐TMDs and perovskite oxide and highlight the importance of spin–orbit–charge–lattice coupling on the intrinsic properties of atomic‐layer heterostructures, which open up a way to manipulate the excitonic effects in monolayer TMDs via an interfacial system.


A new direction for interfacial effects: STO as a substrate
Firstly, from the perspective of the possible interaction between MoS 2 and potential substrates, the key reason STO is chosen as an ideal substrate because its band gap is only slightly higher than that of monolayer-MoS 2 . The comparable band gaps of MoS 2 and STO results in the presence of band overlap at the Fermi level of the MoS2/STO interface. The unique compatibility of these two materials can increase the possibility of interfacial hybridization. Such interaction between a 2D-material and an oxide substrate is absent from MoS 2 on other oxide substrates such as Al 2 O 3 , SiO 2 or even perovskites like the LaAlO 3 .
According to the DFT band alignment diagram (Fig. 2(f)), there is a great likelihood that the S-orbitals of the MoS 2 monolayer hybridized with Ti-orbitals of the STO substrate.
Hence, the STO substrate is treated to be TiO 2 -terminated (001)-STO to provide the means for greater interaction between the monolayer-MoS 2 and STO. Through our comprehensive experimental and computational studies, we demonstrate the presence of interfacial interactions that beyond that of van der Waals interaction. It shows that 2D-TMD have a strong interaction with a suitable TMO substrate where it has a specifically specified surface termination. Our current study opens a new perspective and creates novel opportunities in the study of other TMD/TMO heterostructures. Such interfacial hybridization can possibly affect other interesting phenomena such as superconductivity, ferromagnetic effects, etc in different heterostructure. Hence, the investigation of this interfacial phenomenon in our manuscript has wide interest such that the large scientific community working on heterointerfaces can benefit from our scientific motivation introduced here.
From the perspective of the excitonic properties in STO, we note that STO in its bulk form and recently, in heterostructure systems with other oxides, have shown exotic phenomena such as superconductivity, magnetisms, metal-insulator transitions and a twodimensional electron gas. It is worth mentioning that for more than 45 years, the existence of excitonic effects had been assumed to be absent [1] . It is only until recently resonant excitonic effects and strong electronic correlations were reported in SrTi 1- x Nb x O 3 family [2] . These excitonic effects can interact with a graphene layer through hybridizations at the interface. Many novel physical phenomena such as superconductivity, 2D electron gas, ferromagnetism, etc are reported to take place at the interfaces of perovskite oxides. Hence, a comprehensive experimental and theoretical study to investigate how the coupling between charge, lattice and orbital dynamics would result in the intriguing phenomena would be invaluable. Based on these studies, it is interesting that stacking monolayer-MoS 2 on STO substrates is expected to produce intriguing optical and electronic phenomena. These are the key motivations to revisit the fundamental understanding of heterointerfaces, particularly, between monolayer-MoS 2 and STO.
Spectroscopic ellipsometry measurements and absorption coefficient. We use a J. A. Woollam Co., Inc spectroscopic ellipsometer with photon energy of 0.6-4.5eV to measure the ellipsometry parameters Ψ (the ratio between the amplitude of p-and spolarized reflected light) and Δ (the phase difference between of p-and s-polarized reflected light) in a high vacuum chamber with a base pressure of 1×10 -9 mbar. The substrate layers (bulk SrTiO 3 or Al 2 O 3 ) are also measured under the same conditions. The absorption coefficient of MoS 2 monolayer was extracted from the parameters Ψ and Δ utilizing an air/MoS 2 /STO (or Al 2 O 3 ) multilayer model, where monolayer-MoS 2 consists of a homogeneously uniform medium [3,4] and a composite heterointerface component.
The Ψ and Δ defined as [5] where r p(s) is the reflectivity of p-(s-) polarized light. Using the Fresnel equations, the quantities could be defined as and Here n and θ represent the refractive index and angle of incident, respectively. The i and j represent the two materials. The complex dielectric function ε(ω) = ε 1 (ω) + iε 2 (ω) of media can be obtained using √ where ω is the photon frequency.

The absorption coefficient of media is obtained as
Here, k is the extinction coefficient (the imaginary part of the complex refractive index n) and λ is the light wavelength.
The reflectivity of MoS 2 film on substrate can be expressed as [6] , MoS 2 ). The differences in the optical dielectric function at room temperature and low temperature, ε 2 , are shown in Fig. S2(a,b) (the optical spectra are normalized to clearly show the difference). Figure S2(c) (main text Fig. 2(e)) shows that there is a Wannier-like exciton at ~3.8eV for the STO without MoS 2 . Comparing the STO signals with and without the MoS 2 in Figure S2a, we can clearly see that there is a stronger spectral feature at ~3.8eV for STO with MoS 2 compared to that of STO without MoS 2 . Fig. S2(b), at low temperature, shows two split features at ~3.6eV and ~3.8eV for STO with MoS 2 unlike STO without MoS 2. The stronger features in the former system (D and D' correspondingly) indicates they arise neither due to the reference bulk STO nor the freestanding MoS 2 . Instead, we can deduce that the additional features are attributed to interfacial interactions between MoS 2 and STO.
We conclude that the change in exciton at ~3.8eV is not a mere overlap of optical signals from monolayer-MoS 2 and STO substrate. Instead, it is an optical signature which indicates that the exciton arises due to the interaction at the heterointerface.
A further evidence that the exciton is not a mere overlap of optical signals is that the new exciton in the optical data of the MoS 2 /STO sample resulted in the onset of two optical peaks (at ~3.6 and ~3.8eV) at 77K, which can be attributed to the spin-orbit coupling in MoS 2 . In contrast, there is only one optical peak located at ~3.8eV for bulk STO. This further supports our claim that there is propagation of excitonic effects through the interface.

GW-BSE Calculations of MoS 2 on STO with Different configurations
To further substantiate that there is agreement between experiment and theory, we The most stable configuration for MoS 2 monolayer on STO (001) substrate is the interfacial structure with a maximized potential bonding. The most stable structure is shown in Figure S8(a), where most S atoms are located on the top of the Ti atoms, and the Mo atoms reside on the top O atoms at the STO surface. This stable monolayer-MoS 2 /STO structure gives us an additional excitonic peak at ~4 eV (see Figure S8(b)), this is once again due to the interfacial orbital hybridization as discussed in the main text.
A metal-stable interfacial configuration is shown in Figure S8(c), which has similar interfacial bonding configuration, but its adsorption energy is slightly higher (~60 meV) than that of the structure in Figure S8(a). Interestingly, with the GW-BSE calculation, this metal-stable structure also shows the high-energy excitonic peak (see Figure S8(d)).
This shows that the onset of the new exciton is attributed to the unique interfacial hybridization which is weakly related to how the TMDs placed on the STO. To extract the profiles of the excitonic signals of monolayer-MoS 2 from that of the thick STO substrate at each corresponding temperature, each set of PL data is normalized to the respective maximum of the MoS 2 /STO spectrum multiplied by a constant value to match the maximum intensity of the STO reference spectrum. The normalized spectrum is then extracted (by subtracting spectra with and without MoS 2 ) to visualize the excitonic peaks ( Figures S5 and S6).

High-Energy Excitons D and D' in high-energy photoluminescence spectra.
Note that as compared to the bulk STO reference PL spectrum, the signal-to-noise ratio of the MoS 2 /STO PL spectrum is relatively lower due to variation in the alignment of the MoS 2 /STO sample. This results in a seemingly stronger PL excitation source peak as compared to that of the STO substrate which requires an additional fitting peak to be accounted for. The PL spectral difference is then modelled using two Gaussian lineshapes -for both exciton peaks D and D'. The excitonic peaks at their respective temperatures are provided in Figure S4. They are consistently present in all investigated temperatures, suggesting that these are not experimental artefacts but real signals that arise. A further indication of the presence of these novel many-body phenomena as detected by spectroscopic ellipsometry.
Supplementary Figure S6(a) compares the normalized PL data between MoS 2 /STO and STO at 77K. The maximum of the MoS 2 /STO spectrum is normalized with the maximum intensity of the STO reference spectrum. Although both spectra are similar with a prominent excitonic signal that the STO substrate displays, marked differences are observed at the ~3.60eV (see figure inset) and ~3.80eV region. Besides, these spectral differences are consistently present with repeated measurements at different temperatures ( Figure S5). The spectral differences between monolayer-MoS 2 /STO and STO are studied by a fitting analysis using two Gaussian lineshapes as displayed in Figure S6 in a seemingly stronger PL excitation source peak as compared to that of the STO substrate which requires an additional fitting peak to be accounted for.

High-Energy Excitons D and D' in spectroscopic ellipsometry.
To elucidate additional further insights on how the excitonic transitions evolve with temperature, the section of the absorption spectra within energy range ~3.3-4.2 eV has been extracted and modelled using mixed Lorentzian-Gaussian lineshapes. Two oscillators D and D' each with a combination of Lorentzian (30%) and Gaussian (70%) components have been used to model the absorption spectra at temperatures between 77 and 350K.
Based on the temperature-dependence of the excitonic peak profiles, the binding energies of excitons D and D' can be elucidated. The absorption linewidth, , of each excitonic peaks can be described as the sum of its temperature-independent and temperaturedependent components as shown [7] ( ) Where Δv 0 represents the temperature-independent linewidth; v T denotes the attempted frequency for excitonic thermal dissociation, and E B is the exciton binding energy. The equation has been rearranged into the following form for the purpose of linear fitting: Where ln(ΔE-ΔE 0 ) is plotted as a function of 1/T. ΔE 0 is assumed to be ~78.11meV for exciton D and ~56.67meV D' based on the low-temperature linewidth. The linewidth at each temperature can be calculated based on the first-order derivative of the absorption peak and measuring between the peak and zero-crossing and then doubled to obtained the its full-width at half-maximum (FWHM) for each corresponding temperature [7] .
However, due to the overlapping of multiple features within the energy range and that the excitonic peaks become less distinct with rising temperature, it is not possible to elucidate the linewidth from the data using this technique. Hence, the temperature-dependent excitonic linewidths are instead estimated using the FWHM profiles of the Lorentzian-Gaussian lineshapes.
The natural logarithm of the excitonic transition linewidths of MoS 2 /STO are plotted in Figure S3 as functions of the inverse temperature. By fitting the data with Equation S9, it yields a binding energy of (13.66±1.64)meV for exciton D and (14.48±1.37)meV for exciton D'about an order of magnitude smaller than the low-energy excitons [8] .
The respective estimated binding energies are further verified by considering the temperature dependence of the spectral weights of exciton D and D' ( Figure S4). Note that there is a drastic increase in spectral weight in the ~ 200 K (~0.17meV) temperature regions for both the excitons. While there are minor spectral weight increases in the temperature range above and below, these drastic rises in spectral weight suggest the dissociation of excitons into their individual charged constituents above their respective binding energies. This results in the significant increase in charge carrier population above this temperature range.