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Register a new userSuperposition of intra- and inter-layer excitons in twistronic MoSe$_2$/WSe$_2$ bilayers probed by resonant Raman scattering
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Hybridisation of electronic bands of two-dimensional materials, assembled into twistronic heterostructures, enables one to tune their optoelectronic properties by selecting conditions for resonant interlayer hybridisation. Resonant interlayer hybridisation qualitatively modifies the excitons in such heterostructures, transforming these optically active modes into superposition states of interlayer and intralayer excitons. For MoSe$_2$/WSe$_2$ heterostructures, strong hybridization occurs between the holes in the spin-split valence band of WSe$_2$ and in the top valence band of MoSe$_2$, especially when both are bound to the same electron in the lowest conduction band of WSe$_2$. Here we use resonance Raman scattering to provide direct evidence for the hybridisation of excitons in twistronic MoSe$_2$/WSe$_2$ structures, by observing scattering of specific excitons by phonons in both WSe$_2$ and MoSe$_2$. We also demonstrate that resonance Raman scattering spectroscopy opens up a wide range of possibilities for quantifying the layer composition of the superposition states of the exciton and the interlayer hybridisation parameters in heterostructures of two-dimensional materials.
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Accurately described excitonic properties of transition metal dichalcogenide heterobilayers (HBLs) are crucial to comprehend the optical response and the charge carrier dynamics of them. Excitons in multilayer systems posses inter or intralayer character whose spectral positions depend on their binding energy and the band alignment of the constituent single-layers. In this study, we report the electronic structure and the absorption spectra of MoS$_2$/WS$_2$ and MoSe$_2$/WSe$_2$ HBLs from first-principles calculations. We explore the spectral positions, binding energies and the origins of inter and intralayer excitons and compare our results with experimental observations. The absorption spectra of the systems are obtained by solving the Bethe-Salpeter equation on top of a G$_0$W$_0$ calculation which corrects the independent particle eigenvalues obtained from density functional theory calculations. Our calculations reveal that the lowest energy exciton in both HBLs possesses interlayer character which is decisive regarding their possible device applications. Due to the spatially separated nature of the charge carriers, the binding energy of inter-layer excitons might be expected to be considerably smaller than that of intra-layer ones. However, according to our calculations the binding energy of lowest energy interlayer excitons is only $sim$ 20% lower due to the weaker screening of the Coulomb interaction between layers of the HBLs. Therefore, it can be deduced that the spectral positions of the interlayer excitons with respect to intralayer ones are mostly determined by the band offset of the constituent single-layers. By comparing oscillator strengths and thermal occupation factors, we show that in luminescence at low temperature, the interlayer exciton peak becomes dominant, while in absorption it is almost invisible.
Twistronic van der Waals heterostrutures offer exciting opportunities for engineering optoelectronic properties of nanomaterials. Here, we use multiscale modeling to study trapping of charge carriers and excitons by ferroelectric polarisation and piezoelectric charges by domain structures in twistronic WX$_2$/MoX$_2$ bilayers (X=S,Se). For almost aligned 2H-type bilayers, we find that holes and electrons are trapped in the opposite -- WMo and XX (tungsten over molybdenum {it versus} overlaying chalcogens) -- corners of the honeycomb domain wall network, swapping their position at a twist angle $0.2^{circ}$, with XX corners providing $30$,meV deep traps for the interlayer excitons for all angles. In 3R-type bilayers, both electrons and holes are trapped in triangular 3R stacking domains, where WX$_2$ chalcogens set over MoX$_2$ molybdenums, which act as $130$,meV deep quantum boxes for interlayer excitons for twist angles $lesssim 1^{circ}$, for larger angles shifting towards domain wall network XX stacking sites.
We present a high-resolution resonance Raman study of hBN encapsulated MoSe$_2$ and WSe$_2$ monolayers at 4 K using excitation energies from 1.6 eV to 2.25 eV. We report resonances with the WSe$_2$ A2s and MoSe$_2$ A2s and B2s excited Rydberg states despite their low oscillator strength. When resonant with the 2s states we identify new Raman peaks which are associated with intravalley scattering between different Rydberg states via optical phonons. By calibrating the Raman scattering efficiency and separately constraining the electric dipole matrix elements, we reveal that the scattering rates for k=0 optical phonons are comparable for both 1s and 2s states despite differences in the envelope functions. We also observe multiple new dispersive Raman peaks including a peak at the WSe$_2$ A2s resonance that demonstrates non-linear dispersion and peak-splitting behavior that suggests that the dispersion relations for dark excitonic states at energies near the 2s state are extremely complex.
We investigate WSe$_2$-MoSe$_2$ heterobilayers with different twist angles $theta pm delta$ between the two layers, by low-frequency Raman scattering. In sufficiently aligned samples with $theta=0^circ$, or $theta=60^circ$, and $delta lesssim 3^circ$, we observe an interlayer shear mode (ISM), which is a clear sign of a commensurate bilayer structure, i.e., the layers must undergo an atomic reconstruction to form R-type or H-type stacking orders. We find slightly different ISM energies of about 18~cm$^{-1}$ and 17~cm$^{-1}$ for H-type and R-type reconstructions, respectively, independent of the exact value of $thetapm delta$. Our findings are corroborated by the fact that the ISM is not observed in samples with twist angles, which deviate by $delta > 3^circ$ from $0^circ$ or $60^circ$. This is expected, since in such incommensurate structures, with the possibility of Moir$acute{text{e}}$-lattice formation, there is no restoring force for an ISM. Furthermore, we observe the ISM even in sufficiently aligned heterobilayers, which are encapsulated in hexagonal Boron nitride. This is particularly relevant for the characterization of high-quality heterostructure devices.
Based on emph{ab initio} theoretical calculations of the optical spectra of vertical heterostructures of MoSe$_2$ (or MoS$_2$) and WSe$_2$ sheets, we reveal two spin-orbit-split Rydberg series of excitonic states below the textsl{A} excitons of MoSe$_2$ and WSe$_2$ with a significant binding energy on the order of 250,meV for the first excitons in the series. At the same time, we predict crystalographically aligned MoSe$_2$/WSe$_2$ heterostructures to exhibit an indirect fundamental band gap. Due to the type-II nature of the MoSe$_2$/WSe$_2$ heterostructure, the indirect transition and the exciton Rydberg series corresponding to a direct transition exhibit a distinct interlayer nature with spatial charge separation of the coupled electrons and holes. The experimentally observed long-lived states in photoluminescence spectra of MoX$_2$/WY$_2$ heterostructure are attributed to such interlayer exciton states. Our calculations further suggest an effect of stacking order on the peak energy of the interlayer excitons and their oscillation strengths.
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