Interlayer excitonic states in $\mathrm{Mo}{\mathrm{Se}}_2/\mathrm{Mo}{\mathrm{S}}_2$ van der Waals heterostructures

In the present work, we report different interlayer excitonic states of an aligned $\mathrm{Mo}{\mathrm{Se}}_2/\mathrm{Mo}{\mathrm{S}}_2$ incommensurate van der Waals (vdW) heterostructure (HS). The HS was fabricated by stacking chemical vapor deposited monolayers, and it was studied using photoluminescence (PL) measurements. We observed the emergence of two low-energy peaks in the PL spectrum of the HS measured at 100 K, which were absent in the constituent monolayers. The orbital resolved electronic band structure and the optical absorption considering the electron-hole interaction for these HSs were calculated using first-principles density functional theory simulations, which showed energy band hybridization and the presence of interlayer excitons (ILEs). Based on these observations, the peak at $\sim 1.57$ eV was assigned to a momentum direct ILE, while the other peak at $\sim 1.35$ eV showed feeble emission intensity and was assigned to a momentum indirect ILE. The emergence of both of these excitonic peaks in the HS PL spectrum can be attributed to the formation of a spatially periodic moiré potential at a nanometer length scale resulting in hybridization. Our results can help to understand the physics of ILEs and to engineer vdW HSs for efficient optoelectronic devices.

Figure 1

(a) Schematic of an aligned $\mathrm{Mo}{\mathrm{Se}}_2/\mathrm{Mo}{\mathrm{S}}_2$ HS, i.e., stacked at $0^{\circ }$ showing the moiré pattern due to the incommensurate nature of the HS with a lattice mismatch $\delta \sim 4.4\%$. (b) Optical image of the fabricated HS stacked at $0^{\circ }$ showing the constituent monolayers $\mathrm{Mo}{\mathrm{Se}}_2$ and $\mathrm{Mo}{\mathrm{S}}_2$ marked in blue and red triangles, respectively. (c) Raman spectra of 1L-$\mathrm{Mo}{\mathrm{Se}}_2$ (blue), 1L-$\mathrm{Mo}{\mathrm{S}}_2$ (red), and $\mathrm{Mo}{\mathrm{Se}}_2/\mathrm{Mo}{\mathrm{S}}_2$ HS (black) obtained at RT using 2.54 eV excitation. For clarity, the Raman spectrum of $\mathrm{Mo}{\mathrm{Se}}_2$ is multiplied by a factor of 0.1, and that of HS is shifted up. The dominant characteristic Raman modes of 1L-$\mathrm{Mo}{\mathrm{Se}}_2$ ($A_{1g}, E_{2g}$, and second-order longitudinal acoustic mode $L$) and 1L-$\mathrm{Mo}{\mathrm{S}}_2$ ($E_{2g}$ and $A_{1g}$) are marked with vertical dashed lines. (d) PL spectra of 1L-$\mathrm{Mo}{\mathrm{Se}}_2$, 1L-$\mathrm{Mo}{\mathrm{S}}_2$, and the fabricated HS, normalized with respect to 1L-$\mathrm{Mo}{\mathrm{S}}_2$ obtained at RT using 136 $\mu \mathrm{W}$, 2.54 eV excitation. For clarity, the PL spectrum of HS is multiplied by a factor of 4. The dominant excitonic emission peaks are marked with vertical dashed lines. (e) The deconvolved RT PL spectrum of the fabricated HS into the constituent peaks corresponding to neutral excitons marked as $X_A$ and $X_B$ and the trion marked as $T$ of the respective monolayers.

Figure 2

(a) PL spectra of 1L-$\mathrm{Mo}{\mathrm{Se}}_2$, 1L-$\mathrm{Mo}{\mathrm{S}}_2$, and the fabricated HS, obtained at 100 K using 136 $\mu \mathrm{W}$, 2.54 eV excitation, normalized with respect to that of 1L-$\mathrm{Mo}{\mathrm{S}}_2$. The dominant excitonic emission peaks are marked with vertical dashed lines. The region encircled around 1.5 eV is shown in the inset figure marked as $I{X}_1$, magnified by a factor of 10. The peak shown as a dotted curve in the inset figure is the fit to the corresponding emission. (b) The deconvolved PL spectrum of the fabricated HS shown in (a) into the constituent peaks corresponding to intralayer excitons marked as $X_A$ and $X_B$ and trion marked as $T$ of the respective monolayers and the ILE marked as $I{X}_1$. The inset figure shows the PL spectrum with intensity on a log scale, obtained using 240 $\mu \mathrm{W}$, showing $I{X}_1$ along with another peak marked as $I{X}_2$ observed at $\sim 1.35$ eV. (c) Excitation power ($P_{\text{ex}}$) dependence of $I{X}_1$ emission intensity ($I$) along with the best fit of $I\propto P_{\text{ex}}^{\alpha }$ for $\alpha \sim 1.4$ shown as a black curve. (d) The intralayer trion contribution to the HS PL spectrum, i.e., the $T/X_A$ intensity ratio of the indicated layers for three different $P_{\text{ex}}$.

Figure 3

(a) Schematic of $II{I}^A$ stacked HS showing the unit cell marked by green lines. (b) The orbital-resolved band structure of $II{I}^A$ stacking, where the red and blue bands are purely due to $\mathrm{Mo}{\mathrm{S}}_2$ and $\mathrm{Mo}{\mathrm{Se}}_2$ orbitals, respectively. The green valence band $\mathrm{\Gamma }$-valley indicates equal contributions from both the layers. (c) Effect of the lattice constant on the lowest energy $K-\mathrm{\Gamma }$, i.e., transition from $C_1$ to ${\mathrm{\Gamma }}_1^h$ and $K-K$, i.e., transition from $C_1$ to $V_1$ as marked in (b). The encircled region corresponds to $C_1-{\mathrm{\Gamma }}_1^h$ as the dominant transition. (d) Optical absorption spectra of 1L-$\mathrm{Mo}{\mathrm{S}}_2$ shown in red, 1L-$\mathrm{Mo}{\mathrm{Se}}_2$ shown in blue, and $II{I}^A$ stacked HS shown by a black curve calculated using the BSE. (e) The oscillator strength of the optical transitions in a $II{I}^A$ stacked HS. The region encircled around 1.5 eV in the inset figure, labeled as Interlayer, shows the oscillator strength of optical transitions corresponding to the momentum-direct ILEs. (f) Schematic of the energy band diagram of 1L-$\mathrm{Mo}{\mathrm{Se}}_2$ (left), 1L-$\mathrm{Mo}{\mathrm{S}}_2$ (right), and the maximally hybridized $II{I}^A$ stacked region of HS (center). The levels marked as ${\mathrm{\Gamma }}_1^h$ and ${\mathrm{\Gamma }}_2^h$ are the hybridized valence-band $\mathrm{\Gamma }$-valley, and $K^h$ is the modified valence-band $K$-valley of $\mathrm{Mo}{\mathrm{Se}}_2$.