Excitonic Landscape of Monolayer Transition-Metal Dichalcogenides: Experimental Discrepancies, Theoretical Advances, and Strain Dependence

TL;DR

This study addresses inconsistent reports of exciton binding energies and quasiparticle gaps in monolayer TMDs by combining high-precision GW-BSE calculations with a thorough review of ARPES, PL, and related experiments, including strain as a tunable parameter. The authors demonstrate that many-body corrections dramatically alter valley energetics at $ΔE^v_{KΓ}$ and $ΔE^c_{KΛ}$, yielding A-exciton energies in close agreement with optical measurements and SOC splittings consistent with experiment, while revealing how strain reorders direct and indirect excitons through valley-specific band-edge shifts. By computing both direct and multiple indirect excitons with $k$-resolved weights and introducing strain gauge factors, they quantify how biaxial strain can engineer exciton energies and transitions, including crossings between DX and IDX states. The work provides a coherent framework that reconciles literature discrepancies and establishes strain as a robust, predictive avenue for excited-state engineering in the family of monolayer TMDs, with implications for optoelectronics and valleytronics.

Abstract

Excitons in monolayer transition-metal dichalcogenides (TMDs) have garnered significant attention because of their large binding energies due to weakly screened Coulomb interaction, and direct bandgap at the K/K$^\prime$ point in the hexagonal Brillouin zone featuring spin-polarised bands due to spin-orbit coupling and lack of inversion symmetry. This makes them prospective for next-generation optoelectronic and quantum devices. However, despite the intense research activity, the reported values for exciton binding energies, quasiparticle gaps, and spectral features exhibit substantial variation across both experimental and theoretical studies. In this article, we present a comprehensive and critical assessment of the current understanding of excitonic properties in single-layer TMDs, integrating results from the angle-resolved photoemission spectroscopy (ARPES), photoluminescence (PL) measurements, and other experimental techniques with first-principles theoretical insights. Special emphasis is placed on the comparison and reconciliation of discrepancies observed across different experimental setups and sample qualities. Furthermore, we highlight our state-of-the-art GW-BSE calculations, which include both equilibrium and laterally strained systems, to systematically analyse the behaviour of direct and indirect excitons. By evaluating the effect of strain as a tunable control variable, we demonstrate its potential to engineer excitonic properties, supported by cross-validation against prior theoretical predictions and experimental findings. In doing so, we clarify the sources of discrepancies in the literature and offer a unified perspective on excited-state engineering strategies in two-dimensional TMDs.

Figures (5)

• Figure 1: The calculated PBE (dashed red lines) and G$_0$W$_0$ (blue symbols) band structure of (a) MoS$_2$, (b) MoSe$_2$, (c) WS$_2$, (d) WSe$_2$.
• Figure 2: Calculated PBE (dashed lines) and G$_{0}$W$_{0}$ (solid lines) band-gap transitions under biaxial strain for (a) MoS$_2$, (b) MoSe$_2$, (c) WS$_2$, and (d) WSe$_2$. The quantities $\Delta_{\mathrm{KK}}$, $\Delta^{v}_{\mathrm{K\Gamma}}$, and $\Delta^{c}_{\mathrm{K\Lambda}}$ denote, respectively, the strain-induced change in the direct band gap at K (red circles), the energy difference between the highest valence states at K and $\Gamma$ (blue squares), and the energy separation between the lowest conduction states at K and $\Lambda$ (black triangles). The gray shaded area represents the strain windows where the band gap is direct at K.
• Figure 3: Calculated excitonic weights of MoS$_2$ for (a) IDX$_{\mathrm{K}\Lambda}$ and (b) IDX$_{\mathrm{K}^{\prime}\Lambda}$ (see Table \ref{['table3']}), summed over all bands across the Brillouin zone (Eq. \ref{['eq3']}) and shown for every equivalent $\mathbf{Q}$-vector. The colour scales highlight the regions corresponding to the dominant electron-hole transitions for each chosen excitonic state and momentum.
• Figure 4: Strain dependence of the direct exciton energies for (a) MoS$_2$, (b) MoSe$_2$, (c) WS$_2$, and (d) WSe$_2$. The colourmap indicates the evolution of the normalized 2D polarizability $\alpha_2$. The ground-state A and B excitonic transitions are highlighted, with white dashed lines denoting bright states and gray dashed lines marking dark spin-triplet states.
• Figure 5: Strain dependence of the energies of the indirect excitons,IDX$_{\mathrm{K^{\prime}\Lambda}}$ (blue triangles), IDX$_{\mathrm{K\Lambda}}$ (orange diamonds), IDX$_{\Gamma\Lambda}$ (red diamonds), IDX$_{\Gamma \mathrm{K}}$ (yellow squares), and IDX$_{\mathrm{KK^{\prime}}}$ (rose squares), for (a) MoS$_2$, (b) MoSe$2$, (c) WS$2$, and (d) WSe$2$. The corresponding excitonic weight distributions for (e) DX$_{\Gamma\Lambda}$, (f) IDX$_{\mathrm{\Gamma K}}$, and (g) IDX$_{\mathrm{KK^{\prime}}}$ are also shown, similarly to Fig. \ref{['fig-x1']}. The colour maps represent the normalized weights on a linear scale.