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

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.