Dielectric constant of monolayer transition metal dichalcogenides across excitonic resonances

We analyze the dielectric-function spectra of low dimensional transition metal dichalcogenides (TMDCs) using a fully analytical model of the complex dielectric function that is applicable in fractional dimensional space. We extract the dimensionalities of the $A$ and $B$ excitons as well as their Lorentzian broadening widths by fitting the model to experimental data in the spectral range of photon energies (1.5 - 3 eV). Our results show the significant contribution of the lowest ground exciton state to the dielectric properties of exemplary monolayer materials (MoS$_2$, MoSe$_2$ and WSe$_2$). The exciton dimensionality parametrizes the processes that underlie confinement and many-body Coulomb effects as well as substrate screening effects, which simplifies the analysis of electro-optical properties in low dimensional systems. This study highlights the potential of theoretical models as valuable tools for interpreting the optical spectrum and in seeking an understanding of the correlated dynamics between the $A$ and $B$ excitons on the dielectric function of TMDCs.