Capturing of non-hydrogenic Rydberg series of exciton binding energy in two-dimensional mono-layer WS2 using a modified Coulomb potential in fractional space

2D materials exhibit unique electronic states due to quantum confinement. Among the Group-VI chalcogenides, direct mono-layer WS2 is the most prominent where screening is non-localized, having strongly bound excitons with large binding energies and a pronounced deviation of the excitonic states from the hydrogenic series. State-of-the-art experimental and theoretical methods to determine excitonic Rydberg series employ optical spectroscopy and Bethe-Salpeter (BSE) equation, respectively, but incur high costs, paving the way to develop analytical approaches. We present a generalized hydrogenic model by employing a fractional version of the Coulomb-like potential to capture the excitonic Rydberg series of the fundamental optical transition in mono-layer WS2, based on the fractional scaling of the electron-hole pair interactions through the tuning of the fractional-space parameter β, benchmarked with experimental data and that of with numerical computation of the hydrogenic solution involving the Rytova-Keldysh (R-K) potential model. The enhanced electron-hole interactions lead to a strong dielectric contrast between the mono-layer WS2 and its surrounding environment and causes the deviation of the low-lying excitonic states from the hydrogenic series. The fractional Coulomb potential (FCP) model captures the first two non-hydrogenic states at β < 3, to fit a Coulomb-like to logarithmic change with respect to the excitonic radius and the higher hydrogenic states to have Coulombic interactions at β ≈ 3 in mono-layer WS2. A comparison of the proposed model with an existing model based on Wannier theory reveals a reduction in the relative mean square error of up to 30% for the excitonic series, with only the ground state captured as non-hydrogenic by the latter.