  We demonstrated the potential of the fractional dimensional approach to
understand exciton parameters in the exemplary atomically thin semiconductor
material, a monolayer of WS$_2$. This approach has proved to be successful in
finding the exciton binding energy and quasiparticle bandgap for the WS$_2$
monolayer in varying dielectric environments. A tuning of the quasiparticle
bandgap and binding energy by 141 meV and 188 meV, respectively, has been
achieved by varying the dielectric of the environment from 1.52 to 8.1. The
approach is justified by comparing the changes in the binding energy with the
computational results from the Quantum Electrostatic Heterostructures model.
The fractional dimension found through the excitonic Rydberg series is close to
2.8 for WS$_2$ monolayer in all different dielectric surroundings. Thus, this
approach provides a rapid and robust method for determining the binding energy
of excitons in 2D semiconductors independent of the particular dielectric
environment.
