Energy Spectrum of Two-Dimensional Excitons in a Nonuniform Dielectric Medium

We demonstrate that, in monolayers (MLs) of semiconducting transition metal dichalcogenides, the s-type Rydberg series of excitonic states follows a simple energy ladder: epsilon(n) = -Ry*/(n + delta)(2), n = 1, 2,..., in which Ry* is very close to the Rydberg energy scaled by the dielectric constant of the medium surrounding the ML and by the reduced effective electron-hole mass, whereas the ML polarizability is accounted for only by delta. This is justified by the analysis of experimental data on excitonic resonances, as extracted from magneto-optical measurements of a high-quality WSe2 ML encapsulated in hexagonal boron nitride (hBN), and well reproduced with an analytically solvable Schrodinger equation when approximating the electron-hole potential in the form of a modified Kratzer potential. Applying our convention to other MoSe2, WS2, MoS2 MLs encapsulated in hBN, we estimate an apparent magnitude of delta for each of the studied structures. Intriguingly, delta is found to be close to zero for WSe2 as well as for MoS2 monolayers, what implies that the energy ladder of excitonic states in these two-dimensional structures resembles that of Rydberg states of a three-dimensional hydrogen atom.