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: εₙ=-Ry*/(n+δ)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 δ. 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 Schrödinger 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 δ for each of the studied structures. Intriguingly, δ 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.