Energy spectrum of two-dimensional excitons in a non-uniform dielectric medium

Abstract

We demonstrate that, in monolayers (MLs) of semiconducting transition metal dichalcogenides, the $s$-type Rydberg series of excitonic states follows a simple energy ladder: $\hat{I}{\mu }_n=-R{y}^{\ast }/(n+\hat{I}´{)}^2$, $n$=1,2,\ldots, in which $R{y}^{\ast }$ 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 only accounted for by $\hat{I}´$. This is justified by the analysis of experimental data on excitonic resonances, as extracted from magneto-optical measurements of a high-quality WSe${}_2$ 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, MoSe${}_2$, WS${}_2$, MoS${}_2$ MLs encapsulated in hBN, we estimate an apparent magnitude of $\hat{I}´$ for each of the studied structures. Intriguingly, $\hat{I}´$ is found to be close to zero for WSe${}_2$ as well as for MoS${}_2$ 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.

Manuscript: 6 pages, 4 figures; SM: 11 pages, 12 figures