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

• Published in: Physical review letters 2019-09, Vol.123 (13), p.136801-136801, Article 136801
• Main Authors: Molas, M. R., Slobodeniuk, A. O., Nogajewski, K., Bartos, M., Bala, Ł., Babiński, A., Watanabe, K., Taniguchi, T., Faugeras, C., Potemski, M.
• Format: Article
• Language: English
• Subjects: Boron nitride; Encapsulation; Energy spectra; Excitation spectra; Excitons; Holes (electron deficiencies); Molybdenum disulfide; Monolayers; Optical measurement; Physics; Rydberg series; Rydberg states; Schrodinger equation; Transition metal compounds
• ISSN: 0031-9007; 1079-7114
• DOI: 10.1103/PhysRevLett.123.136801

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.