RYDBERG SERIES OF DARK EXCITONS AND THE CONDUCTION BAND SPIN-ORBIT SPLITTING IN MONOLAYER WSe₂

Piotr Kapuściński and Marek Potemski, LNCMI Grenoble.

Strong Coulomb correlations together with multi-valley electronic bands in the presence of spin-orbit interaction are at the heart of studies of the rich physics of excitons in semiconductor structures made of monolayers of transition-metal dichalcogenides (TMD). These archetypes of two-dimensional systems promise the design of new optoelectronic devices. In intrinsic TMD monolayers (ML) the basic, intravalley, excitons are formed by a hole from the top of the valence band and an electron either from the lower or upper spin-orbit-split conduction subbands: one of these excitons is optically active, the second one is “dark”. Dark excitons become, however, optically active when a high in-plane magnetic field is applied to a TMD ML. This magnetic brightening allowed us to unveil the s-series of Rydberg dark exciton states in a WSe₂ ML, which appears in addition to a conventional bright exciton series. The comparison of energy ladders of bright and dark Rydberg excitons (see figure) is shown to be a method to experimentally evaluate one of the missing band parameters in TMD MLs: The amplitude, of the spin-orbit splitting of the conduction band. Its derived value in WSe₂ ML, Δ_c = 14〗 meV, is significantly lower than that commonly assumed, what calls for revision of theoretical calculations of electronic bands in TMD MLs. Moreover, our results suggest that the difference between the binding energies of bright and dark excitons can be fully explained by the difference in the masses of electrons in the two spin-orbit-split conduction bands, without referring to exchange interactions.

Figure: Energy positions of resonances in a WSe₂ monolayer, associated with bright (red diamonds, ns^B)and dark (grey squares, ns^D) exciton s-series as a function of 1/(n + δ)², where δ = -0.09. Red and grey solid lines follow the model of Coulomb bound states in inhomogeneous medium (monolayer encapsulated in hBN). The dashed red and grey lines denote the band gaps for dark (E^D_g=1.880eV) and bright (E^B_g = 1.894 eV) excitons, while the red and grey arrows show the binding energies of bright (E^B_b= 171 meV) and dark    (E^D_b* = 198 meV) excitons, respectively. The conduction band spin-orbit splitting (Δ_c = 14 meV) is also indicated.

Rydberg series of dark excitons and the conduction band spin-orbit splitting in monolayer WSe₂, P. Kapuściński, A. Delhomme, D. Vaclavkova, A. O. Slobodeniuk, M. Grzeszczyk, M. Bartos, K. Watanabe, T. Taniguchi, C. Faugeras, and M. Potemski,

Commun. Phys. 4, 186 (2021).

https://www.nature.com/articles/s42005-021-00692-3

Contact: Piotr.Kapuscinski@lncmi.cnrs.fr, Marek.Potemski@lncmi.cnrs.fr