Rydberg series of dark excitons and the conduction band spin-orbit splitting in monolayer WSe2

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 monolayers of transition metal dichalcogenides (TMD). Those archetypes of two-dimensional systems promise a design of new optoelectronic devices. In intrinsic TMD monolayers 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 band subbands: one of these excitons is optically active, the second one is dark, although possibly observed under special conditions. Here we demonstrate the s-series of Rydberg dark exciton states in tungsten diselenide monolayer, which appears in addition to a conventional bright exciton series in photoluminescence spectra measured in high in-plane magnetic fields. The comparison of energy ladders of bright and dark Rydberg excitons is shown to be a method to experimentally evaluate one of the missing band parameters in TMD monolayers: the amplitude of the spin-orbit splitting of the conduction band. Excitonic physics dominates the optical response of semiconductor monolayers but single particle band structure parameters are hard to probe experimentally. Here, spin-orbit splitting in the conduction band of monolayer WSe 2 is revealed by the identification of the Rydberg series of dark excitons.