Rydberg series of dark excitons and the conduction band spin-orbit\n splitting in monolayer WSe$_2$

Abstract

Strong Coulomb correlations together with multi-valley electronic bands in\nthe presence of spin-orbit interaction and possible new optoelectronic\napplications are at the heart of studies of the rich physics of excitons in\nsemiconductor structures made of monolayers of transition metal dichalcogenides\n(TMD). In intrinsic TMD monolayers the basic, intravalley excitons are formed\nby a hole from the top of the valence band and an electron either from the\nlower or upper spin-orbit-split conduction band subbands: one of these excitons\nis optically active, the second one is "dark", although possibly observed under\nspecial conditions. Here we demonstrate the s-series of Rydberg dark exciton\nstates in monolayer WSe$_2$, which appears in addition to a conventional bright\nexciton series in photoluminescence spectra measured in high in-plane magnetic\nfields. The comparison of energy ladders of bright and dark Rydberg excitons is\nshown to be a method to experimentally evaluate one of the missing band\nparameters in TMD monolayers: the amplitude of the spin-orbit splitting of the\nconduction band.\n