Measurement of the spin-forbidden dark excitons in MoS2 and MoSe2 monolayers

Abstract

Excitons with binding energies of a few hundreds of meV control the optical properties of transition metal dichalcogenide monolayers. Knowledge of the fine structure of these excitons is therefore essential to understand the optoelectronic properties of these 2D materials. Here we measure the exciton fine structure of MoS 2 and MoSe 2 monolayers encapsulated in boron nitride by magneto-photoluminescence spectroscopy in magnetic fields up to 30 T. The experiments performed in transverse magnetic field reveal a brightening of the spinforbidden dark excitons in MoS 2 monolayer: we find that the dark excitons appear at 14 meV below the bright ones. Measurements performed in tilted magnetic field provide a conceivable description of the neutral exciton fine structure. The experimental results are in agreement with a model taking into account the effect of the exchange interaction on both the bright and dark exciton states as well as the interaction with the magnetic field.

Magneto-optics of layered two-dimensional semiconductors and heterostructures: Progress and prospects

“…Due to the specific sign of the conductionband splitting, the ground-state exciton in WS2, WSe2, and MoS2 is found to be optically "spin forbidden" or "dark" 87,162,[172][173][174][175][176][177][178][179][180][181]164,182,[165][166][167][168][169][170][171] (see Figure 2(b)). In MoSe2 and MoTe2, however, the ground-state exciton is an optically "bright" state due to a reversed conduction band splitting compared to the other three materials 165,[182][183][184][185] (Figure 2(b)). The brightness or the darkness of the groundstate excitons have a strong influence on the temperatureand carrier-density-dependent optical and magnetooptical properties (absorption and PL) of TMDCs 166,167,183,186,187 .…”

“…One puzzle which is a topic of discussion in the community is that the g factor of A excitons in MoS2 monolayer encapsulated with hBN has been found to deviate significantly from the value of 4, 182,201,202 where the values as low as 1.7 are obtained 201 . Authors of Ref.…”

“…The splitting between bright and dark excitons in this geometry is used in determining the electronic g factor of about 2. 182,185 factors of 8, other shake-up processes involving a spin flip of excess electrons from low to upper conduction bands 146 . Recent magneto-PL experiments and theoretical developments have confirmed some of these speculations to be true.…”

“…First, a large numerical aperture (NA) objective lens to collect PL emitted parallel to the sample plane can be used and magneto PL is performed in Faraday geometry 170 . Alternatively, if no PL from dark excitons using high NA objective is observed, one can apply tilted magnetic fields to the sample 181,182 . In this case, a component of the magnetic field within the plane of the sample brightens the dark excitons, and the out-ofplane component splits them.…”

“…From the atomic picture considering contributions from the magnetic moments of the d-orbitals of the transition metal, the g factor of dark excitons is expected to be 8 which is close to the observed values (see Figure 8) 146 . For the case of MoS2, a strong deviation of the dark exciton g factor from other materials is puzzling 182 , and requires further theoretical and experimental work. This is similar to the bright exciton g factor of MoS2 (discussed earlier) where a range of g factors in MoS2 are found (between 1.7 and about 4) depending upon the exciton linewidth in the monolayer 182,201,202 .…”