Abstract
Monolayer transition metal dichalcogenides (TMDs) have been in focus of current research, among others due to their remarkable exciton landscape consisting of bright and dark excitonic states. Although dark excitons are not directly visible in optical spectra, they have a large impact on exciton dynamics and hence their understanding is crucial for potential TMD-based applications. Here, we study brightening mechanisms of dark excitons via interaction with phonons and in-plane magnetic fields. We show clear signatures of momentum- and spin-dark excitons in WS2, WSe2 and MoS2, while the photoluminescence of MoSe2 is only determined by the bright exciton. In particular, we reveal the mechanism behind the brightening of states that are both spin- and momentum-dark in MoS2. Our results are in good agreement with recent experiments and contribute to a better microscopic understanding of the exciton landscape in TMDs.
Highlights
We study brightening mechanisms of dark excitons via interaction with phonons and maintain attribution to the author(s) and the title in-plane magnetic fields
Including a magnetic field in our equation-of-motion approach, we find a field-induced mixing of spinup and spin-down states, which activates the originally spin-dark exciton resulting in an additional peak in optical spectra, cf figure 1(c)
Exploiting (12), we find an analytic expression for the intensity ratio I(D)/I(B) = ξ(TMD, T) B2 which reveals the quadratic behavior shown in the inset of figure 2(a)
Summary
To obtain a microscopic access to the optical response of TMDs after an optical excitation, we apply the density matrix formalism with semiconductor Bloch equations in its core [31,32,33,34]. To include possible features stemming from dark excitons via higher order processes, we have to extend the PL equation by implementing phonon-assisted radiative recombination processes and the impact of a magnetic field. Is the interaction-free part for excitons, photons and phonons with the excitonic energy εiQ in the state i = (si, ηi) with the spin si = ↑↑, ↑↓, ↓↑, ↓↓ and the valley ηi = (KK, KK ′, KΛ, ΓK) as solutions from the Wannier equation, cf (3). To calculate the PL intensity in presence of a magnetic field we solve this equation in the adiabatic limit, i.e. assuming slowly varying exciton occupations compared to the photonassisted polarization [25, 31, 32], yielding. Awnitdhdtehpeheaxsciintognγioη,ccwuhpearteioηnasnNdηi i, excitonic energy εηi are the exciton and spin index
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