Abstract
We describe exciton–polariton modes formed by the interaction between excitons in a 2D layer of a transition metal dichalcogenide embedded in a cylindrical microcavity and the microcavity photons. For this, an expression for the excitonic susceptibility of a semiconductor disk placed in the symmetry plane perpendicular to the axis of the microcavity is derived. Semiclassical theory provides dispersion relations for the polariton modes, while the quantum-mechanical treatment of a simplified model yields the Hopfield coefficients, measuring the degree of exciton–photon mixing in the coupled modes. The density of states (DOS) and its projection onto the photonic and the excitonic subspaces are calculated, taking monolayer MoS2 embedded in a Si3N4 cylinder as an example. The calculated results demonstrate a strong enhancement for certain frequencies of the total and local DOS (and, consequently, of the spontaneous emission rate of a nearby point emitter, i.e., the Purcell effect) caused by the presence of the 2D layer.
Highlights
Excitons in transition metal dichalcogenide (TMD) are very robust, with the binding energy of the order of 0.5 eV and a very small effective Bohr radius,4 which imply the presence of bound excitons at room temperature and above and the possibility of 3D confinement of such an exciton as a whole
Within the perfect EM confinement model, we shall present calculated exciton-polariton modes, the Hopfield coefficients measuring the fraction of exciton and photon in a polariton mode,24 and the emission enhancement factor for a point emitter located in the TMD plane
For the implementation that we have in mind, discussed below, it is interesting to calculate LDOS at the TMD layer, i.e. for z = 0. It is shown the dependence of the LDOS, πR2ρ(loμc)(E; r, z = 0), upon r and energy in the vicinity of the crossing point. As it can be seen from the plots, the local density of states depends strongly on both the energy and the radial position and it is redistributed owing to the presence of the TMD layer
Summary
Strong light-matter coupling takes place in nearly two-dimensional (2D) semiconductors of the transition metal dichalcogenide (TMD) family, making these materials highly interesting for a range of photoelectronic applications including photodetection and lasing, as well as from the fundamental physics point of view. Excitons in TMDs are very robust, with the binding energy of the order of 0.5 eV and a very small effective Bohr radius, which imply the presence of bound excitons at room temperature and above and the possibility of 3D confinement of such an exciton as a whole. The encouraging results include high Rabi splittings (comparable to the best GaAs and II-VI MCs), the existence of exciton-polaritons at room temperature, and 2D-exciton-mediated lasing The latter was achieved with a WGM microdisk resonator containing an embedded WS2 monolayer.. Within the perfect EM confinement model, we shall present calculated exciton-polariton modes (density of states and the dispersion relation), the Hopfield coefficients measuring the fraction of exciton and photon in a polariton mode, and the emission enhancement factor for a point emitter located in the TMD plane (e.g. a point defect) For such an emitter, we shall assume a weak coupling regime and analyze how its emission is enhanced or inhibited (the Purcell effect25) due to the polaritonic background of the microcavity. EXCITONIC SUSCEPTIBILITY OF A 2D SEMICONDUCTOR EMBEDDED IN A CYLINDRICAL CAVITY
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