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The common model to describe exciton-plasmon interaction phenomenologically is the coupled oscillator model. Originally developed for atomic systems rather than solid-state matter, this model treats both excitons and plasmons as single harmonic oscillators coupled via a constant which can be fitted to experiments. In this work, we present a modified coupled oscillator model specifically designed for exciton-plasmon interactions in hybrids composed of two-dimensional excitons, such as in a transition metal dichalcogenide (TMDC) monolayers and metal nanoparticles while maintaining the simplicity of the commonly applied coupled oscillator models. Our approach is based on a microscopic perspective and Maxwell's equations, allowing to analytically derive an effective exciton-plasmon coupling constant. Our findings highlight the importance of the spatial dispersion, i.e., the delocalized nature of TMDC excitons, necessitating the distinction between bright and momentum-dark excitons. Both types of excitons occur at different resonance energies and exhibit a qualitatively different coupling with localized plasmons. We find a strong coupling between the plasmon and momentum-dark excitons, while a weakly coupled bright exciton manifests as an additional, third peak in the spectrum. Consequently, we propose a realistic modeling of the primary spectral features in experiments incorporating three harmonic oscillator equations instead of the conventional two. However, we also shed light on the limitations of the three coupled oscillator model in describing the line shape of extinction and scattering cross section spectra.

Monolayers of transition metal dichalcogenides (TMDC) are direct-gap semiconductors with strong light-matter interactions featuring tightly bound excitons, while plasmonic crystals (PCs), consisting of metal nanoparticles that act as meta-atoms, exhibit collective plasmon modes and allow one to tailor electric fields on the nanoscale. Recent experiments show that TMDC-PC hybrids can reach the strong-coupling limit between excitons and plasmons forming new quasiparticles, so-called plexcitons. To describe this coupling theoretically, we develop a self-consistent Maxwell-Bloch theory for TMDC-PC hybrid structures, which allows us to compute the scattered light in the near- and far-field explicitly and provide guidance for experimental studies. Our calculations reveal a spectral splitting signature of strong coupling of more than $100\,$meV in gold-MoSe$_2$ structures with $30\,$nm nanoparticles, manifesting in a hybridization of exciton and plasmon into two effective plexcitonic bands. In addition to the hybridized states, we find a remaining excitonic mode with significantly smaller coupling to the plasmonic near-field, emitting directly into the far-field. Thus, hybrid spectra in the strong coupling regime can contain three emission peaks.

In recent years, much research has been undertaken to investigate the suitability of two-dimensional materials to act as single-photon sources with high optical and quantum optical quality. Amongst them, transition-metal dichalcogenides, especially WSe$_{2}$, have been one of the subjects of intensive studies. Yet, their single-photon purity and photon indistinguishability, remain the most significant challenges to compete with mature semiconducting systems such as self-assembled InGaAs quantum dots. In this work, we explore the emission properties of quantum emitters in a WSe$_{2}$ monolayer which are induced by metallic nanoparticles. Under quasi-resonant pulsed excitation, we verify clean single-photon emission with a $g^{(2)}(0) = 0.036\pm0.004$. Furthermore, we determine its temperature dependent coherence time via Michelson interferometry, where a value of (13.5$\pm$1.0) ps is extracted for the zero-phonon line (ZPL) at 4 K, which reduces to (9$\pm$2) ps at 8 K. Associated time-resolved photoluminescence experiments reveal a decrease of the decay time from (2.4$\pm$0.1) ns to (0.42$\pm$0.05) ns. This change in decay time is explained by a model which considers a Förster-type resonant energy transfer process, which yields a strong temperature induced energy loss from the SPE to the nearby Ag nanoparticle.

We present a self-consistent Maxwell-Bloch theory to analytically study the interaction between a nanostructure consisting of a metal nanoparticle and a monolayer of transition metal dichalcogenide. For the combined system, we identify an effective eigenvalue equation that governs the center-of-mass motion of the dressed excitons in a plasmon-induced potential. Examination of the dynamical equation of the exciton-plasmon hybrid reveals the existence of bound states with negative eigenenergies, which we interpret as excitons localized in the plasmon-induced potential. The appearance of these bound states in the potential indicates strong coupling between excitons and plasmons. We quantify this coupling regime by computing the scattered light in the near-field explicitly and identify signatures of strong exciton-plasmon coupling with an avoided crossing behavior and an effective Rabi splitting of tens of meV.