| Description |
Dimensionality plays an important role in determining the fundamental nature of excitons as well as their interactions. For example, the binding energy of excitons is orders of magnitude higher in 1D (e.g., carbon nanotubes-CNT) or 2D (e.g., transition metal dichalcogenides-TMDC) semiconductors as compared to conventional 3D semiconductors (e.g., Gallium Arsenide-GaAs). Additionally, the signature of excitonic interactions is strikingly different for 1D systems as compared to 2D/3D systems. In 1D systems (CNTs) the rate of exciton-exciton annihilation deviates from the mean field approximation as the excitons are constrained by the physical dimensions to interact only with their nearest neighbors, resulting in a time-dependent rate. However, in 2D and 3D systems, the excitons are less constrained in space compared to 1D resulting in a time- independent constant annihilation rate, consistent with the mean field approximation. A particularly interesting case is presented by excitons in black phosphorus (BP), where quasi-1D excitons have been observed in atomically thin sheets of BP, resulting in a unique system of 1D excitons in a 2D plane. Here we show that the interaction between excitons in atomically thin BP shows both 1D as well as 2D characteristics depending on exciton density and temperature. We use micro-transient absorption spectroscopy (μ-TAS) to study the exciton-exciton annihilation process in bilayer (2L) BP. We observe the classic 1D time-dependent exciton annihilation dynamics at low exciton density. Interestingly, upon increasing the exciton density the data starts to show time independent rate which is characteristic of a 2D exciton-exciton annihilation process. We also observe more 1D characteristics at low temperature for all exciton densities. We attribute this effect to the anisotropic diffusion of excitons in atomically thin BP. Our data matches well with the phenomenological model of anisotropic diffusion-limited exciton-exciton annihilation. Our work highlights the importance of atomically thin black phosphorus as a unique platform to study novel many-body excitonic interactions.
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