Many-Body Configurational Spectral Splitting between a Trion and a Charged Exciton in a Monolayer Semiconductor

Many-body complexes in semiconductors are important for both fundamental physics and practical device applications. A three-body system of two electrons (e) and one hole (h) or one electron and two holes (2e1h or 1e2h) is commonly believed to form a trion (or a charged exciton) with a spectral peak red-shifted from an exciton. However, both the validity of this understanding and the physical meaning of a trion or charged exciton have not been thoroughly examined. In general, there are two different configurations for a three-body system, or (alternatively or ), which could be considered a charged exciton and trion, respectively. Here, <···> represents an irreducible cluster with respect to Coulomb interactions. In this article, we consider these issues theoretically and experimentally using monolayer MoTe₂ as an example. Experimentally, the photoluminescence spectrum showed two spectral peaks that are 21 and 4 meV below the exciton peak, in contrast to the single "trion" peak from the conventional understanding. Theoretically, the three-body Bethe-Salpeter equation in a two-band model reproduced both spectral features, while the cluster expansion technique allows us to further identify the two peaks with the charged exciton () and the trion (). Importantly, the spectral splitting is a pure many-body splitting and should not be confused with the fine structure of the trion due to spin-split. Additionally, our theory could also explain similar spectral features in previous experiments on MoSe₂, demonstrating the universality of the many-body configurational splitting. Our results provide a more complete understanding of many-body systems.