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, <e><eh> or <eeh> (alternatively <eh><h> or <ehh>), 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 <e><eh> (<eh><h>) and the trion <eeh> (<ehh>). 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.