The quadruplon in a monolayer semiconductor

Abstract The ultimate goal of understanding the structure of matter has spurred a constant search for composite particles, especially high-order correlated entities for nearly all forms of matter, from elementary particles, nuclei, and cold atoms, to condensed matter. So far, composite particles involving two or three constituent particles and their weak-coupling combinations have been experimentally studied, such as the Cooper pairs, excitons, trions, and bi-excitons in condensed matter physics, or diquarks, mesons, and di-mesons in quantum chromodynamics. Although genuine four-particle correlated entities have long been theorized in various materials, alternatively known as quadruplons (Rausch and Potthoff in New J. Phys. 18, 2016), quadrons (Quang et al. in Physica B 602, 2021), or quartets (Jiang et al. in Phys. Rev. B 95, 2017), the only closely related experimental evidence is the tetraquark observation at CERN (LHCb in  Nat. Phys. 18, 751–754, 2022). In this article, we present for the first time the experimental evidence for the existence of a four-body entity in condensed matter, the quadruplon, involving two electrons and two holes in a monolayer of Molybdenum Ditelluride. Using the optical pump–probe technique, we discovered a series of new spectral features in addition to those of excitons and trions. Furthermore, we found that all these spectral features could be reproduced theoretically using transitions between the two-body and four-body complexes based on the Bethe–Salpeter equation. Interestingly, we found that the fourth-order irreducible cluster is necessary and sufficient for the new spectral features by using the corresponding cluster expansion technique. Thus, our experimental results combined with theoretical explanation provide strong evidence for the existence of a genuine four-particle entity, the quadruplon. In contrast to a bi-exciton which consists of two weakly interacting excitons, a quadruplon involves tightly bound four-particle entity without the presence of well-defined excitons. Our results could impact the understanding of the structure of materials in a wide range of physical systems and potentially lead to new photonic applications based on quadruplons.