Spectral Features of the Fourth Order Irreducible Correlations in a Monolayer Semiconductor

Understanding high-order correlations or multi-particle entities in a many-body system is not only of fundamental importance in condensed matter physics, but also critical for many technological applications. So far, higher-order multi-particle irreducible correlations in semiconductors have not been studied beyond the second-order or two-particle case. In this paper, we study the correlation of two electrons and two holes (2e2h) using the four-body Bethe-Salpeter equation (4B-BSE) and applied to the calculation of the helicity-resolved absorption between the two-body and four-body states for a monolayer MoTe2. Surprisingly, we found a rich series of spectral peaks within an energy span of ~40 meV below the exciton that has not been seen before. To understand the origin of the new spectral peaks, the Feynman diagrams of the 4B BSE are recast into the cluster expansion formalism, allowing us to study the individual effects of selected clusters or correlations of various orders. We found that the irreducible clusters of orders up to the 3rd and their factorized combinations cannot explain the spectral features. Importantly, we found that the 4th order irreducible correlation is necessary and sufficient to explain the new features. The 4th order irreducible correlation corresponds to a four-particle irreducible cluster involving two electrons and two holes, alternatively called quadron or quadruplon. The new 4th order correlation or four-particle entity not only enriches our understanding of many-body correlations but also could provide new mechanism for light emission or absorption for possible new optoelectronic devices.