Quasiparticle phono-conversion: filming carriers coalescing into excitons

Condensed matter physics is replete with phenomena involving high-energy free particles coalescing into low-energy bound few-particle states. While the cooling of the individual particles is well understood, the crucial step by which cold free carriers form a bound state remains elusive, involving complex energy and momentum relaxation pathways. Here, by combining ultrafast time- and momentum-resolved photoemission spectroscopy on a monolayer WSe$_2$ with the first-principles excitonic-Bloch equations, we resolve the conversion of initially free electrons and holes at the bandedges into bound excitons. With unprecedented energy resolution, we observe the transient \textit{coexistence} of free-carrier and excitonic bands, accompanied by a transfer of spectral weight between the two. We establish the phononic origin of exciton formation and ascribe this coexistence to a sequential relaxation cascade toward the lowest-energy excitonic states, wherein intermediate states remain weakly populated. The efficiency of this process is controlled by valley multiplicity, large-momentum phonon emission and spin-flip processes. By elucidating how bound states emerge from their elementary constituents, our results point to strategies for engineering exciton formation, with direct implications for optical materials and devices that operate with excitons or free carriers.