  Feshbach resonances play a vital role in the success of cold atoms
investigating strongly-correlated physics. The recent observation of their
solid-state analog in the scattering of holes and intralayer excitons in
transition metal dichalcogenides [Schwartz et al., Science 374, 336 (2021)]
holds compelling promise for bringing fully controllable interactions to the
field of semiconductors. Here, we demonstrate how tunneling-induced layer
hybridization can lead to the emergence of two distinct classes of Feshbach
resonances in atomically thin semiconductors. Based on microscopic scattering
theory we show that these two types of Feshbach resonances allow to tune
interactions between electrons and both short-lived intralayer, as well as
long-lived interlayer excitons. We predict the exciton-electron scattering
phase shift from first principles and show that the exciton-electron coupling
is fully tunable from strong to vanishing interactions. The tunability of
interactions opens the avenue to explore Bose-Fermi mixtures in solid-state
systems in regimes that were previously only accessible in cold atom
experiments.
