  We study induced pairing between two identical fermions mediated by an
attractively interacting quantum impurity in two-dimensional systems. Based on
a Stochastic Variational Method (SVM), we investigate the influence of
confinement and finite interaction range effects on the mass ratio beyond which
the ground state of the quantum three-body problem undergoes a transition from
a composite bosonic trimer to an unbound dimer-fermion state. We find that
confinement as well as a finite interaction range can greatly enhance trimer
stability, bringing it within reach of experimental implementations such as
found in ultracold atom systems. In the context of solid-state physics, our
solution of the confined three-body problem shows that exciton-mediated
interactions can become so dominant that they can even overcome detrimental
Coulomb repulsion between electrons in atomically-thin semiconductors. Our work
thus paves the way towards a universal understanding of boson-induced pairing
across various fermionic systems at finite density, and opens perspectives
towards realizing novel forms of electron pairing beyond the conventional
paradigm of Cooper pair formation.
