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 paper thus paves the way towards a universal understanding of boson-induced pairing across various fermionic systems at finite density, and opens perspectives towards realizing unexplored forms of electron pairing beyond the conventional paradigm of Cooper pair formation.
This work shows that a strongly correlated phase which is gapped to collective spin excitations but gapless to charge fluctuations emerges as a universal feature in one-dimensional fermionic systems obeying certain discrete symmetries whenever one pair of spin-degenerate subbands is occupied and an arbitrarily weak spin-orbit interaction is present. This general result is independent of the details of the one-dimensional confinement, the fermionic spin, or nature of the spin-orbit interaction. In narrow-gap semiconductors, this gap may be of order 10 \textmu{}eV. This strongly correlated phase may be identified both via an anomalous
h/2e flux periodicity in Aharonov-Bohm oscillations and
2e periodic Coulomb blockade, features which reflect the existence of fermionic pairing despite the absence of superconductivity and the repulsive nature of the interaction.
We study a finite-temperature spectrum renormalization and s-wave pairing instability in a system of fermions with an attractive ``current-current'' interaction mediated by an overdamped mode with a dispersion \ensuremath{\omega}=i${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}1}$${\mathit{q}}^{2+\mathrm{\ensuremath{\eta}}}$, 0\ensuremath{\le}\ensuremath{\eta}\ensuremath{\le}1. It generalizes the case of a transverse gauge interaction between spinons in Mott insulators, which drives an instability of a homogeneous resonant valence bond state towards a dimerization.