Temperature-driven BCS–BEC crossover in a coupled boson–fermion system

Motivated by strongly correlated and frustrated systems, we propose a coupled bose-fermi model
in two dimensions that describes the dynamics of pairs of opposite spin fermions scattering into
localized bosons and vice versa. Upon tracing out one of the degrees, either the bosons or fermions,
generates temperature–dependent long range effective interactions between bosons as well as effective
attractive interactions between fermions. Using Monte Carlo techniques we obtain the thermody-
namic properties and phase stiffness as a function of temperature, dominated by vortex–antivortex
unbinding of the bosons. Remarkably in the fermion sector we observe a temperature–induced BCS–
BEC crossover signaled by a distinct change of their spectral properties: the minimum gap locus
moves from the Fermi wave vector to the Γ point. Angle resolved photoemission spectroscopy on
superconducting islands on graphene and bose–fermi mixtures in cold atomic systems are promising
experimental systems to test our predictions.