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

## TL;DR

This paper introduces a 2D bose-fermi model demonstrating a temperature-driven BCS-BEC crossover, with implications for high-temperature superconductors, graphene, and cold atomic systems, using Monte Carlo simulations.

## Contribution

It presents a simple coupled boson-fermion model showing temperature-dependent interactions and a novel BCS-BEC crossover observed through spectral changes.

## Key findings

- Temperature-dependent long-range interactions between bosons.
- Observation of a temperature-induced BCS-BEC crossover.
- Spectral shift from Fermi wave vector to Gamma point.

## Abstract

We propose a simple bose-fermi model in two dimensions, with a coupling that converts pairs of opposite spin fermions into localized bosons and vice versa. We show that 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 thermodynamic 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 $\Gamma$ point. Such a model is relevant for describing aspects of high $T_c$ superconductivity in cuprates and pnictides, superconducting islands on graphene, and bose-fermi mixtures in cold atomic systems.