Functional-renormalization-group approach to strongly coupled Bose-Fermi mixtures in two dimensions

TL;DR

This paper develops a functional-renormalization-group approach to study strongly coupled two-dimensional Bose-Fermi mixtures, revealing phase transitions, spectral properties, and the formation of fermionic composites with potential applications in ultracold atoms and semiconductors.

Contribution

It introduces a novel FRG method that captures bound-state physics and three-body correlations in 2D Bose-Fermi mixtures, elucidating phase behavior and quasiparticle properties.

Findings

Reproduces polaron-to-molecule transition in 2D Fermi gases.

Predicts spectral functions and quasiparticle properties.

Identifies formation of fermionic composites and phase transitions.

Abstract

We study theoretically the phase diagram of strongly coupled two-dimensional Bose-Fermi mixtures interacting with attractive short-range potentials as a function of the particle densities. We focus on the limit where the size of the bound state between a boson and a fermion is small compared to the average interboson separation and develop a functional-renormalization-group approach that accounts for the bound-state physics arising from the extended Fr\"{o}hlich Hamiltonian. By including three-body correlations we are able to reproduce the polaron-to-molecule transition in two-dimensional Fermi gases in the extreme limit of vanishing boson density. We predict frequency- and momentum-resolved spectral functions and study the impact of three-body correlations on quasiparticle properties. At finite boson density, we find that when the bound-state energy exceeds the Fermi energy by a critical value, the fermions and bosons can form a fermionic composite with a well-defined Fermi surface. These composites constitute a Fermi sea of dressed Feshbach molecules in the case of ultracold atoms while in the case of atomically thin semiconductors a trion liquid emerges. As the boson density is increased further, the effective energy gap of the composites decreases, leading to a transition into a strongly correlated phase where polarons are hybridized with molecular degrees of freedom. We highlight the universal connection between two-dimensional semiconductors and ultracold atoms and we discuss perspectives for further exploring the rich structure of strongly coupled Bose-Fermi mixtures in these complementary systems.