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\"ohlich 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.
Highlights
Ever since the theoretical explanation of conventional superconductivity as arising from the attractive interaction between electrons mediated by phonons [1,2], Bose-Fermi mixtures have been the subject of intense research
As we extend our calculation to a finite boson density we retain the expansion around p = 0 for the molecules as we will find that their phase appears in a regime of the phase diagram where nB nF
We investigated the phase diagram of strongly coupled Bose-Fermi mixtures in two dimensions
Summary
Ever since the theoretical explanation of conventional superconductivity as arising from the attractive interaction between electrons mediated by phonons [1,2], Bose-Fermi mixtures have been the subject of intense research. As the strongly coupled regime is entered, one has to consider the extended Fröhlich Hamiltonian in order to account for the pairing to fermionic Feshbach molecules in cold atoms and exciton-electron bound states, called trions, in semiconductors The presence of this novel bound-state physics renders the description of strongly coupled Bose-Fermi mixtures an outstanding theoretical challenge. As the boson density is increased, the effective energy gap of the composites decreases, leading to a transition into a strongly correlated phase where fermions are hybridized with molecular degrees of freedom This extension of a single-boson framework does not take into account the formation of higher-order bound states including more than one boson [80,81,82].
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