Stability and spectral functions of 2D Bose-Fermi mixtures

In this work, we study a 2D ultracold Bose-Fermi mixture in the presence of a broad Fano-Feshbach resonance controlling the interaction between bosons and fermions. To describe this system at zero temperature, we apply to two dimensions an (imaginary time) T-matrix many-body approach that has been previously used successfully for 3D systems. We first analyze the stability of the mixture against phase separation or mechanical collapse as the boson-fermion interaction is varied from weak to strong. To this end, we extend previous work using the same T-matrix formalism, by replacing the Bogoliubov approximation with the more sophisticated Popov theory to better describe the boson-boson repulsion. In this way, we determine the minimum value of the boson-boson repulsion which guarantees mechanical stability of the mixture. We then focus on single-particle spectral properties, which could be relevant for future experiments performing radio-frequency spectroscopy on 2D Bose-Fermi mixtures. To calculate these dynamic quantities, we need to reformulate our theory for real time and frequencies. Our results for the fermionic spectral weight function, from weak- to strong- boson-fermion attraction, show the presence of unexpected single-particle excitations at low-momenta, and a new branch at positive frequencies for sufficiently strong couplings.