Stability of Bose-Fermi mixtures in two dimensions: a lowest-order constrained variational approach

TL;DR

This paper studies the stability of two-dimensional Bose-Fermi mixtures at zero temperature using a variational approach, analyzing how interactions and mass ratios influence the minimal boson-boson repulsion needed for stability.

Contribution

It introduces a non-perturbative variational method to determine stability conditions in 2D Bose-Fermi mixtures with tunable interactions, validated against experimental and quantum Monte Carlo data.

Findings

Equal mass mixtures are more stable, requiring less boson-boson repulsion.

The critical boson-boson coupling depends on interaction strength, density imbalance, and mass ratio.

Small boson-boson interactions can stabilize attractive mixtures across all fermion-boson interactions.

Abstract

We investigate the problem of mechanical stability in two-dimensional Bose-Fermi mixtures at zero temperature, focusing on systems with a tunable Bose-Fermi (BF) interaction and a weak but finite boson-boson (BB) repulsion. The analysis is carried out within the framework of the lowest-order constrained variational (LOCV) approach, which allows for a non-perturbative treatment of strong interspecies correlations while retaining analytical transparency. The BF interaction is modeled by a properly regularized attractive contact potential, enabling the exploration of both the attractive and repulsive energy branches. We determine the minimal BB repulsion required to ensure mechanical stability of the mixture by evaluating the inverse compressibility matrix over the full range of BF coupling strengths, within the domain of validity of the LOCV approximation. The interaction contribution to the energy is benchmarked against available experimental data and Quantum Monte Carlo results in the single-impurity limit, showing good agreement. Our analysis reveals how the critical BB coupling depends on interaction strength, density imbalance, and mass ratio. In particular, we find that mixtures with equal boson and fermion masses exhibit enhanced stability, requiring the smallest BB repulsion to prevent mechanical instability. In this case, a relatively small BB interaction is sufficient to stabilize attractive mixtures for all values of the BF interaction. These results provide a theoretical framework for assessing stability conditions in experimentally realizable two-dimensional Bose-Fermi mixtures with tunable interactions.