Two-dimensional boson-fermion mixtures

TL;DR

This paper investigates the equilibrium properties of two-dimensional boson-fermion mixtures in a pancake-shaped trap, revealing how density-dependent interactions influence stability and phase separation at zero temperature.

Contribution

It introduces a mean-field approach to analyze how two-dimensional scattering modifies density profiles and stability, especially under negative boson-fermion interactions.

Findings

Logarithmic density dependence alters density profiles.

Dimensional crossover stabilizes the mixture against collapse.

Negative scattering length leads to spatial demixing.

Abstract

Using mean-field theory, we study the equilibrium properties of boson-fermion mixtures confined in a harmonic pancake-shaped trap at zero temperature. When the modulus of the s-wave scattering lengths are comparable to the mixture thickness, two-dimensional scattering events introduce a logarithmic dependence on density in the coupling constants, greatly modifying the density profiles themselves. We show that for the case of a negative boson-fermion three-dimensional s-wave scattering length, the dimensional crossover stabilizes the mixture against collapse and drives it towards spatial demixing.