Phase Transitions of Repulsive Two-Component Fermi Gases in Two Dimensions

TL;DR

This paper predicts phase separation and ferromagnetic transitions in two-dimensional repulsive Fermi gases using density-functional theory, highlighting the importance of quantum corrections and metastable states for experimental observations.

Contribution

It introduces a density-functional approach with quantum corrections to accurately predict phase behavior in 2D Fermi gases, extending understanding of itinerant ferromagnetism.

Findings

Universal transition from paramagnetic to ferromagnetic states with increasing interaction strength.

Identification of metastable density configurations in trapped Fermi gases.

Quantum corrections are essential for reliable predictions in mesoscopic systems.

Abstract

We predict the phase separations of two-dimensional Fermi gases with repulsive contact-type interactions between two spin components. Using density-potential functional theory with systematic semiclassical approximations, we address the long-standing problem of itinerant ferromagnetism in realistic settings. We reveal a universal transition from the paramagnetic state at small repulsive interactions towards ferromagnetic density profiles at large interaction strengths, with intricate particle-number dependent phases in between. Building on quantum Monte Carlo results for uniform systems, we benchmark our simulations against Hartree-Fock calculations for a small number of trapped fermions. We thereby demonstrate that our employed corrections to the mean-field interaction energy and especially to the Thomas-Fermi kinetic energy functional are necessary for reliably predicting properties of trapped mesoscopic Fermi gases. The density patterns of the ground state survive at low finite temperatures and confirm the Stoner-type polarization behavior across a universal interaction parameter, albeit with substantial quantitative differences that originate in the trapping potential and the quantum-corrected kinetic energy. We also uncover a zoo of metastable configurations that are energetically comparable to the ground-state density profiles and are thus likely to be observed in experiments. We argue that our density-functional approach can be easily applied to interacting multi-component Fermi gases in general.