Phase Separation of a Repulsive Two-Component Fermi Gas at the Two- to Three-Dimensional Crossover

We present a theoretical analysis of phase separations between tworepulsively interacting components in an ultracold fermionic gas, occurring atthe dimensional crossover in a harmonic trap with varying aspect ratios. Atailored kinetic energy functional is derived and combined with adensity-potential functional approach to develop a framework that isbenchmarked with the orbital-based method. We investigate the changes in thedensity profile of the phase-separated gas under different interactionstrengths and geometries. The analysis reveals the existence of small,partially polarized domains in certain parameter regimes, which is similar tothe purely two-dimensional limit. However, the density profile is furtherenriched by a shell structure found in anisotropic traps. We also track thetransitions that can be driven by either a change in interaction strength ortrap geometry. The developed framework is noted to have applications for othersystems with repulsive interactions that combine continuous and discretedegrees of freedom.