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arXiv:2106.01068 · New Journal of Physics

Phase transitions of repulsive two-component Fermi gases in two dimensions

Martin-Isbjörn Trappe, Piotr T. Grochowski, Jun Hao Hue, Tomasz Karpiuk, Kazimierz Rza̧żewski

Published Sep 29, 2021• 8 citations

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 toward 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 bare contact 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 plethora 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.

DOI: 10.1088/1367-2630/ac2b51

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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 toward 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 bare contact 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 plethora 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.

We investigate separations of trapped balanced two-component atomic Fermi gases with repulsive contact interaction. Candidates for ground-state densities are obtained from the imaginary-time evolution of a nonlinear pseudo-Schr\"odinger equation in three dimensions, rather than from the cumbersome variational equations of the underlying energy density functional. With the employed hydrodynamical approach, gradient corrections to the Thomas-Fermi approximation are conveniently included and are shown to be vital for reliable density profiles. We provide critical repulsion strengths that mark the onset of phase transitions in a harmonic trap. We present transitions from identical density profiles of the two fermion species towards isotropic and anisotropic separations for various confinements, including harmonic and double-well-type traps. Our proposed method is suited for arbitrary trap geometries and can be straightforwardly extended to study dynamics in the light of ongoing experiments on degenerate Fermi gases.

The ground-state properties of two-component repulsive Fermi gases in two dimensions are investigated by means of fixed-node diffusion Monte Carlo simulations. The energy per particle is determined as a function of the intercomponent interaction strength and of the population imbalance. The regime of universality in terms of the

s

-wave scattering length is identified by comparing results for hard-disk and for soft-disk potentials. In the large imbalance regime, the equation of state turns out to be well described by a Landau-Pomeranchuk functional for two-dimensional polarons. To fully characterize this expansion, we determine the polarons' effective mass and their coupling parameter, complementing previous studies on their chemical potential. Furthermore, we extract the magnetic susceptibility from low-imbalance data, finding only small deviations from the mean-field prediction. While the mean-field theory predicts a direct transition from a paramagnetic to a fully ferromagnetic phase, our diffusion Monte Carlo results suggest that the partially ferromagnetic phase is stable in a narrow interval of the interaction parameter. This finding calls for further analyses on the effects due to the fixed-node constraint.

We study ferromagnetism in a repulsively interacting two-component Fermi gas in a harmonic trap. Within a local density approximation, the two components phase separate beyond a critical interaction strength, with one species having a higher density at the trap center. We discuss several easily observable experimental signatures of this transition. The mean-field release energy, its separate kinetic and interaction contributions, as well as the potential energy all depend on the interaction strength and contain a sharp signature of this transition. In addition, the conversion rate of atoms to molecules, arising from three-body collisions, peaks at an interaction strength just beyond the ferromagnetic transition point. We then go beyond the local density approximation and derive an energy functional that includes a term that depends on the local magnetization gradient and acts as a ``surface tension.'' Using this energy functional, we numerically study the energetics of some candidate spin textures that may be stabilized in a harmonic trapping potential at zero net magnetization. We find that a hedgehog state has a lower energy than an ``in-out'' domain-wall state in an isotropic trap. Upon inclusion of trap anisotropy we find that the hedgehog magnetization profile gets distorted due to the surface tension term, this distortion being more apparent for small atom numbers. We estimate that the magnetic dipole interaction does not play a significant role in this system. We consider possible implications for experiments on trapped

^{6}\text{L}\text{i}

and

^{40}\text{K}

gases.

Spin asymmetry of ground states is studied in trapped spin-degenerate (two-component) gases of fermionic atoms with repulsive interaction between different components; and, for a large particle number, the asymmetric (collective ferromagnetic) states are shown to be stable because it can be energetically favorable to increase the Fermi energy of one component rather than increase the interaction energy between up-down components. We formulate the Thomas-Fermi equations and give algebraic methods to solve them. From the Thomas-Fermi solutions, we find three kinds of ground states in the finite system: (1) paramagnetic (spin-symmetric), (2) ferromagnetic (equilibrium), and (3) ferromagnetic (nonequilibrium) states. We present the density profiles and the critical atom numbers for these states obtained analytically, and, in ferromagnetic states, the spin asymmetries are shown to occur in the central region of the trapped gas, and increase with increasing particle number. Based on the obtained results, we discuss the experimental conditions and current difficulties in realizing the ferromagnetic states of the trapped atom gas, which should be overcome.

Itinerant ferromagnetism in cold Fermi gases with repulsive interactions is studied applying the Jastrow-Slater approximation generalized to finite polarization and temperature. For two components at zero temperature, a second-order transition is found at ${\mathit{ak}}_{F}\ensuremath{\simeq}0.90$ compatible with results of quantum-Monte-Carlo (QMC) calculations. Thermodynamic functions and observables, such as the compressibility and spin susceptibility and the resulting fluctuations in number and spin, are calculated. For trapped gases, the resulting cloud radii and kinetic energies are calculated and compared to recent experiments. Spin-polarized systems are recommended for effective separation of large ferromagnetic domains. Collective modes are predicted and tricritical points are calculated for multicomponent systems.

The two-component Fermi gas in a double-well trap is studied using the density functional theory and the density profile of each component is calculated within the Thomas-Fermi approximation. We show that the two components are spatially separate in the two wells once the repulsive interaction exceeds the Stoner point, signaling the occurrence of the ferromagnetic transition. Therefore, the double-well trap helps to explore itinerant ferromagnetism in atomic Fermi gases, since the spontaneous separation can be examined by measuring component populations in one well.