Dilute Fermion Research Articles

Spin excitonic and diffusive modes in superfluid Fermi liquids

The role of the particle-particle $p$-wave spin interaction in Fermi liquids with an $s$-wave pairing is studied. Depending on the sign of the interaction, there arises either a new exciton collective mode below the pair-breaking threshold or a diffusive excitation mode above the threshold. The Landau parameters that control the interaction strength are evaluated for various systems: dilute fermion gases, a degenerate electron liquid, metals, atomic nuclei, and neutron matter. The interaction removes also the square-root singularity in the phase space of pair-breaking processes. How these effects influence the neutrino emissivity in neutron Cooper-pair recombinations in neutron stars is shown.

Asymmetric Fermi superfluid with different atomic species in a harmonic trap

We study the dilute fermion gas with pairing between two species and unequal concentrations in a harmonic trap using the mean-field theory and the local density approximation. We found that the system can exhibit a superfluid shell structure sandwiched by the normal fermions. This superfluid shell structure occurs if the mass ratio is larger than a certain critical value, which increases from the weak-coupling BCS region to the strong-coupling Bose-Einstein condensation (BEC) side. In the strong-coupling BEC regime, the radii of the superfluid phase are less sensitive to the mass ratios and are similar to the case of pairing with equal masses. However, the lighter leftover fermions are easier to mix with the superfluid core than the heavier ones. A partially polarized superfluid can be found if the majority fermions are lighter, whereas phase separation is still found if they are heavier.

Pairing and superfluid properties of dilute fermion gases at unitarity

We study the system of a dilute gas of fermions in three dimensions, with attractive interactions tuned to the unitarity point, using the nonperturbative restricted path-integral Monte Carlo method. The pairing and superfluid properties of this system are calculated at finite temperature. The total energy at very low temperature from our results agrees closely with that of previous ground-state quantum Monte Carlo calculations. We identify the temperature ${T}^{*}\ensuremath{\approx}0.70{ϵ}_{F}$, below which pairing correlations develop, and estimate the critical temperature for the superfluid transition ${T}_{c}\ensuremath{\approx}0.245{ϵ}_{F}$ from a finite size scaling analysis of the superfluid density.

Phase diagram of a dilute fermion gas with density imbalance

We map out the phase diagram of a dilute two-component atomic fermion gas with unequal populations and masses under a Feshbach resonance. As in the case of equal masses, no uniform phase is stable for an intermediate coupling regime. For majority component heavier, the unstable region moves towards the BEC side. When the coupling strength is increased from the normal phase, there is an increased parameter space where the transition is into the FFLO state. The converse is true if the majority is light.

Effective field theory for dilute fermions with pairing

Effective field theory (EFT) methods for a uniform system of fermions with short-range, natural interactions are extended to include pairing correlations, as part of a program to develop a systematic Kohn–Sham density functional theory (DFT) for medium and heavy nuclei. An effective action formalism for local composite operators leads to a free-energy functional that includes pairing by applying an inversion method order by order in the EFT expansion. A consistent renormalization scheme is demonstrated for the uniform system through next-to-leading order, which includes induced-interaction corrections to pairing.

Dilute limit of a strongly-interacting model of spinless fermions and hardcore bosons on the square lattice

In our model, spinless fermions (or hardcore bosons) on a square lattice hop to nearest neighbor sites, and also experience a hard-core repulsion at the nearest neighbor separation. This is the simplest model of correlated electrons and is more tractable for exact diagonalization than the Hubbard model. We study systematically the dilute limit of this model by a combination of analytical and several numerical approaches: the two-particle problem using lattice Green functions and the t-matrix, the few-fermion problem using a modified t-matrix (demonstrating that the interaction energy is well captured by pairwise terms), and for bosons the fitting of the energy as a function of density to Schick’s analytical result for dilute hard disks. We present the first systematic study for a strongly-interacting lattice model of the t-matrix, which appears as the central object in older theories of the existence of a two-dimensional Fermi liquid for dilute fermions with strong interactions. For our model, we can (Lanczos) diagonalize the 7 x 7 system at all fillings and the 20 x 20 system with four particles, thus going far beyond previous diagonalization works on the Hubbard model.

Magnon Exchange Mechanism of Superconductivity in a Generalized Kondo Lattice Model

Magnon exchange mechanism of superconductivity is studied on the basis of the spin fermion model or a generalized Kondo lattice model, where the antiferromagnetic long range or short range order exists in the localized spins. We obtain the effective interaction and the gap equation taking into account the two magnon exchange interaction. The gap equation is solved just below the transition temperature in the quasi-two-dimensional cases. As a result, it is found that the triplet pairing superconductivity is favored for dilute fermion densities, while the singlet pairing is favored for high densities. The transition temperature is found to be very low for realistic parameters. The possibility that the superconductivity by the magnon exchange interaction is observed experimentally is discussed.

A dilute system of fermions in a boson background

In this paper the properties of a dilute fermion system in a background capable of supporting boson excitations are discussed. A decoupling-procedure for the Green functions is introduced which reduces the problem to a calculation of the collective excitations of the system. The background is found to renormalize the fermions and modify their interaction. Expressions for the fermion effective mass are given and connections with recent work on 3He in 4He are discussed.