Generalized Crossover in Interacting Fermions within the Low-Energy Expansion

Abstract

We generalize the Bardeen-Cooper-Schrieffer-Bose-Einstein-condensation (BCS-BEC) crossover of two-component fermions, which is realized by tuning the $s$-wave scattering length $a$ between the fermions, to the case of an arbitrary effective range $r_{\mathrm{e}}$. By using the Nozières-Schmitt-Rink (NSR) approach, we show another crossover by changing $r_{\mathrm{e}}$ and present several similarities and differences between these two crossovers. Furthermore, the region ($r_{\mathrm{e}}>a/2$) where the effective range expansion breaks down and the Hamiltonian becomes non-Hermitian is found, being consistent with the Wigner's causality bound. Our results are universal for low-density interacting fermions with low-energy constants $a$ and $r_{\mathrm{e}}$ and are directly relevant to ultracold Fermi atomic gases as well as dilute neutron matter.

6 pages, 4 figures, accepted by J. Phys. Soc. Jpn

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Cited by in corpus (9)

• Unitary $p$-wave Fermi gas in one dimension
• Theory of strongly paired fermions with arbitrary short-range interactions
• Role of the effective range in the density-induced BEC-BCS crossover
• From odd-even staggering to the pairing gap in neutron matter
• Role of the confinement-induced effective range on the thermodynamics of a strongly correlated Fermi gas in two dimensions
• Brueckner $G$-matrix approach to two-dimensional Fermi gases with the finite-range attractive interaction
• Superfluid neutron matter with a twist
• Non-Hermitian $p$-wave superfluid and effects of the inelastic three-body loss in a one-dimensional spin-polarized Fermi gas
• Finite-range effect in the two-dimensional density-induced BCS-BEC crossover