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arXiv:2610.24565

Surface corrections and vortex energetics in the Thomas--Fermi limit of a self-bound unitary Fermi superfluid

Bao-Duy Le

Published Oct 17, 2026• 0 citations
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Abstract

We study a spin-balanced unitary Fermi superfluid bound by an attractive $1/r$ interaction within an extended Thomas--Fermi density functional. Its large-particle-number limit is the Lane--Emden polytrope of index $3/2$. We prove the leading gradient correction to the ground-state energy and strong convergence of the density amplitude. A rescaled surface problem predicts the next energy correction and the leading integrated density error. Matching a vortex core to the polytropic bulk gives the energetic threshold of a singly quantized central vortex, including the constant beyond the leading logarithm. Linearizing the same surface problem predicts a local energetic threshold for collective surface excitations that, in the natural TF frequency units, decreases more slowly with particle number than the central-vortex threshold. Radial stationary, spherical Bogoliubov--Poisson, and axisymmetric real-time calculations test the predicted energy corrections and vortex matching, and resolve finite-size surface-mode minima whose approach to the continuum surface coefficient is followed to $N\simeq4\times10^6$. For the reference gradient coefficient the vortex constant is $c_1=-0.535$, and the surface Landau scale is $1.417\,ω_K(\hbar_{\rm eff}^2/2R_{\rm TF})^{1/6}\propto N^{-1/9}$; sector energies at $N\simeq4.6\times10^5$, computed after the fit, agree with the extrapolated vortex threshold to $10^{-4}$. These results distinguish the accuracy of the Thomas--Fermi bulk from the gradient physics that controls the surface and vortex core, and separate vortex energetics from the open problem of nonlinear vortex entry.

DOI
10.48550/arxiv.2610.24565

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We investigate the odd-even staggering in the harmonically-trapped unitary Fermi gas at large particle-number charge QQQ. Using both a large-NNN BdG description and a complementary large-charge EFT method, we show that for odd particle number the extra fermion forms an edge-localized quasiparticle near the Thomas-Fermi surface rather than a bulk excitation. In the edge limit, the microscopic BdG problem reduces to a universal coupled Airy system whose lowest positive eigenvalue fixes the leading odd-even splitting energy, χ ξ1/6(24Q)1/9 ℏω+⋯χ\,ξ^{1/6}(24Q)^{1/9}\,\hbarω+ \cdotsχξ1/6(24Q)1/9ℏω+⋯ where ξξξ is the Bertsch parameter, and χχχ is a universal edge coefficient. The associated EFT describes a fermionic mode confined to the boundary and coupled to the superfluid Goldstone field, reproducing the same QQQ scaling while introducing a dependence on two low-energy constants. Finally, we numerically compute the spectrum and confirm the predicted scaling and localization properties.
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The spatial distribution of vortex bound states is often anisotropic, which is correlated with the underlying property of materials. In this work, we examine the effects of Fermi surface anisotropy on vortex bound states. The large-scale calculation of vortex bound states is introduced in the presence of fourfold or twofold Fermi surface by solving the Bogoliubov–de Gennes (BdG) equations. Two kinds of quasiparticles' behaviors can be extracted from the local density of states (LDOS) around a vortex. The angle-dependent quasiparticles will move from high energy to low energy when the angle varies from curvature maxima to minima of the Fermi surface, while the angle-independent quasiparticles tend to stay at a relatively higher energy. In addition, the weight of angle-dependent quasiparticles can be enhanced by the increasing anisotropy degree of Fermi surface.