The name is absent

15

cylindrical symmetry of the system and discretize the p-z plane on a triangular mesh using
a finite element scheme, which reduces the system to 2D effectively.

3.1.2 BdG Formalism

Let us consider a Fermi gas distributed in two hyperfine spin states. The Fermi system
across a broad Feshbach resonance, which is realized in ⁶Li or ⁴⁰K atoms, can be well

described by the single-channel Hamiltonian as following:

with the creation and annihilation operators of fermions, ≠τ_r(r) and ≠_σ-(r).

Following the procedure in Reference [22], we can obtain the Bogoliubov-de Gennes

(BdG) equations [21] which take the form
where the single-particle Hamiltonian is given by

H_σ = -n²V²∕(2m) + V_eχt(r) - μ_σ(cr =↑, J,)                  (3.3)

The quasiparticle energies E₇ take both positive and negative values. The order parameter
and the densities are given by Δ = g X, u_iv*f(E_i), n↑ = X₁ ∣u,∣²∕(E,), and n_i = X_l∙ ∣v,∣²∕(-E,∙)
where f(E) = [exp(E∕kT) + 1]~¹ is the Fermi distribution function and the densities must
be constrained as N↑,_i = ʃ dr n↑j(r), g is the bare coupling constant which will be replaced
by the s-wave scattering length a_s via the regularization prescription: (4πħ²a_s∕m~)~^l = l∕g+

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