Tkachenko modes in a superfluid Fermi gas at unitarity

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In the pure 2D situation, where ℏ ​ ω z ≫ μ \hbar\omega_{z}\gg\mu ( ω z \omega_{z} is the axial trap frequency) and the 2D equation of state holds, γ = 1 \gamma=1 for both Bose and Fermi gases

Cited in the paper.

In the case of Fermi superfluids, there exist fermionic bound states localized in the vortex cores caroli64 whose energy, at unitarity, is of order of the Fermi energy sensarma06 . Since the Tkachenko modes have much smaller energy, the coupling between these two kinds of excitations can be safely ignored

Cited in the paper.

This condition should not be confused with the condition Ω 2 / c s 2 ​ k 2 ∼ ℏ ​ Ω ​ N v / μ 0 ≪ 1 \Omega^{2}/c_{s}^{2}k^{2}\sim\hbar\Omega N_{v}/\mu_{0}\ll 1 characterizing the incompressible limit of the Tkachenko dispersion law

Cited in the paper.

The estimate becomes even more accurate if one employs the sound velocity averaged over the whole cloud baym03

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