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Andreev–Bashkin entrainment makes the hydrodynamics of the binary superfluid solution particularly interesting. We investigate stability and motion of quantum vortices in such system.

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  1. The vortex energy (see below) is dominated by the distant flow, which is essentially incompressible in liquids. This approximation may be violated in gaseous systems, where the densities are equally important variables.

  2. Particularly, if L is interpreted as a proper penetration depth, then the present analysis remains mostly valid for electrically charged superfluids [2, 11].

  3. We only discuss the global stability here. The existence of metastable vortex configurations requires further investigation.

  4. The vector between two lattice nodes with the smallest Euclidean norm.

  5. Analysis in higher dimensions is more cumbersome. In the s-dimensional case (for an s-species superfluid), there exist \(2^s-1\) stable vortex flavors.

  6. The total external force required to keep the vortex (per unit length) at rest in a moving fluid is given by:

    $$\begin{aligned} f^l=2\pi \hbar e^{lk} \sum \limits _{\alpha } j_\alpha ^k \frac{n_\alpha }{m_\alpha }. \end{aligned}$$

    This force may be provided, e.g., by some pinning potential or an electric field acting on trapped charges.


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I thank Sergey Kafanov, Vladimir Marchenko, Sam Patrick, Sivan Refaeli-Abramson and Edouard Sonin for useful discussions. This work was partially supported by the MOIA grant #714481. Present research would have been impossible without the protection by the IDF.

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Melnikovsky, L.A. Vortices in Andreev–Bashkin Superfluids. J Low Temp Phys (2024).

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