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Half-Quantum Vortices in Polar Phase of Superfluid \(^{3}\)He

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Abstract

The magnetic dipole-dipole interaction does not prevent existence of half-quantum vortices in the polar phase of superfluid \(^{3}\)He which can be stable in uniaxial anisotropic aerogel. Here we discuss this exotic possibility. After developing a phenomenological theory of phase transition from the normal to the polar superfluid state and then to axipolar superfluid state we calculate the NMR properties of such type superfluids at the rest or under rotation when liquid is filled by an array either single quantum or half quantum vortices.

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Notes

  1. In fact the second “anisotropy” term in formula (28) is valid for for p-wave superfluid with an order parameter being the product of spin and orbital parts. In general it is somewhat more compex.

  2. V. V. Dmitriev, privite communication. Note, that to calculate the numerical values for different combinations of \(\beta _i\) coefficients one has to take into account the difference in definitions of \(\beta _i\) in present paper and \(\beta _i^H\) in Ref. 27. Namely, there is the following correspondence

    $$\begin{aligned} \beta _1=\beta _1^H,~\beta _2=\beta _3^H,~\beta _3=\beta _5^H,~\beta _4=\beta _2^H,~\beta _5=\beta _4^H. \end{aligned}$$

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Acknowledgments

I am indebted to V.V. Dmitriev for useful discussions and numerous helpful remarks in process of the manuscript preparation.

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Authors and Affiliations

  1. Commissariat a l’Energie Atomique, INAC/SPSMS, 38054 , Grenoble, France

    V. P. Mineev

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  1. V. P. Mineev
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Correspondence to V. P. Mineev.

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Mineev, V.P. Half-Quantum Vortices in Polar Phase of Superfluid \(^{3}\)He. J Low Temp Phys 177, 48–58 (2014). https://doi.org/10.1007/s10909-014-1189-2

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