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arXiv:2111.13640

su(N) Mermin-Ho relation

Emi Yukawa

Published Nov 26, 2021• 0 citations
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Abstract

The Mermin-Ho relation expresses the vorticity of a coreless su(2) vortex in terms of the spin-1 or l vector which characterizes fully polarized superfluid textures. We generalize it to an su(N) vortex which is applicable to arbitrarily polarized superfluid textures with higher spin or angular momentum. The obtained relation is expressed in terms of the mean-field generators and their structure factors.

DOI
10.48550/arxiv.2111.13640

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The Mermin-Ho relation expresses the vorticity of a coreless su(2) vortex in terms of the spin-1 or l vector which characterizes fully polarized superfluid textures. We generalize it to an su(N) vortex which is applicable to arbitrarily polarized superfluid textures with higher spin or angular momentum. The obtained relation is expressed in terms of the mean-field generators and their structure factors.
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As an example of the skyrmion lattice, the structure of Mermin-Ho vortex lattice in superfluids 3He^{3}\text{H}\text{e}3He is studied by self-consistent Eilenberger theory and by Bogoliubov-de Gennes theory. We identify how the intrinsic orbital angular momentum l\mathbf{l}l of ppp-wave Cooper pairs contributes to spatial structures of the pair potential, current flow, and quasiparticle states. There are two types of vortices depending on the l\mathbf{l}l direction relative to rotation. Only one of them has zero-energy bound states appearing even in coreless vortices due to intrinsic topological reasons.
The Mermin-Ho and Anderson-Toulouse coreless vortices are demonstrated to be thermodynamically stable in ferromagnetic F = 1 spinor Bose-Einstein condensates under rotation. We have carried out extensive calculations of the Gross-Pitaevskii equations by assuming uniform density along the z axis and comparing the energies of other competing non-axis-symmetric or singular vortices. The phase diagram is thereby established in a plane of the rotation drive vs the total magnetization. Their stability is also checked by calculating collective modes based on the Bogoliubov equations.