Vortices in spin-0 superfluids carry magnetic flux

Vortices in spin-0 superfluids generically carry magnetic fields inside their cores, so that even neutral superfluid vortices may be thought of as magnetic flux tubes. We give a systematic analysis of this ‘vortex magnetic effect’ using effective field theory, clarifying earlier literature on the subject. Our analysis shows that in superfluid helium-4 the vortex magnetic effect may be large enough to be experimentally detectable.

Figure 1

One-loop diagrams with and without an explicit $\varphi$ field. The dashed line represents Coulomb exchange, and the double line $\mathrm{\Psi }$ represents the result of taking all Coulomb ladder diagrams into account to produce the neutral external states. The top and bottom solid lines denote ${\varphi }_{+}$ and ${\varphi }_{-}$ respectively.

Figure 2

One-loop diagrams giving rise to the couplings between $\mathbf{E},\mathbf{B}$ and $\mathit{\rho },\mathit{\omega }$ defined in Eq. (7). The bold line denotes $\varphi$ and the top and bottom solid lines denote ${\varphi }_{+}$ and ${\varphi }_{-}$ respectively.