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Journal of Low Temperature Physics

Triple-Core Structure of the Double-Core Vortex in Superfluid $$^3$$He-B

Riku Rantanen

Published Mar 17, 2026• 0 citations
Publisher

Abstract

Abstract The order parameter of superfluid $$^3$$ 3 He involves nine complex components, and the multicomponent structure allows quantized vortices in superfluid $$^3$$ 3 He to have complicated cores. One of the vortices found in the B phase is the double-core vortex, which has been often described as a pair of two half-quantum vortices (HQVs) connected by a domain wall. Our numerical calculations of the core structure suggest an alternative representation of the vortex as a combination of three vortices, one in each component of the spin-triplet superfluid. Based on the results we present a qualitative analytical model for the triple-core structure of the double-core vortex. Additionally we numerically calculate the structure of a double-core vortex stretched between pinning sites, and show that the HQV picture becomes more applicable when separation between subcores becomes large.

DOI
10.1007/s10909-026-03394-8

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Triple-core structure of the double-core vortex in superfluid 3^33He-B
The order parameter of superfluid 3^33He involves nine complex components, and the multicomponent structure allows quantized vortices in superfluid 3^33He to have complicated cores. One of the vortices found in the B phase is the double-core vortex, which has been often described as a pair of two half-quantum vortices (HQVs) connected by a domain wall. Our numerical calculations of the core structure suggest an alternative representation of the vortex as a combination of three vortices, one in each component of the spin-triplet superfluid. Based on the results we present a qualitative analytical model for the triple-core structure of the double-core vortex. Additionally we numerically calculate the structure of a double-core vortex stretched between pinning sites, and show that the HQV picture becomes more applicable when separation between subcores becomes large.
Quantized vorticity is a property of quantum fluids that has been widely studied in various types of superfluids, either with or without spin [77],[86],[87] and Chapter 6. Superfluids with a two component (spinor) order parameter are characterized by a different type of vortex than those found in conventional scalar superfluids [99]-[102]. This new type of vortex is the so called half quantum vortex (HQV). HQVs have lower energy with respect to full vortices and constitute the elementary excitations of spinor superfluids. When circumventing their core, the phase and the polarization vector experience a ±π rotation. In this sense, HQV can be understood as a half phase vortex combined with a half polarization vortex [99]. In 4He superfluids, the HQV cannot be formed as the spin degree of freedom is absent. However, in 3He [99],[100] or in triplet superconductors [101],[102], the order parameter has two or more components, so that the formation of HQV is possible. So far, experiments have not presented any direct evidence for HQV in 3He [103], while more reliable indications of existence of HQV have been reported in cuprate superconductors [104].
The half quantum vortex (HQV) in condensates has been studied, since it was predicted by Volovik and Mineev, and independently by Cross and Brinkman in superfluid 3 He-A phase. However, no experimental evidence for its existence has been reported until recently. Motivated by a recent experimental report by Yamashita et al. ( AIP Conf. Proc. , 850 (2006) 185; private communication) we study the HQVs in superfluid 3 He confined between two parallel plates with a gap D ∼10 μm in the presence of a magnetic field H ∼26 mT perpendicular to the parallel plates. We find that the bound HQVs are more stable than the singular vortices and free pairs of HQVs, when the rotation perpendicular to the parallel plates is below the critical speed, Ω c =2∼12 rad/s, if the magnetic healing length, ξ H is about 2–5 μm. The bound pair of HQVs accompanies the tilting of -vector out of the plane, which leads to an additional absorption in NMR spectra. Our study appears to describe the temperature and rotation dependence of the observed satellite NMR signal, which supports the existence of the HQVs in 3 He.
We investigate a magnetic susceptibility of vortices in the B phase of multicomponent triplet superfluid 3He^{3}\text{H}\text{e}3He focusing on a contribution of bound fermionic states localized within vortex cores. Several order-parameter configurations relevant to different types of quantized vortices in 3He^{3}\text{H}\text{e}3He B are considered. It is shown quite generally that an ac magnetic susceptibility has a sharp peak at the frequency corresponding to the energy of interlevel spacing in the spectrum of bound fermions. We suggest that measuring of a magnetic resonance within vortex cores can provide a direct probe of a discrete spectrum of bound vortex-core excitations.
We demonstrate that the confinement of half-quantized vortices (HQVs) in coherently coupled Bose-Einstein condensates simulates certain aspects of the confinement in a theory like SU(2)\text{SU}(2)SU(2) quantum chromodynamics (QCD) in 2+1 space-time dimensions. By identifying the circulation of superfluid velocity as the baryon number and the relative phase between two components as a dual gluon, we identify HQVs in a single component as electrically charged particles with a half baryon number. Further, we show that only singlet states of the relative phase of two components can stably exist as bound states of vortices, that is, a pair of vortices in each component (a baryon) and a pair of a vortex and an antivortex in the same component (a meson). We then study the dynamics of a baryon and meson; a baryon is static at equilibrium and rotates once it deviates from the equilibrium, while a meson moves with constant velocity. For both baryons and mesons we verify a linear confinement and determine that they are broken, thus creating other baryons or mesons in the middle when two constituent vortices are separated by more than some critical distance, resembling QCD.
We consider quantized vortices in two-component Bose-Einstein condensates and three-component Fermi gases with attractive interactions. In these systems, the vortex core can be either empty (normal in the fermion case) or filled with another superfluid. We determine critical values of the parameters---chemical potentials, scattering lengths, and, for Fermi gases, temperature---at which the transition between the two types of vortices occurs. Population imbalance can lead to superfluid core (coreless) vorticity in multicomponent superfluids which otherwise support only usual vortices. For multicomponent Fermi gases, we construct the phase diagram, including regions of coreless vorticity. We extend our results to trapped bosons and fermions using an appropriate local approximation, which goes beyond the usual Thomas-Fermi approximation for trapped bosons.