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arXiv:2105.01257 · Physical review. B./Physical review. B

Half-quantum vortices in nematic and chiral phases of He3

Robert C. Regan, Joshua Wiman, James A. Sauls

Published Jul 30, 2021• 11 citations
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Abstract

We report theoretical results for the stability of half-quantum vortices (HQVs) in the superfluid phases of $^{3}\mathrm{He}$ confined in highly anisotropic Nafen aerogel. Superfluidity of $^{3}\mathrm{He}$ confined in Nafen is the realization of a ``nematic superfluid'' with Cooper pairs condensed into a single $p$-wave orbital aligned along the anisotropy axis of the Nafen aerogel. In addition to the nematic phase, we predict a second ``chiral'' phase that onsets at a lower transition temperature. This chiral phase spontaneously breaks time-reversal symmetry and is a topological superfluid. Both superfluid phases are equal-spin pairing condensates that host arrays of HQVs as equilibrium states of rotating superfluid $^{3}\mathrm{He}$. We present results for the structure of HQVs, including magnetic and topological signatures of HQVs in both the nematic and chiral phases of $^{3}\mathrm{He}$-Nafen.

DOI
10.1103/physrevb.104.024513

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We report theoretical results for the stability of half-quantum vortices (HQVs) in the superfluid phases of 3He^{3}\mathrm{He}3He confined in highly anisotropic Nafen aerogel. Superfluidity of 3He^{3}\mathrm{He}3He confined in Nafen is the realization of a nematic superfluid'' with Cooper pairs condensed into a single $p$-wave orbital aligned along the anisotropy axis of the Nafen aerogel. In addition to the nematic phase, we predict a second chiral'' phase that onsets at a lower transition temperature. This chiral phase spontaneously breaks time-reversal symmetry and is a topological superfluid. Both superfluid phases are equal-spin pairing condensates that host arrays of HQVs as equilibrium states of rotating superfluid 3He^{3}\mathrm{He}3He. We present results for the structure of HQVs, including magnetic and topological signatures of HQVs in both the nematic and chiral phases of 3He^{3}\mathrm{He}3He-Nafen.
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.
Strong interactions that favor chiral p-wave pairing, combined with strong pair breaking by confining boundaries, are shown to lead to new equilibrium states with different broken symmetries. Based on a strong-coupling extension of the Ginzburg-Landau theory that accurately accounts for the thermodynamics and phase diagram of the bulk phases of superfluid ^{3}He, we predict new phases of superfluid ^{3}He for confined geometries that spontaneously break rotational and translational symmetry in combination with parity and time-reversal symmetry. One of the newly predicted phases exhibits a unique combination of chiral and helical order that is energetically stable in cylindrical channels of radius approaching the Cooper pair coherence length, e.g., R∼100 nm. Precise numerical minimization of the free energy yields a broad region of stability of the helical phase as a function of pressure and temperature, in addition to three translationally invariant phases with distinct broken spin and orbital rotation symmetries. The helical phase is stable at both high and low pressures and favored by boundaries with strong pair breaking. We present calculations of transverse NMR frequency shifts as functions of rf pulse tipping angle, magnetic field orientation, and temperature as signatures of these broken symmetry phases.
3 He is an example of the system with non-trivial Cooper paring. A few different superfluid phases are known in this system. Recently the new one, the polar phase, have been observed in 3 He confined in nematically ordered aerogel. A number of various topological defects including half-quantum vortices can exist the polar phase. In this work, we present theoretical and numerical studies of linear nuclear magnetic resonance in the polar phase both in the uniform order-parameter texture and in the presence of half-quantum vortices.
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 report results of experiments with superfluid ^{3}He confined in aerogels with parallel strands which lead to anisotropic scattering of ^{3}He quasiparticles. We vary boundary conditions for the scattering by covering the strands with different numbers of atomic ^{4}He layers and observe that the superfluid phase diagram and the nature of superfluid phases strongly depend on the coverage. We assume the main reason for these phenomena is a magnetic channel of the scattering which becomes important at low coverages and can be essential in other Fermi systems with triplet pairing.
We report on the observation of half-quantum vortices (HQVs) in the easy-plane polar phase of an antiferromagnetic spinor Bose-Einstein condensate. Using in situ magnetization-sensitive imaging, we observe that pairs of HQVs with opposite core magnetization are generated when singly charged quantum vortices are injected into the condensate. The dynamics of HQV pair formation is characterized by measuring the temporal evolutions of the pair separation distance and the core magnetization, which reveals the short-range nature of the repulsive interactions between the HQVs. We find that spin fluctuations arising from thermal population of transverse magnon excitations do not significantly affect the HQV pair formation dynamics. Our results demonstrate the instability of a singly charged vortex in the antiferromagnetic spinor condensate.