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Register a new userSingular Vortex in Narrow Cylinders of Superfluid 3He-A Phase
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Motivated by the on-going rotating cryostat experiments in ISSP, Univ. of Tokyo, we explore the textures and vortices in superfluid 3He-A phase confined in narrow cylinders, whose radii are R=50mum and 115mum. The calculations are based on the Ginzburg-Landau (GL) framework, which fully takes into account the orbital (l-vector) and spin (d-vector) degrees of freedom for chiral p-wave pairing superfluid. The GL free energy functional is solved numerically by using best known GL parameters appropriate for the actual experimental situations at P=3.2MPa and H=21.6mT. We identify the ground state l-vector configuration as radial disgyration (RD) texture with the polar core both at rest and low rotations and associated d-vector textures for both narrow cylinder systems under high magnetic fields. The RD which has a singularity at center, changes into Mermin-Ho texture above the critical rotation speed which is determined precisely, providing an experimental check for own proposal.
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It is established theoretically that an ordered state with continuous symmetry is inherently unstable to arbitrarily small amounts of disorder [1, 2]. This principle is of central importance in a wide variety of condensed systems including superconducting vortices [3, 4], Ising spin models [5] and their dynamics [6], and liquid crystals in porous media [7, 8], where some degree of disorder is ubiquitous, although its experimental observation has been elusive. Based on these ideas it was predicted [9] that 3He in high porosity aerogel would become a superfluid glass. We report here our nuclear magnetic resonance measurements on 3He in aerogel demonstrating destruction of long range orientational order of the intrinsic superfluid orbital angular momentum, confirming the existence of a superfluid glass. In contrast, 3He-A generated by warming from superfluid 3He-B has perfect long-range orientational order providing a mechanism for switching off this effect.
Motivated by a recent experiment on the superfluid 3He A-phase with a chiral p-wave pairing confined in a thin slab, we propose designing a concrete experimental setup for observing the Majorana edge modes that appear around the circumference edge region. We solve the quasi-classical Eilenberger equation, which is quantitatively reliable, to evaluate several observables. To derive the property inherent to the Majorana edge state, the full quantum mechanical Bogoliubov-de Gennes equation is solved in this setting. On the basis of the results obtained, we perform decisive experiments to check the Majorana nature.
We have found the precise stability region of the half quantum vortex (HQV) for superfluid $^3$He A phase confined in parallel plates with a narrow gap under rotation. Standard Ginzburg-Landau free energy, which is well established, is solved to locate the stability region spanned by temperature $T$ and rotation speed ($/Omega$). This $/Omega$-$T$ stability region is wide enough to check it experimentally in available experimental setup. The detailed order parameter structure of HQV characterized by A$_1$ core is given to facilitate the physical reasons of its stability over other vortices or textures.
Superfluid 3He is an unconventional neutral superfluid in a p-wave state with three different superfluid phases each identified by a unique set of characteristic broken symmetries and non- trivial topology. Despite natural immunity of 3He from defects and impurity of any kind, it has been found that they can be artificially introduced with high porosity silica aerogel. Furthermore, it has been shown that this modified quantum liquid becomes a superfluid with remarkably sharp thermodynamic transitions from the normal state and between its various phases. They include new superfluid phases that are stabilized by anisotropy from uniform strain imposed on the silica aerogel framework and they include new phenomena in a new class of anisotropic aerogels consisting of nematically ordered alumina strands. The study of superfluid 3He in the presence of correlated, quenched disorder from aerogel, serves as a model for understanding the effect of impurities on the symmetry and topology of unconventional superconductors.
The total angular momentum associated with the edge mass current flowing at the boundary in the superfluid $^3$He A-phase confined in a disk is proved to be $L=Nhbar/2$, consisting of $L^{rm MJ}=Nhbar$ from the Majorana quasi-particles (QPs) and $L^{rm cont}=-Nhbar/2$ from the continuum state. We show it based on an analytic solution of the chiral order parameter for quasi-classical Eilenberger equation. Important analytic expressions are obtained for mass current, angular momentum, and density of states (DOS). Notably the DOS of the Majorana QPs is exactly $N_0/2$ ($N_0$: normal state DOS) responsible for the factor 2 difference between $L^{rm MJ}$ and $L^{rm cont}$. The current decreases as $E^{-3}$ against the energy $E$, and $L(T) propto -T^2$. This analytic solution is fully backed up by numerically solving the Eilenberger equation. We touch on the so-called intrinsic angular momentum problem.
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