Half quantum vortex in superfluid $^3$He-A phase in parallel plate geometry

We have studied theoretically the flow of superfluid 3He-A in parallel-plate geometry. The equilibrium order-parameter texture is calculated numerically in two spatial dimensions consisting of the coordinates along the flow direction and perpendicular to the plates. The calculations have been done using the hydrostatic theory in the Ginzburg-Landau region and assuming a large external magnetic field perpendicular to the plane of calculation. We have studied a uniform texture ...

Superfluid $^3$He-B possesses three locally stable vortices known as a normal-core vortex ($o$-vortex), an A-phase-core vortex ($v$-vortex), and a double-core vortex ($d$-vortex). In this work, we study the effects of a magnetic field parallel or perpendicular to the vortex axis on these structures by solving the two-dimensional Ginzburg-Landau equation for two different sets of strong coupling correction. The energies of the $v$- and $d$-vortices have nontrivial dependence o...

This article reviews recent developments in the physics of quantized vortices in superfluid helium and atomic Bose-Einstein condensates. Quantized vortices appear in low-temperature quantum condensed systems as the direct product of Bose-Einstein condensation. Quantized vortices were first discovered in superfluid 4He in the 1950s, and have since been studied with a primary focus on the quantum hydrodynamics of this system. Since the discovery of superfluid 3He in 1972, quant...

The superfluid $^3$He formed by spin-triplet $p$-wave Cooper pairs is a typical topological superfluid. In the superfluid $^3$He B-phase, several kinds of vortices classified by spatial symmetries $P_1$, $P_2$, and $P_3$ are produced, where $P_1$ is inversion symmetry, $P_2$ is magnetic reflection symmetry, and $P_3$ is magnetic $\pi$-rotation symmetry. We have calculated the vortex bound states by the Bogoliubov-de Gennes theory and the quasiclassical Eilenberger theory, and...

In He-3 superfluids quantized vorticity can take many different forms: It can appear as distributed periodic textures, as sheets, or as lines. In the anisotropic He-3A phase in most cases the amplitude of the order parameter remains constant throughout the vortex structure and only its orientation changes in space. In the quasi-isotropic He-3B phase vortex lines have a hard core where the order parameter has reduced, but finite amplitude. The different structures have been fi...

Symmetries of the physical world have guided formulation of fundamental laws, including relativistic quantum field theory and understanding of possible states of matter. Topological defects (TDs) often control the universal behavior of macroscopic quantum systems, while topology and broken symmetries determine allowed TDs. Taking advantage of the symmetry-breaking patterns in the phase diagram of nanoconfined superfluid $^3$He, we show that half-quantum vortices (HQVs) -- lin...

We present the first theoretical calculation of the pressure-temperature-field phase diagram for the vortex phases of rotating superfluid $^3$He-B. Based on a strong-coupling extension of the Ginzburg-Landau theory that accounts for the relative stability of the bulk A and B phases of $^3$He at all pressures, we report calculations for the internal structure and free energies of distinct broken-symmetry vortices in rotating superfluid $^3$He-B. Theoretical results for the equ...

Turbulence in superfluids depends crucially on the dissipative damping in vortex motion. This is observed in the B phase of superfluid 3He where the dynamics of quantized vortices changes radically in character as a function of temperature. An abrupt transition to turbulence is the most peculiar consequence. As distinct from viscous hydrodynamics, this transition to turbulence is not governed by the velocity-dependent Reynolds number, but by a velocity-independent dimensionle...

Half-quantum vortices (HQVs) can exist in a superconductor or superfluid with an exact or approximate U(1) \times U(1) symmetry, for instance in spinor condensates, 3He-A, Sr2RuO4, and possibly cuprate superconductors with stripe order. In this paper, we show that a lattice of HQVs can be stabilized at finite temperature even when it does not have lower energy than the lattice of full vortices at T = 0 since there is a gain in configurational entropy when a full vortex fracti...

We report the observation of vortex formation upon the absorption of a thermal neutron in a rotating container of superfluid $^3$He-B. The nuclear reaction n + $^3$He = p + $^3$H + 0.76MeV heats a cigar shaped region of the superfluid into the normal phase. The subsequent cooling of this region back through the superfluid transition results in the nucleation of quantized vortices. Depending on the superflow velocity, sufficiently large vortex rings grow under the influence of...