Introduction to the vortex sheet of superfluid He-A

It is well known that superfluids respond to rotation by forming vortex lines. It has been recently discovered that a different type of state consisting of a vortex sheet, instead of lines, can be created in the A phase of superfluid ³He. This paper presents an introduction to the vortex sheet. We first discuss ⁴He, where a vortex sheet is unstable. The way to realize a stable sheet in ³He-A is called a vortex soliton. It consists of a topologically stable domain wall to which nonsingular vorticity is bound. The vortex soliton has been observed by nuclear magnetic resonance, and its most prominent experimental properties are explained. The macroscopic shape of the sheet and the superfluid flow in a rotating container are discussed.     

Bifurcations in the growth process of a vortex sheet in rotating superfluid

Vortex-sheet growth is considered. Broken symmetry bifurcations are found in the growth process. The collective elasticity theory for a well-developed vortex sheet is presented, which is similar to that of smectic liquid crystals. The bifurcations in the limit of a much folded vortex sheet correspond to the Helfrich instability in smectics and cholesterics.     

Majorana bound state in rotating superfluid 3He-A between parallel plates

A concrete and experimentally feasible example for testing the putative Majorana zero-energy state bound in a vortex is theoretically proposed for a parallel plate geometry of superfluid 3He-A phase. We examine the experimental setup in connection with ongoing rotating cryostat experiments. The theoretical analysis is based on the well-established Ginzburg-Landau functional, supplemented by microscopic calculations of the Bogoliubov-de Gennes equation, both of which allow the precise location of the parameter regions of the Majorana state to be found in realistic situations.     

Spin wave and vortex excitations of superfluid 3He-A in parallel-plate geometry

Quantized vortices with half-integer circulation, which are forbidden from existing in a conventional superfluid because of the single valueness of the wave function, are theoretically predicted to exist in superfluid 3He-A if the order parameters l over and d over form l over perpendicular d over texture. To form the l over perpendicular d over texture, we confined the superfluid between parallel plates with a 12.5 microm gap and applied a magnetic field of H=26.7 mT perpendicular to the plates to take NMR and orient d over perpendicular to l over. NMR spectra exhibit a negative-shift peak which probes that the uniform l over perpendicular d over texture is realized in our cell and show a new satellite signal under rotation. The rotation dependence of the satellite signal is interpreted that a Fréedericksz transition of l over texture is induced by rotation above 1.0 rad/s and vortices start to appear above 1.8 rad/s.     

Vortex formation and annihilation in three textures of rotating superfluid 3He-A

Textures, textural transformation, and formation and annihilation of a single vortex were investigated in narrow cylinders with 100 microm radius in A-phase under rotation up to 6.28 rad/sec. Three textures were found, depending on the cooling conditions of the sample through the superfluid transition temperature T(c). We found the gyromagnetic effect of textures; that is, two textures (A or B) could be selected either by applying a magnetic field in parallel or anti-parallel to the rotation axis. The critical angular speed of a single vortex formation Omega(f) and that of annihilation Omega(a) for each texture were measured. The textural transformation in type A texture was induced by rotation. Both type A and B textures held macroscopic angular momentum along the rotation axis. We identified the texture for type A, B, and C as Mermin-Ho, radial disgyration, and a soliton type of defect along the axis, respectively.     

Critical velocity of continuous vortex nucleation in a slab of superfluid 3He-A

A flow-induced Fréedericksz transition is observed in a 0.26 mm thick disk-shaped slab of superfluid 3He-A using a rotating cryostat and a torsional oscillator, and it is used to detect vortices in zero magnetic field. The phenomena are studied as a function of magnetic field normal to the slab. In defect-free l texture the critical velocity for vortex nucleation is 0.5 mm/s, but in the presence of a domain wall it is reduced to approximately Planck's over 2pi /2ma(c), where a(c)(H) is the field-dependent radius of the vortex soft core. The vortices nucleate at a distance at least 0.3 mm from the outer edge of the disk.     

Three-dimensional dynamics of a vortex array in rotating superfluid

This work studies numerically three-dimensional formation of a vortex array in a rotating cylindrical vessel. The formation process and the resulting equilibrium pattern are affected by pinning sites on the vessel’s bottom.     

Low-temperature effective electromagnetism in superfluid 3He-A

A general low-temperature effective action for the order parameter in the superfluid phase A of helium 3 is derived. In a symmetric case, when the Fermi velocity equals the transverse velocity of low energy fermionic quasiparticles, the action is the standard relativistic electromagnetic action.     

Flow-induced soliton lattice in superfluid 3He-A

It is shown that in the presence of superflow, υ_s, parallel to a strong magnetic field H (|H| ? 20 Oe), the uniform texture becomes unstable againts the formation of a one dimensional soliton lattice forυ_s ? υ_c2 (≈1 mm/s). The period of the resulting soliton lattice as well as the related NMR frequencies are determined as functions of υ_s.     

Abelian Chern-Simons term in superfluid 3He-A

We show in this paper that an Abelian Chern-Simons term is induced in (2 + 1)- and (3 + 1)-dimensional rotating superfluid ³He-A and that it plays an important role in its dynamics. Because U(1) symmetry is spontaneously broken in ³He-A, a Goldstone mode appears and contributes to the induced Chern-Simons term. We found that the coefficient of the Chern-Simons term, which is equivalent to Hall conductance, depends on an infra-red cut-off of the Goldstone mode, and that the orbital angular momentum of ³He-A in a cylinder geometry is derived from the Chern-Simons term.     

The effect of electric field on superfluid 3He-A

The effect of an electric field on the l? vector in the A phase of ³He is reexamined. The effect appears roughly by a factor 5 smaller than that predicted by Delrieu previously.