Transitions from vortex lines to sheets: interplay of topology and dynamics in an anisotropic superfluid

In isotropic macroscopic quantum systems vortex lines can be formed while in anisotropic systems also vortex sheets are possible. Based on measurements of superfluid 3He-A, we present the principles which select between these two competing forms of quantized vorticity: sheets displace lines if the frequency of the external drive exceeds a critical limit. The resulting topologically stable state consists of multiple vortex sheets and has much faster dynamics than the state with vortex lines.     

Composite defect extends analogy between cosmology and 3He

Spin-mass vortices have been observed to form in rotating superfluid 3He-B, following the absorption of a thermal neutron and a rapid transition from the normal to the superfluid state. The spin-mass vortex is a composite defect which consists of a planar soliton (wall) which terminates on a linear core (string). This observation fits well within the framework of a cosmological scenario for defect formation, known as the Kibble-Zurek mechanism. It suggests that in the early Universe analogous cosmological defects might have formed.     

Measurements on the vortex sheet in rotating superfluid He-A

When a cylindrical container filled with superfluid ³He---A is rotated around its symmetry axis, several different configurations of quantized vorticity are possible: which of them will be preferred depends on the specifics how the rotating state is formed. The most unusual is the vortex sheet, a domain wall in the order parameter texture into which vortex lines are confined. This metastable structure has the lowest critical velocity of formation if a domain wall with the appropriate orientation is already present in the container. In this case the vortex sheet becomes the preferred rotating state which provides the solid-body rotation of the superfluid component on an averaged scale. Its presence can be identified from the cw NMR spectrum which samples the order parameter texture. Here the experimental properties of the vortex sheet are reviewed, as deduced from NMR measurements.     

The overlap matrix and the Slater-Koster interpolation scheme

The usual assumption of a unit overlap matrix in the LCAO interpolation scheme of Slater and Koster leads to an inconsistency, which is discussed in general terms and demonstrated for the layered 1T-polytype of the semiconductor ZrS₂.     

Annihilation of quantized vortex lines in rotating<Superscript>3</Superscript>He-A

The maximum number of vortex lines at a given angular velocity Ω is obtained during deceleration when vortices annihilate at the wall of the container. The width of the vortex-free region in the decelerated state has been measured by cw NMR for vortex lines with singular and continuous core structures. It corresponds to the limit of stability of peripheral vortices for single and double quantization respectively.     

Twisted vortex state

We study a twisted vortex bundle where quantized vortices form helices circling around the axis of the bundle in a "force-free" configuration. Such a state is created by injecting vortices into a rotating vortex-free superfluid. Using continuum theory we determine the structure and the relaxation of the twisted state. This is confirmed by numerical calculations. We also present experimental evidence of the twisted vortex state in superfluid 3He-B.     

Vortex arrays of coexisting singly and doubly quantized vortex lines in<Superscript>3</Superscript>He-A

In superfluid³He-A singly and doubly quantized vortex lines can coexist in a rotating container. We measure with NMR techniques the radial distribution of the two vortex types in an array of vortex lines. The radial composition is found to depend on the procedure by which the array has been formed. The result shows that in superfluid³He the energy barriers separating different configurations of the vortex array are inpenetrably high for a metastable state to relax.