Vortex Sheet in Superfluid ³He-A

A new state of rotating superfluid ³He-A has been found experimentally and explained theoretically. Usually superfluids respond to rotation by creating an array of vortex lines. The lines are parallel to the rotation axis, and the circulation around them is quantized. The new state consists of a vortex sheet, where the vorticity is located on a 2 dimensional sheet instead of 1 D lines. In contrast to other superfluids, the sheet is stable in the A phase because of its internal structure. The sheet has as a backbone a topologically stable domain wall called soliton. Non-singular vorticity is then bound to the soliton. The structure of the vortex sheet is calculated by means of variational approximations. This allows calculation of the frequency shifts and the amplitudes of NMR satellite peaks. The calculations are in good agreement with experiments. The vortex sheet is one out of six different vortex types in superfluid ³He-A.

In a rotating container the vortex sheet is parallel to the rotation axis z but in the x-y plane it folds to equidistant layers. The distance between the layers is larger but on the same order of magnitude as the distance between vortex lines. The folding of the vortex sheet is studied by numerical simulations. The lines where the vortex sheet touches the side wall are essential for the response of the sheet to changes in the rotation velocity. The figure here has only one sheet and two connection lines. By modulating the rotation velocity it is possible to create a state that has more connection lines, and thus faster response to changes in the rotation velocity.

A different type of vortex sheet occurs on the interface of A and B phases.

Publications

• Ü. Parts, E.V. Thuneberg, G.E. Volovik, J.H. Koivuniemi, V.M.H. Ruutu, M. Heinilä, J.M. Karimäki, and M. Krusius: Vortex sheet in rotating superfluid ³He-A, Phys. Rev. Lett. 72, 3839 (1994).
• Ü. Parts, J.H. Koivuniemi, M. Krusius, V.M.H. Ruutu, E.V. Thuneberg, and G.E. Volovik: Bragg reflection from equidistant planes of vortex-sheets in rotating ³He-A, Pis'ma Zh. Eksp. Teor. Fiz. 59, 816 (1994) [JETP Lett. 59, 851 (1994)].
• E.V. Thuneberg: Introduction to the vortex sheet of superfluid ³He-A, Physica B 210, 287 (1995).
• M.T. Heinilä and G.E. Volovik, Bifurcations in the growth process of a vortex sheet in rotating superfluid, Physica B 210, 300 (1995).
• Ü. Parts, V.M.H. Ruutu, J.H. Koivuniemi, M. Krusius, E.V. Thuneberg, and G.E. Volovik: Measurements on the vortex sheet in rotating superfluid ³He-A, Physica B 210, 311 (1995).
• E.V. Thuneberg: Vortex sheet in superfluid ³He-A, Czechoslovak J. Phys. 46 Suppl., 2937 (1996).
• O.V. Lounasmaa and E. Thuneberg: Vortices in rotating superfluid ³He, Proc. Natl. Acad. Sci. USA 96, 7760 (1999).
• V.B. Eltsov, R. Blaauwgeers, M. Krusius, J.J. Ruohio, and R. Schanen: Dynamic response of the equilibrium vortex sheet in rotating ³He-A, Physica B 284-288, 252 (2000).
• V.B. Eltsov, R. Blaauwgeers, N.B. Kopnin, M. Krusius, J.J. Ruohio, R. Schanen, and E.V. Thuneberg: Transitions from vortex lines to sheets: interplay of topology and dynamics in an anisotropic superfluid, Phys. Rev. Lett. 88, 65301 (2002), cond-mat/0109092.

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