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Physical Review Letters

Vortices with spontaneously broken axisymmetry in B3

M.M. Salomaa, Григорий Ефимович Воловик

Published Jan 27, 1986• 158 citations
Publisher

Abstract

This paper reports the discovery of a new breaking of symmetry of the quantized vortex lines in superfluid $^{3}\mathit{B}$: Vortices with broken axisymmetry are found energetically more favorable than any of the axisymmetric ones in the weak-coupling limit. Based on our extensive numerical minimization of the vortex free-energy functional, we identify the vortices occurring in rotating $^{3}\mathit{B}$ at low pressures as v vortices having---in addition to broken space parity P---also broken axisymmetry Q with the nonaxisymmetry quantum number \ensuremath{\Vert}Q\ensuremath{\Vert}=2, and with superfluid core in the axiplanar state.

DOI
10.1103/physrevlett.56.363

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This paper reports the discovery of a new breaking of symmetry of the quantized vortex lines in superfluid 3B^{3}\mathit{B}3B: Vortices with broken axisymmetry are found energetically more favorable than any of the axisymmetric ones in the weak-coupling limit. Based on our extensive numerical minimization of the vortex free-energy functional, we identify the vortices occurring in rotating 3B^{3}\mathit{B}3B at low pressures as v vortices having---in addition to broken space parity P---also broken axisymmetry Q with the nonaxisymmetry quantum number \ensuremath{\Vert}Q\ensuremath{\Vert}=2, and with superfluid core in the axiplanar state.
We present experimental proof that in rotating 3B^{3}\mathit{B}3B the vortex-core transition temperature TV{\mathit{T}}_{\mathit{V}}TV​ separates axisymmetric vortices above TV{\mathit{T}}_{\mathit{V}}TV​ from vortices with spontaneously broken axial symmetry below TV{\mathit{T}}_{\mathit{V}}TV​. The nonaxisymmetry is observed in the presence of coherent spin precession as a new soft Goldstone mode, manifested as oscillations and spiral twisting of the core anisotropy axis. These are driven by the precessing spin via spin-orbit coupling and lead to magnetic relaxation from viscous losses, which depend on vortex pinning.
A numerical solution of the Ginzburg-Landau equations for superfluid 3B^{3}\mathit{B}3B vortices gives the following results: The low-pressure vortex is a new ``double core vortex'' whose rotational symmetry around the vortex axis is broken. The high-pressure vortex is the v vortex. The theory gives a transition between these vortices which is in excellent agreement with experiments.
The pressure dependence of the vortex core in rotating 3B^{3}\mathit{B}3B is studied in the Ginzburg-Landau formalism with two distinct models of the strong-coupling corrections. The parametrization of Sauls and Serene [Phys. Rev. B 24, 183 (1981)] predicts a transition from a core with large magnetic moment below \ensuremath{\sim}10 bars to one with small magnetic moment for higher pressures, in qualitative agreement with experiments. The earlier one-parameter model of Brinkman, Serene, and Anderson predicts no such transition, with the core having a large moment for all values of the parameter \ensuremath{\delta}.
The core of the singly quantized nonaxisymmetric v -vortex in rotating 3 He- B is found to display novel topological structure: it is a bound pair of vortices with half-integer circulation . The topology for flaring-out of vorticity from the real space to the momentum space, due to boojums (nodes) on the Fermi surface, is discussed for both the axisymmetric and nonaxisymmetric v -vortices. This difference in topology may explain the physical nature of the observed first-order vortex-core transition in rotating superfluid 3 He- B .
This paper reports the discovery of a new vortex phenomenon in superfluid 3B^{3}\mathit{B}3B. A single filament of quantized vortex line precesses as a solid body around a wire extending along the axis of a cylinder. The precession frequency equals the angular velocity of the apparatus at which the presence of a single quantum of circulation minimizes the system's free energy. The period of precession is related to the circulation quantum and the dimensions of the apparatus. Thus a measurement of the precession period is an accurate determination of the quantum unit. We find \ensuremath{\kappa}=(1.020\ifmmode\pm\else\textpm\fi{}0.03)h/2m3{\mathit{m}}_{3}m3​, where m3{\mathit{m}}_{3}m3​ is the mass of the 3He^{3}\mathrm{He}3He atom.
We give a general review of recent developments in the theory of vortices in superfluids and superconductors, discussing why the dynamics of vortices is important, and why some key results are still controversial. We discuss work that we have done on the dynamics of quantized vortices in a superfluid. Despite the fact that this problem has been recognized as important for forty years, there is still a lot of controversy about the forces on and masses of quantized vortices. We think that one can get unambiguous answers by considering a broken symmetry state that consists of one vortex in an infinite ideal system. We argue for a Magnus force that is proportional to the superfluid density, and we find that the effective mass density of a vortex in a neutral superfluid is divergent at low frequencies. We have generalized some of the results for a neutral superfluid to a charged system.