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Physical review. B, Condensed matter

Dynamics of vortices in neutral superfluids with noninteracting phonons

Jean-Yves Fortin

Published Mar 30, 2001• 1 citation
Publisher

Abstract

The transverse force on an isolated and moving vortex in a neutral superfluid at rest is evaluated at finite temperature in the case of noninteracting phonons. Using the Thouless, Ao, Niu (TAN) [Phys. Rev. Lett. 76, 3758 (1996)] general theory, we show that the transverse force is exactly equal to the superfluid Magnus force. We extend this theory in the case of a slowly moving vortex on a circular trajectory, and find an additional contribution coming from the centrifugal reaction. This term gives a negative vortex mass due to the phonons and diverges logarithmically at low frequency. The friction force is also evaluated for zero and finite frequencies, and compared with the scattering theory.

DOI
10.1103/physrevb.63.174502

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The transverse force on an isolated and moving vortex in a neutral superfluid at rest is evaluated at finite temperature in the case of noninteracting phonons. Using the Thouless, Ao, Niu (TAN) [Phys. Rev. Lett. 76, 3758 (1996)] general theory, we show that the transverse force is exactly equal to the superfluid Magnus force. We extend this theory in the case of a slowly moving vortex on a circular trajectory, and find an additional contribution coming from the centrifugal reaction. This term gives a negative vortex mass due to the phonons and diverges logarithmically at low frequency. The friction force is also evaluated for zero and finite frequencies, and compared with the scattering theory.
The transverse force acting on a quantized vortex in a superfluid is a problem that has eluded a complete understanding for more than three decades. In this Letter I calculate the superfluid velocity part of the transverse force in a way closely related to Laughlin's argument for the quantization of conductance in the quantum Hall effect. A combination of this result, the vortex velocity part of the transverse force found by Thouless, Ao, and Niu [Phys. Rev. Lett. 76, 3758 (1996)], and Galilean invariance shows that there cannot be a transverse force proportional to the normal fluid velocity.
We obtain the explicit expression of the friction on a moving quantized vortex, following the formulation of Thouless, Ao and Niu. It is shown that the friction on a moving vortex is sensitive to details but does not change the transverse force. We provide a general thermodynamic interpretation for the mutual independence of the transverse force and the friction. The friction is evaluated for the case of quasiparticle contributions in a clean fermionic superfluid, showing a new feature of logarithmic divergence. PACS#s: 67.40.Vs; 47.37.+8 In physical systems few qualities have generic values independent of material details. When such cases occur, usually there are either symmetry or topology reasons[1]. The controversy over dynamics of quantized vortices in superfluids or superconductors[2, 3] may be partly understood as due to the apparent conflict between the exact results[4, 5, 6] with the existence of
Recent work gives a transverse force on an isolated moving vortex which is independent of the normal fluid velocity, but it is widely believed that the asymmetry of phonon scattering by a vortex leads to a transverse force dependent on the relative motion of the normal component and the vortex. We show that a widely accepted derivation of the transverse force is in error, and that a careful evaluation leads to a much smaller transverse force. We argue that a different approach is needed to get the correct expression.
Adiabatic effective action for vortices in neutral and charged superfluids at zero temperature are calculated using the topological Landau-Ginzburg theory recently proposed by Hatsuda, Yahikozawa, Ao and Thouless, and vortex dynamics are examined. The Berry phase term arising in the effective action naturally yields the Magnus force in both neutral and charged superfluids. It is shown that in neutral superfluid there is only one degree of freedom, namely the center of vorticities, and the vortex energy is proportional to the sum of all vorticities so that it is finite only for the vanishing total vorticity of the system. On the other hand the effective mass and the vortex energy for a vortex in charged superfluids are defined individually as expected. The effects of the vortex core on these quantities are also estimated. The possible depinning scenario which is governed by the Magnus force and the inertial mass is also discussed.
The forces on the vortex, transverse to its velocity, are considered. In addition to the superfluid Magnus force from the condensate (superfluid component), there are transverse forces from thermal quasiparticles and external fields violating the Galilean invariance. The forces between quasiparticles and the vortex originate from interference of quasiparticles with trajectories on the left and on the right from the vortex like similar forces for electrons interacting with the thin magnetic-flux tube (the Aharonov-Bohm effect). These forces are derived for phonons from the equations of superfluid hydrodynamics, and for BCS quasiparticles from the Bogolyubov--de Gennes equations. The effect of external fields breaking Galilean invariance is analyzed for vortices in the two-dimensional Josephson junction array. The symmetry analysis of the classical equations for the array shows that the total transverse force on the vortex vanishes. Therefore the Hall effect which is linear in the transverse force is absent also. This means that the Magnus force from the superfluid component exactly cancels with the transverse force from the external fields. The results of other approaches are also brought together for discussion.
We obtain the explicit expression of the friction on a moving quantized vortex, following the formulation of Thouless, Ao and Niu. It is shown that the friction on a moving vortex is sensitive to details but does not change the transverse force. We provide a general thermodynamic interpretation for the mutual independence of the transverse force and the friction. The friction is evaluated for the case of quasiparticle contributions in a clean fermionic superfluid, showing a new feature of logarithmic divergence.