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arXiv:cond-mat/9606210 · Physical Review Letters

Comment on “Transverse Force on a Quantized Vortex in a Superfluid”

Григорий Ефимович Воловик

Published Nov 25, 1996• 17 citations
arXivHTMLPDF

Abstract

The result of Thouless, Ao and Niu (TAN), that the mutual friction parameter $d_\perp =0$, contradicts to the experiments made in rotating 3He-B by Manchester group. The Manchester group observed that $d_\perp <0$ at low temperature and approaches 1 at high temperature. The reason of the contradiction is that TAN did not take into account the Iordanskii force on the vortex and the spectral flow force, which comes from the anomaly related to the low-energy bound states of fermions in cores of quantized vortices. The Iordanskii force is responsible for the negative $d_\perp <0$ at low temperature, while due to the spectral flow $d_\perp$ approaches 1 at high temperature. Relation of the spectral flow anomaly with the paradoxes of the linear and angular momenta in gapless superfluids is discussed.

DOI
10.1103/physrevlett.77.4687

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The result of Thouless, Ao and Niu (TAN), that the mutual friction parameter d⊥=0d_\perp =0d⊥​=0, contradicts to the experiments made in rotating 3He-B by Manchester group. The Manchester group observed that d⊥<0d_\perp <0d⊥​<0 at low temperature and approaches 1 at high temperature. The reason of the contradiction is that TAN did not take into account the Iordanskii force on the vortex and the spectral flow force, which comes from the anomaly related to the low-energy bound states of fermions in cores of quantized vortices. The Iordanskii force is responsible for the negative d⊥<0d_\perp <0d⊥​<0 at low temperature, while due to the spectral flow d⊥d_\perpd⊥​ approaches 1 at high temperature. Relation of the spectral flow anomaly with the paradoxes of the linear and angular momenta in gapless superfluids is discussed.
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
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.
Abstract There are four forces acting on a vortex moving with respect to normal and superfluid components of the liquid: three reactive forces (Magnus, Iordanskii, and Kopnin forces) and the Stokes friction force. The Iordanskii force comes from the analog of the gravitational Aharonov–Bohm effect and are discussed later in the book. The Kopnin or spectral flow force appears only in fermionic superfluids. This chapter discusses the Kopnin force acting on a singular vortex. The origin of this force is the phenomenon of chiral anomaly, but as distinct from the force acting on continuous vortex discussed in Chapter 18, the Adler–Bell–Jackiw equation for chiral anomaly is not applicable. The anomaly is now related to the spectral flow of fermion zero modes in the vortex core, which is caused by motion of the vortex with respect to the normal component. The spectral flow leads to generation of linear momentum by a vortex core, which is then transferred to the normal component. This process is similar to the generation of baryonic charge by the cores of cosmic strings and serves as the analog of Callan–Harvey mechanism of cancellation of anomalies. The temperature dependence of the spectral flow force is obtained from solution of kinetic equation for fermion zero modes. The resulting force acting on a vortex has been measured in experiments on vortex dynamics in 3He-B. Existence of two forces in addition to conventional Magnus and friction forces — Iordanskii and Kopnin forces – has been verified.
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.
A non-dissipative force F nd acting on a vortex in Fermi superfluids and superconductors is calculated taking into account the spectral flow of fermion zero modes in the vortex core. The spectral-flow effect casts a new light on the problem of mutual friction in superfluids. We demonstrate that, for vortices in an isotropic system, the reactive mutual friction parameter D ' ( T ) is negative in the collisionless regime and it is positive in the hydrodynamic regime. This agrees with 3 He-B measurements, which thus give the experimental verification of the spectral-flow effect on the vortex dynamics.
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.