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arXiv:cond-mat/9603094 · TURKISH JOURNAL OF PHYSICS

Fermions on Quantized Vortices in Superfluids and Superconductors

Григорий Ефимович Воловик

Published Jan 1, 1996• 6 citations
arXivHTMLPDF

Abstract

The bound states of fermions in cores of quantized vortices in superconductors and Fermi superfluids and their influence on the vortex dynamics are discussed. The role of the spectral flow of the fermions through the gap nodes is emphasized.
DOI
10.55730/1300-0101.2551

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The quantized vortex in a superfluid or superconducting Fermi system may contain gapless fermionic excitations localized in the vortex core. The number of branches of the gapless excitations-fermionic zero modes-depends on the core structure and may change from 0 to epsilon F / Delta >>1. The author investigated the possibility of the existence of the fermionic zero modes localized in the cores of axisymmetric vs. vortices in superfluid 3 He-B. The zero modes exist if the core radius exceeds the coherence length.
We introduce a comprehensive theoretical framework for the fermionic superfluid dynamics, grounded on a local extension of the time-dependent density functional theory. With this approach, we describe the generation and the real-time evolution and interaction of quantized vortices, the large-amplitude collective modes, as well as the loss of superfluidity at high flow velocities. We demonstrate the formation of vortex rings and provide a microscopic description of the crossing and reconnection of quantized vortex lines in a fermion superfluid, which provide the mechanism for the emergence of quantum turbulence at very low temperatures. We observe that superfluidity often survives when these systems are stirred with velocities far exceeding the speed of sound.
Excitations in vortex cores in superconductors and other Fermi superfluids are single-particle excitations with a peculiar energy spectrum. These excitations are responsible for many important thermodynamic properties such as specific heat, London penetration length, etc. They also determine the dynamic characteristics of superconductors and superfluids through their interaction with vortices. Flux flow resistance, the Hall effect in type II superconductors and the mutual friction in superfluids are the most important phenomena which strongly depend on vortex core excitations. These phenomena determine the electromagnetic responses of type II superconductors and the hydrodynamic behaviour of superfluids and are of great significance for practical applications of superconducting devices and for understanding the most fundamental properties of correlated electrons and other Fermi particles. In this review we consider the dynamic properties of superconductors and superfluids and outline the basic ideas and results on the vortex dynamics in clean superfluid Fermi systems. The forces acting on moving vortices are discussed including the problem of the transverse force which was a matter of confusion for quite some time. We formulate the equations of the vortex dynamics, which include all the forces and the inertial term associated with excitations bound to the moving vortex.
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.