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Journal of Physics Condensed Matter

Localized fermions on quantized vortices in superfluid3He-B

Григорий Ефимович Воловик

Published Jan 21, 1991• 15 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/3/3/010

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We study a single quantized vortex in the fermionic component of a mixture of Fermi superfluid and Bose-Einstein condensate. As the density ratio between the boson and the fermion components is tuned, we identify a transition in the vortex-core structure, across which fermions in the vortex core become completely depleted even in the weak-coupling Bardeen-Cooper-Schrieffer regime. This is accompanied by changes in key properties of the vortex state, as well as by the localization of the Bose-Einstein condensate in the vortex core. The transition in the vortex-core structure can be experimentally probed in Bose-Fermi superfluid mixtures by detecting the size and visibility of the vortices.
We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.
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 .
We investigate a magnetic susceptibility of vortices in the B phase of multicomponent triplet superfluid 3He^{3}\text{H}\text{e}3He focusing on a contribution of bound fermionic states localized within vortex cores. Several order-parameter configurations relevant to different types of quantized vortices in 3He^{3}\text{H}\text{e}3He B are considered. It is shown quite generally that an ac magnetic susceptibility has a sharp peak at the frequency corresponding to the energy of interlevel spacing in the spectrum of bound fermions. We suggest that measuring of a magnetic resonance within vortex cores can provide a direct probe of a discrete spectrum of bound vortex-core excitations.
In order to clarify the structure of a singly quantized vortex in a superfluid fermion gas near the Feshbach resonance, we numerically solve the generalized Bogoliubov-de Gennes equation in the boson-fermion model. The superfluid gap, which contains contributions from both condensed fermion pairs and condensed bosons, is self-consistently determined, and the quasiparticle excitation levels bound in the vortex core are explicitly shown. We find that the boson condensate contributes to enhance the matter density depletion and the discreteness of localized quasiparticle spectrum inside the core. It is predicted that the matter density depletion and the discrete core levels are detectable in the vicinity of the BCS-Bose-Einstein condensation crossover point.