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arXiv:cond-mat/0012350

What can superconductivity learn from quantized vorticity in He-3 superfluids?

Григорий Ефимович Воловик, V. B. Eltsov, M. Krusius

Published Dec 19, 2000• 0 citations
arXivHTMLPDF

Abstract

In He-3 superfluids quantized vorticity can take many different forms: It can appear as distributed periodic textures, as sheets, or as lines. In the anisotropic He-3A phase in most cases the amplitude of the order parameter remains constant throughout the vortex structure and only its orientation changes in space. In the quasi-isotropic He-3B phase vortex lines have a hard core where the order parameter has reduced, but finite amplitude. The different structures have been firmly identified, based on both measurement and calculation. What parallels can be drawn from this information to the new unconventional superconductors or Bose-Einstein condensates?

DOI
10.48550/arxiv.cond-mat/0012350

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In He-3 superfluids quantized vorticity can take many different forms: It can appear as distributed periodic textures, as sheets, or as lines. In the anisotropic He-3A phase in most cases the amplitude of the order parameter remains constant throughout the vortex structure and only its orientation changes in space. In the quasi-isotropic He-3B phase vortex lines have a hard core where the order parameter has reduced, but finite amplitude. The different structures have been firmly identified, based on both measurement and calculation. What parallels can be drawn from this information to the new unconventional superconductors or Bose-Einstein condensates?
This doctoral thesis consists of experimental studies on rotating superfluid helium-3 at millikelvin temperatures. Superfluid 3He provides an example of ordered systems where quantum phenomena are visible on a macroscopic scale. The order parameter is described by a 3x3 complex matrix leading to different superfluid phases with different properties. The A and B phases support topologically different kinds of defects, most notably vortex lines. Vortex lines are most easily created and studied in uniform rotation. Because of quantum nature, the circulation around the vortices is quantized in units of κ0 = h/2m3.\n\nIn superfluid 3He nuclear magnetic resonance (NMR) provides a means to distinguish between different types of vortices and count them one by one. During the course of this work the sensitivity of the NMR spectrometer was improved by an order of magnitude, which enabled the direct measurement of the circulation of a vortex in the A phase that carries two circulation quanta (2κ0). Up to now the circulation of the known quantized vortex types in other quantum fluids, which include superfluid 4He, superconductors, and Bose-Einstein -condensates, has been singly quantized.\n\nOther NMR experiments reported in the thesis are: (1) The first qualitative measurements of vortex annihilation in the A and B phases of 3He. These measurements tell the lowest rotation velocity that stabilizes an array of vortex lines with a given number of vortices, and how it depends on the type of the defect. (2) Studies of vortex arrays with both singly and doubly quantized A phase vortex lines coexisting in the experimental container. 3He-A provides a unique system in which this kind of arrangement can be done. (3) In order to improve the vortex detection sensitivity in the B phase even further, the response of different nonlinear spin precession modes to superfluid-normal fluid counterflow was studied. A new mode, where the orbital angular momentum is oriented transverse to the external magnetic field, was found.
Quantized vorticity is a property of quantum fluids that has been widely studied in various types of superfluids, either with or without spin [77],[86],[87] and Chapter 6. Superfluids with a two component (spinor) order parameter are characterized by a different type of vortex than those found in conventional scalar superfluids [99]-[102]. This new type of vortex is the so called half quantum vortex (HQV). HQVs have lower energy with respect to full vortices and constitute the elementary excitations of spinor superfluids. When circumventing their core, the phase and the polarization vector experience a ±π rotation. In this sense, HQV can be understood as a half phase vortex combined with a half polarization vortex [99]. In 4He superfluids, the HQV cannot be formed as the spin degree of freedom is absent. However, in 3He [99],[100] or in triplet superconductors [101],[102], the order parameter has two or more components, so that the formation of HQV is possible. So far, experiments have not presented any direct evidence for HQV in 3He [103], while more reliable indications of existence of HQV have been reported in cuprate superconductors [104].
The authors consider the core structures of quantised vortex lines in Bose and Fermi superfluid systems. They emphasise the result that, within the core of a singly quantised vortex line in a Bose superfluid, there spontaneously appears a condensate of boson pairs in a relative d-wave state, instead of the normal fluid. Also, in the case of the singly quantised Abrikosov vortex line in a superconductor, instead of normal electrons there emerges a novel state of superconductivity, in which a condensate of bosons made of four fermions appears. In particular, they discuss these core structures as further examples for the flaring-out of the vortex singularity into higher dimensions, in analogy with the extended-space topology of the superfluid 3 He-B vortex core; they also relate this generic behaviour to the Laughlin state within the quantum Hall effect.
The static and dynamic properties of vortices in dipolar Bose-Einstein condensates (dBECs) can be considerably modified relative to their nondipolar counterparts by the anisotropic and long-ranged nature of the dipole-dipole interaction. Working in a uniform dBEC, we analyze the structure of single vortices and the dynamics of vortex pairs, investigating the deviations from the nondipolar paradigm. For a straight vortex line, we find that the induced dipolar interaction potential is axially anisotropic when the dipole moments have a nonzero projection orthogonal to the vortex line. This results in a corresponding elongation of the vortex core along this projection as well as an anisotropic superfluid phase and enhanced compressibility in the vicinity of the vortex core. Consequently, the trajectories of like-signed vortex pairs are described by a family of elliptical and oval-like curves rather than the familiar circular orbits. Similarly for opposite-signed vortex pairs their translation speeds along the binormal are found to be dipole-interaction dependent. We expect that these findings will shed light on the underlying mechanisms of many-vortex phenomena in dBECs such as quantum turbulence, vortex reconnections, and vortex lattices. Published by the American Physical Society 2024
Quantized vortices play a key role in superfluidity and superconductivity. We have observed the formation of highly ordered vortex lattices in a rotating Bose-condensed gas. These triangular lattices contained over 100 vortices with lifetimes of several seconds. Individual vortices persisted up to 40 seconds. The lattices could be generated over a wide range of rotation frequencies and trap geometries, shedding light on the formation process. Our observation of dislocations, irregular structure, and dynamics indicates that gaseous Bose-Einstein condensates may be a model system for the study of vortex matter.