The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
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Josephson Effects and Textural Dynamics in Superfluid Helium Three

Janne Viljas

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics for public examination and debate in Auditorium F1 at Helsinki University of Technology (Espoo, Finland) on the 4th of June, 2004, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-7009-9)   [511 KB]
Dissertation is also available in print (ISBN 951-22-7008-0)

Abstract

As liquid helium three is cooled to temperatures below 1 mK, it becomes a superfluid. In this state it is able to support dissipationless mass supercurrents. Analogously to what happens for superconducting metals, when two volumes of the superfluid are brought into contact through a "weak link", phenomena known as Josephson effects arise. These are associated with supercurrents which depend periodically on the difference between the quantum-mechanical phases of the superfluid order parameters. However, the order parameter in helium three is far more complicated than that in conventional superconductors, and this gives rise to new features in the physics of weak links.

In this thesis we present theoretical and numerical considerations of the Josephson effects and dissipative currents in weak links of superfluid helium three, in particular its B phase. We use our results to analyze recent experiments.

In the case of small point contacts, we calculate the equilibrium current-phase relations, as well as the dissipative currents due to multiple Andreev reflections when the contact is biased by a pressure head. These calculations are made using quasiclassical theory. We take self-consistently into account the effects of microscopically rough surfaces on the order parameter, which is important for obtaining quantitatively correct results. For apertures whose sizes are on the order of the temperature-dependent coherence length, we compute current-phase relations using Ginzburg-Landau theory. In this case we also consider weak links involving the superfluid A phase. Using a hydrodynamical approach to the B phase, we also consider large arrays of apertures, where we introduce the new concept of "anisotextural" Josephson effect. This effect depends crucially on the presence of the spin-orbit degrees of freedom in the order parameter, and is not possible in conventional superconductors. We use this concept to interpret experiments made with array-type weak links, where so-called "pi-states" and unexpected dissipation effects were found.

This thesis consists of an overview and of the following 6 publications:

  1. Viljas J. K. and Thuneberg E. V., 1999. Theory of the π state in 3He Josephson junctions. Physical Review Letters 83, number 19, pages 3868-3871. © 1999 American Physical Society. By permission.
  2. Viljas J. K. and Thuneberg E. V., 2002. Pinhole calculations of the Josephson effect in 3He-B. Physical Review B 65, pages 064530 : 1-19. © 2002 American Physical Society. By permission.
  3. Viljas J. K. and Thuneberg E. V., 2002. Equilibrium simulations of 2D weak links in p-wave superfluids. Journal of Low Temperature Physics 129, numbers 5-6, pages 423-471.
  4. Viljas J. K. and Thuneberg E. V., 2003. Stability of A-B phase boundary in a constriction. Physica B 329-333, pages 86-87. © 2003 Elsevier Science. By permission.
  5. Viljas J. K. and Thuneberg E. V., 2004. Dissipative currents in superfluid 3He-B weak links. Journal of Low Temperature Physics 134, numbers 1-2, pages 743-748.
  6. Viljas J. K. and Thuneberg E. V., 2004. Dissipative currents in superfluid 3He weak links. Helsinki University of Technology, Low Temperature Laboratory publications, Report TKK-KYL-011. Physical Review Letters, submitted for publication.

Keywords: superfluidity, Josephson effect, helium-3, texture, quasiclassical theory

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© 2004 Helsinki University of Technology

Last update 2011-05-26