The planar phase of superfluid helium-3

Abstract

The introduction to this thesis reviews the theory of anisotropic superfluid phases of liquid He-3. After an initial discussion of Landau's theory of the Fermi-liquid, the concept of Cooper-pairing is put forward and incorporated in the B. C. S theory of anisotropic superfluids. Special attention is then focussed on the Ginzburg-Landau region, close to the transition temperature, where the total free energy comprising of the bulk, dipole-dipole and bending energies can be expanded in terms of an order parameter.

An attempt is then made to calculate the most general order parameter for the relatively unknown Planar phase of He-3. Having achieved this, singular and non-singular textures (including solitons) are classified using topological homotopy group methods. The effects of an applied magnetic field and of boundary conditions at the walls of the container are also discussed.Whereas topology only serves as a useful tool to indicate the type of textures which may occur in the Planar phase, a more detailed treatment, to establish their existence, involves the application of Euler-Lagrange equations for local minima.

The question of stability is then resolved by looking at two different types of perturbation. The first involves setting up the equations for spin-dynamics and performing small deviations away from the minimum of the dipole-dipole energy enabling, for example, N. M. R frequencies of different textures to be found. The second type is thermal, which does not result in such a profound deviation, but nevertheless yields distinct resonance frequencies. Next, the power spectra arising from N. M. R experiments is calculated with the purpose of rigorously identifying each type of texture.

The Planar phase can also exhibit surface and magnetic solitons. The detailed form of the latter is calculated by modifying the order parameter to includesurface effects, and performing a variational calculation on the total surface free energy, in a parallel plate geometry. In the case of magnetic solitons the contribution of a static magnetic field has to be considered. This, together with the bending energy, is again minimised by a variational calculation. Having established the detailed form of these structures, their N. M. R frequencies and power spectra are calculated.

Finally, attention is focussed on trying to calculate the attenuation of zero sound propagating in a uniform texture of the Planarphase. The work is restricted to the collisionless regime and is undertaken using the concepts of Kinetic Theory as opposed to the method of Green's functions.