Theoretical investigations of superfluid helium-3 films
In this thesis I am presenting a theoretical study of superfluid 3He, spatially confined to a film geometry. Superfluidity of 3He in films was experimentally discovered about 20 years ago. By now there is clear evidence that not everything is understood about the physics of strongly confined 3He. There is a number of experiments that suggest new phenomena and possible new superfluid phases of 3 He in thin films.
We consider free films in the zero pressure environment. Liquid 3He is bounded on two sides by two infinite parallel surfaces. The quasiparticle reflection off the free interface of the film is specular. The substrate that supports the film, is modelled by Ovchinnikov boundary conditions for a fully diffuse surface, or by the specular boundary conditions for a smooth surface.
The spatial confinemet affects many different properties of systems with unconventional pairing. The problems that we consider in this work include the suppression of the order parameter and the transition temperature into the superfluid state, the thermodynamic properties of films with thickness D [special characters omitted] 700 nm, transitions between different phases as a function of film thickness and the existence of new superfluid states in 3He films.
From analysis of third sound modes we conclude that there is new physics or a new phase in films with D < 500 nm. This conclusion is also supported by a number of other experiments.
The results that we obtain show that the thin-film phase of superfluid 3He is gapless with density of states having a continuous band of low-energy excitations that appear due to quasiparticle scattering off a diffuse substrate. These excitations are the Andreev bound states formed near scattering surfaces. These excitations give rise to thermodynamic functions that have the low-temperature power-law behavior similar to that of the normal state functions. For example, the heat capacity of thin films should be linear in temperature, as compared with higher power laws of the bulk superfluid phases.
We found a new superfluid phase of 3He in films. The new phase breaks the translational invariance in the plane of the film. The phase diagram of superfluid 3He in films is modified by the presence of this phase. The new phase lies in the region between the planar and B-phases. Transition from the planar state is the second-order instability into a state with a simple harmonic periodicity in the plane of the film. The B-phase goes into the new phase by formation of a single domain wall in the film. This state is an example of phases that are not possible in the bulk, and is somewhat similar to the Fulde-Ferrel-Larkin-Ovchinnikov state in supercoductors.