Landau-Ginsburg equations for an anisotropic superfluid

Abstract

A discussion of an anisotropic ($p$ state) Fermi superfluid with a spatially varying order parameter is presented. We restrict ourself to the Landau-Ginzburg region and consider spatial variations governed by the linear gap equation. The kernel of the linearized gap equation is shown to be related to a current-current correlation function of quasiparticles in the normal state. This relation permits the calculation of the two coherence lengths ${\ensuremath{\xi}}_{L}$ and ${\ensuremath{\xi}}_{T}$ defined earlier in the framework of a phenomenological Landau-Ginzburg theory, and a discussion of boundary conditions for the order parameter at interfaces. A significant anisotropy in the coherence lengths is found (${\ensuremath{\xi}}_{L}=\sqrt{3}{\ensuremath{\xi}}_{T}$), which reflects itself in the nature of the supercurrents. The boundary conditions at specularly and diffusely reflecting surfaces lead us to expect that the vector $\stackrel{^}{l}$, which describes the orbital angular momentum of a Cooper pair in an "axial" state, is anchored normal to the walls. Some consequences of these results on various experimental problems (fourth sound, monodomain production, Josephson couplings, behavior in thin capillaries) are briefly discussed.