Angular Momentum of Anisotropic Superfluids at Finite Temperatures

With proper care on the boundary conditions, the total orbital angular momentum L _z at finite temperatures is microscopically calculated for the Anderson-Brinkman-Morel state in a cylinder with axial symmetry about the z axis, i.e. the textures considered by McClure and Takagi at T =0. The pairing in this geometry occurs between m and 1- m one-particle states, where m denotes the axial quantum number. It is found that L _z decreases from its zero temperature value \(\frac{\hbar}{2} {\cal N}\), with N the total particle number, in the same way as the components of the superfluid density tensor. Responsible for this reduction is identified to be the phase shift between m and 1- m quasiparticle states caused by the difference in the centrifugal potentials. This fact implies that the plane-wave representation is not suitable for the problem.