BROKEN TIME-REVERSAL SYMMETRY OF ANISOTROPIC SUPERFLUIDITY

Broken time-reversal (T) symmetry of anisotropic superfluidity implies topological change of the whole Fermi sphere. An infinite string pierces through the Fermi sphere; the phase of the pair state \k, -k]s is multivalued around it; and at T=0, the one-particle occupation number n(s)(k) vanishes on the string. Through these observations, this paper settles the problem of the intrinsic orbital angular momentum in He-3-A: The momentum density at T=0 is given by g=N(s)Mv(s)+(1/4)delx(N(s)hl)BAR -(h/2)C0l(l.delx1)BAR with C0=0, namely, the third term is absent due to n(s)(k)=0 for k//1. The process reveals that the Green's function approach based on the plane wave expansion fails to describe the topological change. Also, the conclusion raises several basic problems such as the divergence of H(c2) for T-breaking superconductivity. Finally, this paper presents a principle connecting the magnetic field with the phase singularity of the wave function. Its implications to the charged-anyon model and the Dirac monopole are also discussed.