Edge mass current and the role of Majorana fermions in A-phase superfluid 3He

The total angular momentum associated with the edge mass current flowing at the boundary in the superfluid He-3 A phase confined in a disk is proved to be L = Nh/2, consisting of L-MJ = Nh from the Majorana quasiparticles (QPs) and L-cont = -Nh/2 from the continuum state. We show this based on an analytic solution of the chiral order parameter for the quasiclassical Eilenberger equation. Important analytic expressions are obtained for mass current, angular momentum, and density of states (DOS). Notably the DOS of the Majorana QPs is exactly N-0/2 (N-0: normal state DOS) responsible for the factor 2 difference between L-MJ and L-cont. The current decreases as E-3 against the energy E, and L(T) alpha -T-2. This analytic solution is fully backed up by numerically solving the Eilenberger equation. We touch on the so-called intrinsic angular momentum problem.