Edge mass current and roles of Majorana Fermions in superfluid 3He A-phase

TL;DR

This paper analytically and numerically investigates the edge mass current and angular momentum in superfluid 3He A-phase, highlighting the role of Majorana quasiparticles and their contribution to the total angular momentum.

Contribution

It provides an exact analytic solution for the edge mass current and angular momentum in superfluid 3He A-phase, emphasizing the specific role of Majorana quasiparticles.

Findings

Majorana quasiparticles contribute Nħ to angular momentum.

The density of states for Majorana QPs is exactly half of the normal state.

The edge current decreases as E^{-3} with energy, and angular momentum scales as -T^2.

Abstract

The total angular momentum associated with the edge mass current flowing at the boundary in the superfluid $^3$He A-phase confined in a disk is proved to be $L=N\hbar/2$, consisting of $L^{\rm MJ}=N\hbar$ from the Majorana quasi-particles (QPs) and $L^{\rm cont}=-N\hbar/2$ from the continuum state. We show it based on an analytic solution of the chiral order parameter for quasi-classical 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 $L^{\rm MJ}$ and $L^{\rm cont}$. The current decreases as $E^{-3}$ against the energy $E$, and $L(T) \propto -T^2$. This analytic solution is fully backed up by numerically solving the Eilenberger equation. We touch on the so-called intrinsic angular momentum problem.