A half-quantum vortex for spinful fermions is equivalent to a single-quantum vortex of spinless fermions? in a $p$-wave superconductor

Question

Reference: "Non-abelian statistics of half-quantum vortices in p-wave superconductors" D. A. Ivanov Phys. Rev. Lett. 86, 268 (2001)
https://doi.org/10.1103/PhysRevLett.86.268, journal version.

This free access paper (only in PRL version not arxiv version) says a confusing tongue twister statement:

(1) "a half-quantum vortex for spinful fermions is equivalent to a single-quantum vortex in a p-wave superconductor of spinless fermions."

• Should this statement be written really as instead:

(2) "a half-quantum vortex for spinful fermions in a p-wave superconductor is equivalent to a single-quantum vortex of spinless fermions in a p-wave superconductor"?

• How to make sense the statement (1) or (2), together with the title of paper: "half-quantum vortices in p-wave superconductors?"

• why is this true? What counts as a half-quantum vortex vs a single-quantum vortex? Is that a $\pi$ versus $2 \pi$ flux? Is that in a unit of $hc/e$ versus $hc/2e$? Also should the p-wave superconductor already have the spinful fermions? should why spinless fermions in a p-wave superconductor?

• Does a usual BCS $Z_2$ gauged superconductor have a half-quantum vortex or a single-quantum vortex? Is that a $\pi$ or a $2 \pi$ flux? Is that in a unit of $hc/e$ versus $hc/2e$?

This post imported from StackExchange Physics at 2020-12-15 17:03 (UTC), posted by SE-user annie marie heart