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

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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
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