Fusion rules and vortices in $p_x+ip_y$ superconductors

Details Fusion rules and vortices in $p_x+ip_y$ superconductors Fusion rules and vortices in $p_x+ip_y$ superconductors

2005-05-20

arxiv.org/abs/cond-mat/0505515v3

Phys. Rev. B 73, 014505 (2006)

Physics

Condensed Matter

Superconductivity

23 pages, REVTEX4

Scientific paper

10.1103/PhysRevB.73.014505

The "half-quantum" vortices ($\sigma$) and quasiparticles ($\psi$) in a two-dimensional $p_x+ip_y$ superconductor obey the Ising-like fusion rules $\psi\times \psi=1$, $\sigma\times \psi=\sigma$, and $\sigma\times \sigma= 1+\psi$. We explain how the physical fusion of vortex-antivortex pairs allows us to use these rules to read out the information encoded in the topologically protected space of degenerate ground states. We comment on the potential applicability of this fact to quantum computation. Modified 11/30/05 to reflect manuscript as accepted for publication. Includes corrected last section.

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