Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortices in a $p_x+i{p}_y$ superconductor

We propose a simple way to stabilize half-quantum vortices in superconducting strontium ruthenate, assuming the order parameter is of chiral $p_x+i{p}_y$ symmetry, as is suggested by recent experiments. The method, first given by Salomaa and Volovik in the context of Helium-3, is very naturally suited for strontium ruthenate, which has a layered, quasi-two-dimensional, perovskite crystal structure. We propose possible experiments to detect their non-Abelian braiding statistics. These experiments are of potential importance for topological quantum computation.

Figure 1

In the experimental geometry depicted above, a thin film of ${\mathrm{Sr}}_2\mathrm{Ru}{\mathrm{O}}_4$ has a central hole with a flux $\Phi$ through it. When an electrical current flows in the $y$ direction, depinned vortices flow in the $x$ direction. This generates a voltage drop in the $x$ direction. If the motion of a vortex is coherent, then there will be interference between trajectories that go around either side of the hole. The nature of this interference will depend strongly on whether the number of half-quantum vortices in the hole is odd or even.