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Superconducting Phase with Fractional Vortices in the Frustrated Kagome Wire Network at f=1/2

In classical XY kagome antiferromagnets, there can be a novel low temperature phase where $ψ^3=e^{i3θ}$ has quasi-long-range order but $ψ$ is disordered, as well as more conventional antiferromagnetic phases where $ψ$ is ordered in various possible patterns ($θ$ is the angle of orientation of the spin). To investigate when these phases exist in a physical system, we study superconducting kagome wire networks in a transverse magnetic field when the magnetic flux through an elementary triangle is a half of a flux quantum. Within Ginzburg-Landau theory, we calculate the helicity moduli of each phase to estimate the Kosterlitz-Thouless (KT) transition temperatures. Then at the KT temperatures, we estimate the barriers to move vortices and effects that lift the large degeneracy in the possible $ψ$ patterns. The effects we have considered are inductive couplings, non-zero wire width, and the order-by-disorder effect due to thermal fluctuations. The first two effects prefer $q=0$ patterns while the last one selects a $\sqrt{3}\times\sqrt{3}$ pattern of supercurrents. Using the parameters of recent experiments, we conclude that at the KT temperature, the non-zero wire width effect dominates, which stabilizes a conventional superconducting phase with a $q=0$ current pattern. However, by adjusting the experimental parameters, for example by bending the wires a little, it appears that the novel $ψ^3$ superconducting phase can instead be stabilized. The barriers to vortex motion are low enough that the system can equilibrate into this phase.