Superconducting phase with fractional vortices in the frustrated kagomé wire network at f=1/2

In classical XY kagomé antiferromagnets, there can be a low-temperature phase where ψ³=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 kagomé 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 the effects that lift the large degeneracy in the possible ψ patterns. The effects we have considered are inductive couplings, nonzero 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 √3 × √3 pattern of supercurrents. Using the parameters of recent experiments, we conclude that at the KT temperature, the nonzero 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 ψ³ superconducting phase can instead be stabilized. The barriers to vortex motion are low enough that the system can equilibrate into this phase.