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We report an anomalous matching effect in MoGe thin films containing pairs ofcircular holes arranged in such a way that four of those pairs meet at eachvertex point of a square lattice. A remarkably pronounced fractional matchingwas observed in the magnetic field dependences of both the resistance and thecritical current. At the half matching field the critical current can be evenhigher than that at zero field. This has never been observed before forvortices in superconductors with pinning arrays. Numerical simulations withinthe nonlinear Ginzburg-Landau theory reveal a square vortex ice configurationin the ground state at the half matching field and demonstrate similarcharacteristic features in the field dependence of the critical current,confirming the experimental realization of an artificial ice system forvortices for the first time.

Realization of Artificial Ice Systems for Magnetic Vortices in a Superconducting MoGe Thin-film with Patterned Nanostructures