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Thin superconducting YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ films are patterned witha vortex-pin lattice consisting of columnar defect regions (CDs) with 180 nmdiameter and 300 nm spacing. They are fabricated by irradiation with 75 keVHe$^+$ ions through a stencil mask. Peaks of the critical current reveal thecommensurate trapping of vortices in domains near the edges of the sample. Uponramping an external magnetic field, the positions of the critical current peaksare shifted from their equilibrium values to lower magnetic fields in virginand to higher fields in field-saturated down-sweep curves, respectively. Basedon previous theoretical predictions, this irreversibility is interpreted as anonuniform, terrace-like critical state, in which individual domains areoccupied by a constant number of vortices per pinning site. Themagnetoresistance, probed at low current densities, is hysteretic and angledependent and exhibits minima that correspond to the peaks of the criticalcurrent. The minima's positions scale with the component of the magnetic fieldparallel to the axes of the CDs, as long as the tilted vortices can beaccommodated within the CDs. This behavior, different from unirradiated films,confirms that the CDs dominate the pinning.

superconductor science and technology/superconductor science and technology

Unconventional critical state in YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ thin  films with a vortex-pin lattice fabricated by masked He$^+$ ion beam  irradiation