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The transverse (Hall) voltage in thin films of the high-temperaturesuperconductor YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ with an artificial periodicpinning array is investigated. Columnar defect regions along thecrystallographic $c$ axis, in which superconductivity is suppressed, arecreated by irradiation with He$^+$ ions through a silicon stencil mask. Thecommensurate arrangement of magnetic flux quanta with the artificial defectlattice is confirmed by maxima of the critical current and minima of theresistance, respectively. The magnetic field dependence of the transversevoltage reveals a commensurability effect characterized by a narrow peak of theHall coefficient with reversed polarity compared to the background signal. Thissignature of vortex matching disappears at larger vortex velocitiessubstantiating its close connection with enhanced pinning of vortices at theperiodic pinning landscape.

physical review. b./physical review. b

Transverse vortex commensurability effect and sign change of the Hall  voltage in superconducting YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ thin films with a  nanoscale periodic pinning landscape