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  1. ; ; (, Physical Review B: Solid state)
    We simulate the motion of a commensurate vortex lattice in a periodic lattice of artificial circular pinning sites having different diameters, pinning strengths, and spacings using the time-dependent Ginzburg-Landau formalism. Above some critical DC current density Jc, the vortices depin, and the resulting steady-state motion then induces an oscillatory electric field E (t) with a defect "hopping" frequency f0, which depends on the applied current density and the pinning landscape characteristics. The frequency generated can be locked to an applied AC current density over some range of frequencies, which depends on the amplitude of the DC as well as the AC current densities. Both synchronous and asynchronous collective hopping behaviors are studied as a function of the supercell size of the simulated system and the (asymptotic) synchronization threshold current densities determined. 
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    Free, publicly-accessible full text available December 21, 2025