Controllable step motors and rectifiers of magnetic flux quanta using periodic arrays of asymmetric pinning defects

We study the transport of vortices in superconductors with regular arrays of asymmetric pinning wells when applying an alternating electrical current. The asymmetric traps are modelled by the superposition of two interpenetrating square lattices of weak and strong pinning centers with separation smaller than the lattice constant. We show that this system can induce a net rectifying or diode effect for the vortex motion, including collective step-motor-type dynamics, where many vortices move forward a controlled and exact number of pin-lattice spacings at each cycle of the ac driving force. This system exhibits a remarkable net dc response with striking sawtooth-type oscillations. The net dc voltage response V-dc of the ac-driven vortices versus both the half period P and the amplitude F-L of the "square wave" ac drive has been detailed in the present work. The influence of the equilibrium thermal noise, the shift between the two pinning sublattices, the degree of translational and orientational disorder, and the size of the simulation system on the V-dc response of the vortex motion at ac drive has also been addressed. Devil staircase and Arnold's tongue structures are revealed. We also analytically derive all the key features of our numerical results. This system provides a very controllable stepmotor for the control of collective motion. Our results apply mutatis mutandis to arrays of Josephson junctions, colloidal systems with optical traps, Wigner crystals, and any system with repelling movable objects that can be pinned by a lattice of traps.