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

Abstract

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.

Vortex configurations and critical parameters in superconducting thin films containing antidot arrays: Nonlinear Ginzburg-Landau theory

“…In this respect, arrays of microholes (antidots) 1,2,3,4,5,6,7,8,9,10,11,12 and submicron magnetic dots, 13,14,15 have been studied, as their presence in the SC film strongly modifies the vortex structure compared to the one in non-patterned films. 16,17 Direct imaging experiments, 1 magnetization and transport measurements, 2,3,4,5 and theoretical simulations 18,19,20,21,22 of vortex structures in samples with periodic pinning centers have shown that the vortices form highly ordered configurations at integer H n = nΦ 0 /S and at some fractional H p/q = p q Φ 0 /S (n,p,q being integers) matching fields, where Φ 0 = hc/2e = 2.07 · 10 −7 Gcm 2 is the flux quantum, and S is the area of the primitive cell of the artificial lattice. This remarkable variety of stabilized vortex lattices may even be broadened by multiple possible degeneracies.…”

“…For example, extensive molecular dynamics simulations 18,19,20,21,22 in the London limit have been performed in an attempt to calculate the vortex structure and their dynamics in a periodic pinning potential. Although the general behavior of vortex lattices was accurately described, made approximations are valid only in certain range of parameters.…”

Rectification and flux reversals for vortices interacting with triangular traps

“…Vortex ratchets can be created via asymmetric periodic pinning lines [9,10], asymmetric channels, or the asymmetry introduced by multiple ac drives in a system with a symmetric substrate [11,12]. Ratchets constructed of periodic twodimensional (2D) arrays of asymmetric pinning sites have also been proposed [13]. Recently, both positive and negative vortex rectification have been experimentally realized in periodic arrays of triangular pinning sites [15].…”

“…Much of the physics of vortices interacting with periodic pinning is also observed for repulsively interacting colloids in periodic optical trap arrays [6][7][8]. In addition to the basic science issues, vortices interacting with periodic pinning arrays are relevant to possible technological applications of superconductors, such as critical current enhancement or controlled motion of flux for new types of devices.Several methods have been proposed for using periodic pinning or controlled disorder in superconductors to create vortex ratchets, rectifiers, and logic devices [9][10][11][12][13]. As in general ratchet systems, which can be deterministic or stochastic in nature [14], a vortex ratchet transforms an ac input into a dc response.…”

“…Several methods have been proposed for using periodic pinning or controlled disorder in superconductors to create vortex ratchets, rectifiers, and logic devices [9][10][11][12][13]. As in general ratchet systems, which can be deterministic or stochastic in nature [14], a vortex ratchet transforms an ac input into a dc response.…”