Coherent and Incoherent Vortex Flow States in Crossed Channels

We examine vortex flow states in periodic square pinning arrays with one row and one column of pinning sites removed to create an easy flow crossed channel geometry. When a drive is simultaneously applied along both major symmetry axes of the pinning array such that vortices move in both channels, a series of coherent flow states develop in the channel intersection at rational ratios of the drive components in each symmetry direction when the vortices can cross the intersection without local collisions. The coherent flow states are correlated with a series of anomalies in the velocity force curves, and in some cases can produce negative differential conductivity. The same general behavior could also be realized in other systems including colloids, particle traffic in microfluidic devices, or Wigner crystals in crossed one-dimensional channels. A wide variety of different types of vortex commensurability and dynamics can be realized in superconductors containing a periodic array of artificial pinning sites [1,2]. For fields at which the number of vortices is an integer multiple or rational fraction of the number of pinning sites, various types of vortex crystalline states occur which are associated with peaks in the critical current [1–7]. When there are more vortices than pinning sites, it is possible to have highly mobile interstitial vortices between vortices located at the pinning sites [2,5,8,9]. One-dimensional interstitial vortex motion between pinned vortices has been realized in systems with artificially fabricated weak pinning channels [10–13]. In these channel geometries, oscillations in the critical current and resistance can arise as a function of vortex density due to changes in the number of vortex rows moving within the channels. One aspect of vortex dynamics in periodic pinning arrays that has not been studied is vortex motion in systems where groups of pins are removed to form easy flow channels for interstitial vortices. In this work we examine the vortex motion in a system with a square pinning array where a row and a column of pins are removed to create intersecting channels. Vortices moving in the two channels are forced to interact at the channel intersection and can experience interference phenomena. Such a pinning geometry is very feasible to create experimentally, and the removal of individual pinning sites to create diluted pinning arrays has already been achieved [14]. Driving of vortices with crossed external drives and measurement of the perpendicular voltage responses has also been demonstrated [15]. We first study the effective matching field where the number of vortices equals the number of pinning sites in the unmodified square array and there are an equal number of interstitial vortices in each channel. We fix an external drive along one of the channel directions such that the vortices in that channel flow, and then slowly increase a second drive in the perpendicular direction, causing the vortices in the second channel to flow and interact with the moving vortices in the first channel. We find a series of transitions between disordered flows where the crossing vortices collide and ordered or coherent flows where the vortex motion through the intersection is synchronized and no collisions occur. The ordered phases create a series of anomalies in both velocity components. We also find negative differential resistance upon passing into and out of the ordered phases when vortices in one channel must slow down as the drive is increased in order to maintain an ordered flow. The overall structure of the transport curve is a devil’s staircase. It is distinct from the devil’s staircase structures found for vortices [16] or colloids [17, 18] moving over periodic pinning arrays. In Refs. [16–18], the velocity vector locks to symmetry directions of the pinning array, so the devil’s staircase structure occurs even in the limit of a single isolated particle moving over the array. In our system, the locking phases vanish in the limit of a single interstitial particle moving in the channels and are replaced by what we term a vortex gating effect in which the motion abruptly switches from one direction to the other. The dynamics of vortices in structured pin-