Disorder-induced power-law response of a superconducting vortex on a plane

Abstract

We report drive-response experiments on individual superconducting vortices on a plane, a realization for a 1+1-dimensional directed polymer in random media. For this we use magnetic force microscopy (MFM) to image and manipulate individual vortices trapped on a twin boundary in YBCO near optimal doping. We find that when we drag a vortex with the magnetic tip it moves in a series of jumps. As theory suggests the jump-size distribution does not depend on the applied force and is consistent with power-law behavior. The measured power is much larger than widely accepted theoretical calculations.While the dynamics of driven systems in ordered media are well understood, disorder gives rise to much more elaborate behavior. Particularly interesting are phenomena arising from the interplay between disorder and elasticity [1, 2] such as the conformations of polyelectrolytes [3] (e.g. polypeptides and DNA [4]), kinetic roughening of driven interfaces (e.g. wetting in paper [5,6], magnetic and ferroelectric domain wall motion [7][8][9][10], the growth of bacterial colony edges [5]), non-equilibrium effects that occur in randomly stirred fluids [11] and more. Superconducting vortices, in materials in which they behave like elastic strings, are among the most important examples of such systems [12]. Despite a dearth of direct experimental proof, these quantized whirlpools of supercurrent are considered textbook examples of the theory of directed polymers in random media (DPRM) [13][14][15], a foundation model for systems where disorder and elasticity compete. This model, that yields many results that are considered generic and universal, provides the backdrop for our experiment.Here we concentrate on vortices that are trapped on a twin boundary (TB), a planar defect in YBa 2 Cu 3 O 7−δ (YBCO) [16]. We cool the sample through the superconducting transition temperature T c in the presence of an external magnetic field H = Hẑ, which directs the curve along which vortices cross the sample. Figure 1a depicts a vortex away from a TB (V in Fig. 1a) that is free to meander in the d ⊥ = 2 directions perpendicular to H. For a vortex trapped on a TB (TBV in Fig. 1a) the meandering is limited to a plane, i.e. d ⊥ = 1. We concentrate on TB-vortices both because the reduced dimensionality makes data analysis simpler and, more importantly, because, unlike DPRM in higher dimensions, 1 + 1-DPRM is a tractable model [17].The path of a vortex across a sample is determined by the competition between elasticity and disorder: while meandering allows a vortex to lower the energy of the system by locating its core near defects, the associated stretching is limited by finite line tension κ [12]. As a result the unavoidable random disorder in a sample can make the optimal path for an isolated vortex elaborate. Despite this, DPRM theory provides many predictions for disorder-averaged quantities [18]. For example, the thermal and disorder averaged offset distance from the field axisẑ (∆) scales like a power-law given by the wandering exponent ζ(

Diamagnetic vortex barrier stripes in underdopedBaFe2(As1−xPx)2

“…In the latter we bring the tip so close to superconducting vortices that the force the tip exerts can move them away from the pinning site they are trapped in. This is useful because the way vortices move can reveal information that is not available to other surface sensitive techniques 25,57,59,60 . In surveillance mode we retract the tip far enough from the surface for the forces the tip exerts to be too weak to depin vortices in the sample.…”

“…Similar effects are common in vortex MFM 64 and are frequently considered a disadvantage of this technique. Here we used this ability deliberately 25,43,57,59 to attempt to drag vortices across stripes. To this end we cooled the sample in a field oriented to give attractive vortices.…”

“…When this happens the TB acts as a pinning site because of the reduced energetic cost of locating a vortex core on it. Such pinning behavior has been observed in the cuprates 13,14,16,21,25 where TBs also act as channels that are easy for vortices to move along, and hard for them to cross [17][18][19][20][21]25 . Other behavior is also possible.…”

“…TBs are not limited to FeSCs -they occur in many superconductors, including cuprates [13][14][15][16][17][18][19][20][21][22][23][24][25] , and are important for several reasons. In Fe-SCs their properties encode information about the nature of the superconducting phase and its competing orders [26][27][28] .…”

Driven Interfaces: From Flow to Creep Through Model Reduction

“…Extensions of the approach we have described could be interesting to understand the dynamics and jump statistics of driven vortices in superconductors presenting dislocation planes (experiments of [71]), in relation to the recent theoretical work of Ref. [72].…”