Do Vortices Entangle?

Abstract

We propose an experiment for directly constructing and locally probing topologically entangled states of superconducting vortices which can be performed with present-day technology. Calculations using an elastic string vortex model indicate that as the pitch (the winding angle divided by the vertical distance) increases, the vortices approach each other. At values of the pitch higher than a maximum value the entangled state becomes unstable to collapse via a singularity of the model. We provide predicted experimental signatures for both vortex entanglement and vortex cutting. The local probe we propose can also be used to explore a wide range of other quantities. PACS: 74.25.Qt, 74.25.Sv The high superconducting transition temperatures of compounds such as YBa 2 Cu 3 O (7−δ) (YBCO) and BiSr 2 Ca 2 CuO 8 (BSCCO) lead to a very rich set of behaviors of the magnetic vortices which form inside the material in the presence of an applied magnetic field. Thermal fluctuations are significant over a wide range of the (H,T) phase diagram [1], causing the lattice of stiff vortex lines to melt well below T c . The nature of this molten state has remained a subject of intense debate.Since there can be significant thermally-induced wiggling along the length of the vortex in the liquid state, Nelson proposed that neighboring vortex lines may become entangled with each other, in analogy with a superfluidity transition in a boson system [2]. This entanglement could produce a dramatic increase in the viscosity of the vortex liquid [3][4][5], similar to that which occurs for entangled polymers. As a result, vortex pinning by random disorder in the sample would be enhanced, so that the resistivity would drop in the entangled state.In order for the vortices to entangle, it is crucial that neighboring lines not cut through each other easily [6] and reconnect into a disentangled state. Estimates of the cutting barrier vary widely [3,5,[7][8][9][10], ranging from 50k B T to of order k B T , leaving the question of whether vortices can easily cut in the liquid state unresolved. Numerical simulations performed in limits ranging from the low-field London regime to the high-field lowest Landau level regime have proven similarly ambiguous, with some simulations interpreted as providing evidence for entanglement [11] and others interpreted as showing that the lines cut and do not entangle [9,12,13]. The simulations are limited both by the models chosen and by the system sizes that can be simulated. Models based on the boson analogy lack long-range interactions along the vortex line, which can stiffen the vortices and might reduce entanglement. [7,14,15]. In the frustrated 3D XY model, there are multiple ways to define a path followed by a vortex line, some of which are consistent with entanglement, and others which are not [12].Since theoretical and numerical evidence for entanglement have proven inconclusive up to this point, it is natural to turn to experiments to resolve the issue. Unfortunately experimental evidence for or against ent...

Anomalous field-induced growth of fluctuations in dynamics of a biased intruder moving in a quiescent medium

“…Brownian Dynamics simulations have revealed the MCM for a driven colloid in a λ-DNA solution [1,3], or for BIs in colloidal crystals [4]. Remarkably, the MCM not only enhance the drag force exerted on the BI, but also induce effective interactions between the BIs, when more than one BI is present [5][6][7][8].…”

Shear Thinning and Local Melting of Colloidal Crystals

“…1(d)]. The fluctuations around Ár ss are due the intermittent nature of the probe's motion through the crystal: pushing the encountered particles away and subsequently ''hopping'' from site to site [9,17,18]. The data presented here all correspond to the steady state regime.…”

“…Figure 1(a)-1(c) shows three snapshots of a crystal through which a probe particle is being dragged from left to right at a velocity of 0:25 m=s. As is clearly inferred from the disordered area behind the probe particle, the drag leads to the formation of numerous defects resulting in local melting [9,[15][16][17][18]. Although the colloidal crystal is slightly compressed in front of the probe particle, the crystal remains remarkably intact in this region.…”

Active microrheology in active matter systems: Mobility, intermittency, and avalanches

“…Other studies have examined anomalous diffusion properties of the probe 9,10 , features of the driven particle velocity fluctuations, and threshold-tomotion or depinning type phenomena [11][12][13] . In ordered systems, a driven particle can induce localized melting 14 or shear thinning effects 15 . Driven particles or intruders have also been used to study the onset of jamming as a function of the system density [16][17][18][19][20] .…”