Hyperuniform patterns nucleated at low temperatures: Insight from vortex matter imaged in unprecedentedly large fields-of-view

TL;DR

The paper addresses whether large-scale 2D hyperuniform patterns can be nucleated in real materials by using low-temperature vortex structures as templates. It employs magnetic decoration imaging of thick Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+bdelta}$ samples under field cooling to map up to ~33,000 vortex positions and analyzes the two-dimensional structure factor $S(q)$ to quantify hyperuniformity. The results show $S(q)$ decays algebraically with exponent $\\alpha$ in the range $\\approx 1.4$–$1.46$, and fits to a dispersive-elastic-constant form $S(q) = C (q/q_0) (1 + D (q/q_0))$ indicate a type-II hyperuniformity, with a finite-size crossover length $l_{fs} \\gtrsim 180 a$. This demonstrates a scalable route to synthesize large-area hyperuniform patterns via a vortex-template in thick superconductors, with implications for devices requiring suppressed density fluctuations at large scales.

Abstract

Hyperuniform patterns present enhanced physical properties that make them the new generation of cutting-edge technological devices. Synthesizing devices with tens of thousands of components arranged in a hyperuniform fashion has thus become a breakthrough to achieve in order to implement these technologies. Here we provide evidence that extended two-dimensional hyperuniform patterns spanning tens of thousands of components can be nucleated using as a template the low-temperature vortex structure obtained in pristine Bi2Sr2CaCu2O8 samples after following a field-cooling protocol.

Figures (2)

• Figure 1: Structural properties of vortex matter nucleated at 30 Oe in pristine Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$.(a) Zoom-in of a magnetic decoration of vortices in the sample with the largest surveyed field-of-view spanning 33 000 vortices. The zoom-in shows around 3 000 vortices imaged as white dots corresponding to the Fe clusters decorating vortex positions at the sample surface. (b) Delaunay triangulations of the largest studied field-of-view with 33 000 vortices in the same sample. Blue lines bond first neighbors and vortices highlighted in red are non-sixfold coordinated topological defects in the structure.
• Figure 2: Structure factor data of vortex matter nucleated at 30 Oe in pristine Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$.(a) Two-dimensional structure factor of the largest studied field-of-view computed after digitalizing the positions of roughly 33 000 vortices. Bragg spots (yellow features) appear at the Bragg wavevector $q_{0}$. The magnitude of $S(q_{\rm x},q_{\rm y})$ is averaged along an infinitesimal circle of radius $q$, see dotted white lines, in order to obtain the angularly-averaged structure factor $S(q)$. (b) $S(q)$ data for the smallest (blue open dots) and largest (pink open dots) studied fields-of-view including 4 000 and 33 000 vortices, respectively. Red and orange lines are algebraic fits up to $q/q_{0} = 0.4$ yielding the exponents $\alpha$ indicated in the legend. (c) Same data fitted in the same $q/q_{0}$ range with the function $S(q) =C (q/q_0)\!\left(1 + D\,(q/q_0)\right)$ theoretically predicted for $\alpha=1$ type II hyperuniformity with dispersive elastic constants (see text). Obtained fitting parameters with their errors indicated in the legend.