Finite-size and quenching effects on hyperuniform structures formed during cooling

Abstract

The outstanding physical properties of hyperuniform condensed matter systems holds significant promise for technological applications and studying effects that may disrupt this hidden order is therefore very important. Vortex matter in superconductors is a model system to study this problem since imaging experiments have revealed that correlated disorder in the host media and finite size effects disrupt the hyperuniformity of the in-plane arrangement of vortices. Here we report simulations of layered interacting elastic lines as a model for the vortex lattice in three-dimensional superconductors, following a cooling protocol that closely mimics the experimental conditions. We show that finite-thickness effects limiting the hyperuniformity range arise both in equilibrium and out-of-equilibrium. Our results provide a theoretical framework to draw a realistic road-map on synthesizing hyperuniform materials when cooling structures on finite host media with disorder.

Figures (12)

• Figure 1: Schematics of the model used in the Langevin dynamics simulations. Vortices are represented as stacks of particles (“pancakes”) coupled elastically along $z$ and interacting via London potentials within each layer.
• Figure 2: Temperature-quench protocol used in simulations mimicking field-cooling experimental conditions: Equilibration at $T_{\rm i}$, linear cooling during $t_{\rm ramp}$, and equilibration at $T_{\rm f}$.
• Figure 3: Vortex configurations and defect density during the quench for the thickest sample studied ($N_{z}=35$). (a) Evolution of the defect density $\rho_{\rm def}$ as a function of time and temperature. (b--f) Delaunay triangulations of the top layer at representative stages of the quench: (b) equilibrated high-temperature liquid, (c) at the temperature at which $\rho_{\rm def}\!\approx\!30\%$ and (d) $\!\approx\!10\%$, (e) at the end of the ramp at $T_{\rm f}=0.001$, and (f) final configuration after equilibration. Non–sixfold vortices are marked in red.
• Figure 4: Structure factor of the vortex lattice for the thickest sample studied at different stages of the quenching protocol. (a) Angularly averaged $S(q)$ at representative times/temperatures and (b) $S(q)/T$ for the same data. (c--g) Two-dimensional structure factors corresponding to the indicated temperatures. Results averaged over 35 layers and 4 independent simulations.
• Figure 5: Angularly averaged structure factor normalized by $T$ and $q$ for the thickest sample studied with $N_{z}=35$, averaged over 4 simulation runs. (a) Low-$q/q_{0}$ data, where deviation from a constant signals loss of equilibrium upon cooling. (b) Intermediate-$q/q_{0} \geq 0.15$ with arrows marking the temperature of departure from equilibrium for each wavevector.