Figure 1

(Color online) Normalized critical current, $J_c$ versus normalized magnetic flux, $\Phi /{\Phi }_1$ ($\propto$ number of vortices $N_v$), for different QP APS [shown by solid blue (dark gray) lines]: (a) square-triangle quasiperiodic tiling, (b) square-triangle nonpisot tiling, (c) Goodman-Strauss tiling, and (d) nonpisot Penrose tiling. Insets show the corresponding tiling patterns. For comparison, the function $J_c\left(\Phi /{\Phi }_1\right)$ for a fivefold Penrose-tiling APS is shown by a red (gray) line. The $J_c\left(\Phi /{\Phi }_1\right)$ curves are shown for $f_p/f_0=2$ and $r_p/\lambda =0.1$. These values of $f_p$ and $r_p$ are also used in Figs. 2, 3, 4.Reuse & Permissions

Figure 2

(Color online) Flow pattern for vortices driven by an external current illustrating the holelike vortex conductivity in the Shield-tiling APS for $\Phi \lesssim {\Phi }_1$: $\Phi \approx 0.95{\Phi }_1$. The pinning sites are shown by filled large red (gray) circles. Vortex positions are shown for ten successive time intervals $t_i$, where $i=1–10$: by open small circles, for $i=1–9$, and by filled small green (gray) circles, for $i=10$. The Lorentz force drives vortices from the left to the right. Most of the vortices do not move: their positions just slightly change (polarized) with respect to the centers of the pinning sites. The trajectories of moving vortices (from the left to the right) are shown by thick blue (gray) arrows. The motion of vortices results in effective propagation of vacancies (holes) from the right to the left (shown by thin dashed black arrows), including holes entering the sample from outside, as in the region marked by the dotted rectangle. Newly created holes are shown by thin solid black circles while annihilated holes (i.e., filled by vortices) are shown by thin dashed black circles.Reuse & Permissions

Figure 3

(Color online) Normalized critical current (experiment and theory), $J_c$ versus normalized magnetic flux, $\Phi /{\Phi }_1$ ($\propto$ number of vortices $N_v$), for different QP APS [solid blue (dark gray) line]: (a) Watanabe-Ito-Soma tiling, (b) Tuebingen tiling, and (c) Shield tiling. Insets show the corresponding tiling patterns. The function $J_c\left(\Phi /{\Phi }_1\right)$ for a fivefold Penrose-tiling APS is shown by red (gray) line, for comparison.Reuse & Permissions

Figure 4

(Color online) Distribution of vortices in a Shield-tiling APS calculated for: $\Phi ={\Phi }_1$ (a) and $\Phi =1.18{\Phi }_1$ (b). The vortices are shown by green (light gray) solid dots while the pinning sites by red (gray) open circles.Reuse & Permissions