Microscopic picture of the critical state in a superconductor with a periodic array of antidots

By using scanning Hall microscopy we visualize the progressive formation of the critical state with individual vortex resolution in a Pb thin film with a periodic pinning array. Slightly above the first penetration field, we directly observe a terraced critical state as proposed theoretically by Cooley and Grishin [Phys. Rev. Lett. 74, 2788 (1995)]. However, at higher fields, the flux front tends to disorder and the classical Bean profile is restored. This study allows us to establish a clear link between the widely used integrated response measurements in the superconducting state and the nanoscale landscape defined by individual vortices.

Figure 1

(a) Layout of the investigated sample. The upper panel shows the transport bridge with a 3-mm-long patterned area. The lower panel shows a zoom-in close to the sample’s border. The box delimited by the dashed line indicates the area where most of the scanning Hall microscopy images were obtained. (b)–(e) show scanning Hall probe microscopy images obtained at the sample’s border, as indicated by the dashed box in (a) after cooling down to $T=6.9$ K in presence of a field (b) $H=0.63H_1$, (c) $H=H_1$, (d) $H=1.3H_1$, and (e) $H=2H_1$. The image in (b) is accompanied by the theoretically predicted vortex distribution (Ref. [12]). The white dashed line indicates the sample’s border. The field picked up by the Hall cross on top of a single quantum vortex is $~2.5$ G.

Figure 2

SHPM images obtained at the sample’s border as indicated by the dashed box in Fig. 1 after ZFC at $T=6.9$ K for a field (a) $H=0.35$ Oe, (b) $H=0.65$ Oe, (c) $H=0.8$ Oe, (d) $H=1.05$ Oe, and [inset of (e)] $H=H_1=2.7$ Oe. (e) shows the local field $B_{\text{loc}}$ corresponding to the density of vortices in the scanning area as a function of the external field at $T=6.9$ K.

Figure 3

(a) External periodic field $H$ and locally averaged field $B_{\text{loc}}$ as a function of time. (b) Same data as in (a), showing $B_{\text{loc}}$ as a function of $H$. (c)–(e) show SHPM images of the vortex distribution for $T=7$ K obtained at the border of the sample for $H=+0.3$ Oe, $H=0.0$ Oe, and $H=-0.3$ Oe, respectively. The field picked up by the Hall cross on top of a positive single-quantum vortex is $~+2.5$ G, whereas the field on top of a single quantized antivortex is $~$$-2.5$ G.