Figure 1: Distribution of vortices after field cooling to T=4.2 K reveals the distribution of pinning centres.

(a–d) Scanning Hall probe microscopy images taken at the applied magnetic field B₀=0.3 G (a), 0.6 G (b), 1.2 G (c) and 2.4 G (d). Scale bar, 4μm. At the lowest fields (a,b), only single quantum vortices are observed which are located at pinning centres. At higher fields (c,d), when all the pinning centres are occupied (c), giant vortices with vorticity L=2 and interstitial single quantum vortices appear. Interstitial vortices (like that indicated by the dotted circle in c) appear brighter than pinned vortices (indicated by the dashed circle). The field profiles, measured along the dashed lines I to VII in a and c, are shown in e and f for pinned and interstitial vortices, respectively. Here r is the distance from the centre of a vortex. The solid lines in e and f are fittings based on the monopole model. Since at pinning sites the local density of superconducting charge carriers is reduced and hence the penetration length λ is larger than outside these sites, the magnetic field induced by a pinned vortex spreads over a wider area and the field magnitude at the vortex centre appears lower as compared with those for an interstitial vortex. The histograms of λ+z₀ values calculated from the monopole model (g) yield an average value of 0.89 and 0.82 μm for the pinned and interstitial vortices, respectively, showing that indeed, interstitial vortices correspond to a smaller λ as compared with pinned ones. (h) Total vorticity of vortices observed in the scanned area as a function of applied field. The solid line is the expected value N_vortex=B₀S/Φ₀, where S=16 × 16 μm² is the size of scanned area and Φ₀=h/2e is flux quantum. The vertical dashed lines indicate the fields above which 2Φ₀- and 3Φ₀-vortices appear.