Suppression of Geometric Barrier in Type II Superconducting Strips

We study the magnetic response of a superconducting double strip, i.e., two parallel coplanar thin strips of width $2w$, thickness $d \ll w$ and of infinite length, separated by a gap of width $2s$ and subject to a perpendicular magnetic field $H$. The magnetic properties of this system are governed by the presence of a geometric energy barrier for vortex penetration which we investigate as a function of applied field $H$ and gap parameter $s$. The new results deal with the case of a narrow gap $s \ll w$, where the field penetration from the inner edges is facilitated by large flux focusing. Upon reducing the gap width $2s$, we observe a considerable rearrangement of the screening currents, leading to a strong reduction of the penetration field and the overall magnetization loop, with a suppression factor reaching $\sim (d/w)^{1/2}$ as the gap drops below the sample thickness, $2s < d$. We compare our results with similar systems of different shapes (elliptic, rectangular platelet) and include effects of surface barriers as well. Furthermore, we verify that corrections arising from the magnetic response of the Shubnikov phase in the penetrated state are small and can be omitted. Extending the analysis to multiple strips, we determine the specific sequence of flux penetrations into the different strips. Our studies are relevant for the understanding of platelet shaped samples with cracks or the penetration into layered superconductors at oblique magnetic fields.