Inﬂuence of edge barriers on vortex dynamics in thin weak-pinning superconducting strips B. L. T. Plourde* and D. J. Van Harlingen Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801 D. Yu. Vodolazov Department of Physics, Nizhny Novgorod University, Gagarin Avenue 23, 603600, Nizhny Novgorod, Russia R. Besseling, M. B. S. Hesselberth, and P. H. Kes Kamerlingh Onnes Laboratorium, Leiden University, P. O. Box 9504, 2300 RA Leiden, The Netherlands Received 17 November 2000; published 5 June 2001 We introduce a type of vortex entry edge barrier which controls the critical current in a perpendicular magnetic ﬁeld in thin-ﬁlm weak-pinning superconducting strips. Measurements of the critical current in thin- ﬁlm amorphous-MoGe strips show a linear decrease with increasing magnetic ﬁeld strength at low magnetic ﬁelds, and a crossover at a well-deﬁned threshold ﬁeld to an inverse power-law decay that is independent of the strip width. This behavior has not been observed previously due to bulk pinning, which only becomes domi- nant in our MoGe samples at high magnetic ﬁelds. To describe our results, we present calculations of the current distribution in thin superconducting strips with a ﬁnite penetration depth and negligible bulk pinning, and show that the measured critical currents in our MoGe samples correspond to a current density at the strip edge which approaches the Ginzburg-Landau depairing limit. Shape variations and defects along the strip edges inﬂuence the vortex entry conditions, leading to deviations from the ideal behavior, including offsets in the critical current maximum with respect to zero ﬁeld. DOI: 10.1103/PhysRevB.64.014503 PACS numbers: 74.60.Jg, 74.76.-w Sample edges play an important role in the dynamics of vortices in superconductors. In addition to intervortex forces and bulk pinning at defect sites, which limit vortex ﬂow in uniform superconductors, interactions with the edges of a superconductor can signiﬁcantly affect vortex transport in ﬁnite size superconducting structures and thin-ﬁlm devices. The vortex screening current distribution is distorted near a surface so that the boundary condition of no normal current ﬂow at the surface is satisﬁed. This distortion creates a sur- face barrier, ﬁrst considered by Bean and Livingston, 1 and delays the entry of vortices until a magnetic ﬁeld strength which can be much greater than the lower critical ﬁeld H c 1 when vortex nucleation in the bulk ﬁrst becomes energeti- cally favorable. Another type of vortex entry barrier can oc- cur in superconductors with a large demagnetizing factor, such as thin platelet crystals in a perpendicular magnetic ﬁeld. The associated strong curvature of the ﬁeld lines at the sample edges results in a broad distribution of the screening currents across the entire top and bottom surfaces of the sample. If the sample is thicker than the penetration depth, then the curved ﬁeld lines can cause the entry of tilted vortex segments at the sample corners. As the segments penetrate further into the superconductor, the length of the segment increases initially, leading to an energetic barrier against vor- tex entry. These so-called geometrical barriers have been studied extensively, particularly in wide, thick samples of the type-II superconductors. 2–4 In this paper, we consider a different regime for which the sample thickness is much less than the penetration depth so that the vortices behave essentially as 2D objects. In this thin-ﬁlm limit, the vortices cannot cut across the sample cor- ners, but the large demagnetizing factor again leads to a broad current distribution across the strip width, while the vortices still interact with the sample edge via a Bean- Livingston surface barrier mechanism. This hybrid effect, which we call an edge barrier, is particularly important for understanding vortex phenomena in microfabricated thin- ﬁlm devices, including ﬂux-ﬂow noise processes in super- conducting quantum interference device, 5 vortex transport in weak-pinning channels, 6–8 and the realization of asymmetric vortex ratchet devices. 9 To investigate the effect of the edge barrier on the dynamics of vortices, we have measured the magnetic ﬁeld dependence of the critical current of patterned thin-ﬁlm amorphous MoGe strips. The weak bulk pinning of this material ensures that the critical current is dominated by the vortex interactions with the strip edge over a wide range of magnetic ﬁeld. We observe several distinct regimes of magnetic ﬁeld dependence which we identify with different vortex distributions within the strip. In order to ﬁt our data quantitatively, we have calculated the current distribution and vortex entry conditions for thin-ﬁlm strips in which the thin-ﬁlm transverse penetration depth is comparable to the strip width, the regime appropriate for our samples and most relevant for typical thin-ﬁlm superconductor devices. Using standard photolithographic processing and Ar ion milling, we fabricated strips ranging in width from 10 to 40  m from 200 nm thick ﬁlms of amorphous MoGe. Films were sputter deposited onto silicon substrates and had the following properties: superconducting transition temperature T c =6.5 K, normal state resistivity  n =180   cm, and critical ﬁeld slope dB c 2 / dT | T c =2.8 T/K. The superconduct- ing transition-metal glasses have been studied extensively because of their weak vortex pinning, 10 typically exhibiting bulk critical current densities less than 10 4 A/cm 2 at low magnetic ﬁelds, several orders of magnitude lower than most superconducting materials. Because of the short electronic PHYSICAL REVIEW B, VOLUME 64, 014503 0163-1829/2001/641/0145036/$20.00 ©2001 The American Physical Society 64 014503-1