The Significance of Edge-Barrier Pinning in Superconducting Bridges

Edge-barrier pinning in thin superconducting films provides additional pinning over that of the bulk pinning. When using bridges greater than 1 $\mu $m to determine the critical current density (J$_{c})$ of films, this additional pinning is typically ignored. However, theoretical and experimental data presented here indicate that this pinning enhancement is non-negligible with bridge widths of less than 100 $\mu $m and on par with the bulk pinning at a few microns. In the present study, bridges in YBa$_{2}$Cu$_{3}$O$_{7-\delta }$ (YBCO) thin films were repeatedly narrowed to avoid issues of sample to sample variation. Bridge widths starting at 500 $\mu $m and 50 $\mu $m were patterned by photolithography with subsequent narrowing performed by photolithography and focused ion beam milling, respectively. Transport J$_{c}$ was determined after each bridge size. Theoretical analysis follows that of J.R Clem [e.g. Elistratov et al, Phys. Rev. B 66, 220506 (2002)]. Theoretical implications of the narrow bridge effect on J$_{c}$(H) and J$_{c}$(T) plots are not simple scalar changes. Based on these results presented here, two key points are: 1) J$_{c}$ data comparison among institutions using different bridge sizes can provide improper conclusions (similarly as not accounting for film thickness), and 2) the J$_{c}$(T) and J$_{c}$(H) curve shapes are skewed differently for different widths. The implication of these effects will be discussed.