Influence of spatial variations in the lower critical field on the equilibrium field penetration into superconductors

The thermodynamic lower critical field Hc1 in Bi2 Sr2 CaCu2 O8+y crystals, in the presence of columnar defects, was determined using magneto-optical measurements combined with the shaking technique. We observe a downward shift in Hc1 due to columnar defects. Using partially irradiated samples, we show that small local variations in Hc1 dramatically affect the way the field penetrates into superconductors. We present a theoretical model which provides a quantitative fit to the experimental results and explains how the influence of small sample inhomogeneities is enhanced by geometrical effects and leads to significant variations in the local-field distribution and penetration.