A theoretical description of the influence of surface irregularities (such as wedge-like cracks) on the Bean-Livingston energy barrier is presented. A careful quantitative estimate of the field of the first vortex entry H* into a homogeneous bulk superconductor with crack-like defects is obtained. This estimate is based on an exact analytical solution for the Meissner current distribution in a bulk superconductor with a single two-dimensional infinitely thin crack. This thin crack is characterized by the lowest H* value, and, thus, appears to be the best gate for vortex entry.
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