  We study the influence of surface Andreev bound states in d-wave
superconductors on the Bean-Livingston surface barrier for entry of a vortex
line into a strongly type-II superconductor. Starting from Eilenberger theory
we derive a generalization of London theory to incorporate the anomalous
surface currents arising from the Andreev bound states. This allows us to find
an analytical expression for the modification of the Bean-Livingston barrier in
terms of a single parameter describing the influence of the Andreev bound
states. We find that the field of first vortex entry is significantly enhanced.
Also, the depinning field for vortices near the surface is renormalized. Both
effects are temperature dependent and depend on the orientation of the surface
relative to the d-wave gap function.
