  We demonstrate that in a d-wave superconductor the bulk nonlinear Meissner
effect is dominated by a surface effect due to Andreev bound states at low
temperatures. The contribution of this surface effect to the nonlinear response
coefficient follows a 1/T^3 law with opposite sign compared to the bulk 1/T
behavior. The cross-over from bulk dominated behavior to surface dominated
behavior occurs at a temperature of T/T_c ~ 1/sqrt(kappa). We present an
approximate analytical calculation, which supports our numerical calculations
and provides a qualitative understanding of the effect. The effect can be
probed by intermodulation distortion experiments.
