Disorder effects on the intrinsic nonlinear current density in YBa$_2$Cu$_3$O$_{7-\delta}$

We present harmonic generation measurements of the intrinsic nonlinear current density $j_2$ of YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) films at temperatures close the $T_c$. Experiments on a range of different quality samples allow us to extract the dependence of $j_2$ on the penetration depth of the superconductor. In order to model these results, we calculate the intrinsic nonlinear current response of $d_{x^2-y^2}$-wave superconductors in the Meissner regime in the presence of nonmagnetic impurities within the self-consistent T-matrix approximation.