Doping dependent time-reversal symmetric nonlinearity of YBa_2Cu_3O_7-d thin films

We have measured the temperature dependent third harmonic response from a series of under-doped YBa_2Cu_3O_7-d thin films to address the mechanism of nonlinearity in these samples. We find that the intrinsic Ginzburg-Landau nonlinearity near Tc is doping dependent, with the sample becoming more nonlinear as it is under-doped. The results are consistent with the doping dependence of the condensation energy of YBa_2Cu_3O_7-d.