  We measure the local harmonic generation from superconducting thin films at
microwave frequencies to investigate the intrinsic nonlinear Meissner effect
near Tc in zero magnetic field. Both second and third harmonic generation are
measured to identify time-reversal symmetry breaking (TRSB) and time-reversal
symmetric (TRS) nonlinearities. We perform a systematic doping-dependent study
of the nonlinear response and find that the TRS characteristic nonlinearity
current density scale follows the doping dependence of the de-pairing critical
current density. We also extract a spontaneous TRSB characteristic current
density scale that onsets at Tc, grows with decreasing temperature, and
systematically decreases in magnitude (at fixed T/Tc) with under-doping. The
origin of this current scale could be Josephson circulating currents or the
spontaneous magnetization associated with a TRSB order parameter.
