Doping-dependent nonlinear Meissner effect and spontaneous currents in high-T-c superconductors

We measure the local harmonic generation from superconducting thin films at microwave frequencies to investigate the intrinsic nonlinear Meissner effect near T-c in the 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 depairing critical current density. We also extract a spontaneous TRSB characteristic current density scale that onsets at T-c, grows with decreasing temperature, and systematically decreases in magnitude (at fixed T/T-c) with underdoping. The origin of this current scale could be Josephson circulating currents or the spontaneous magnetization associated with a TRSB order parameter.