Doping-Dependent Nonlinear Meissner Effect and Spontaneous Currents in   High-Tc Superconductors
  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. 
Sheng-Chiang Lee, Mathew Sullivan, Gregory R. Ruchti, Steven M.   Anlage, Benjamin Palmer, B. Maiorov, and E. Osquiguil