Measurement of Localized Nonlinear Microwave Response of 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 zero magnetic field. Both second and third harmonic generation are measured to identify time-reversal symmetry breaking (TRSB) and time-reversal symmetric (TRS) nonlinearities. The microscope can measure the local nonlinear response of a bicrystal grain boundary [Sheng-Chiang Lee and Steven M. Anlage, Physica C 408-410, 324 (2004); cond-mat/0408170]. We also performed 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 [cond-mat/0405595]. We 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 under-doping. The origin of this current scale could be Josephson circulating currents or the spontaneous magnetization associated with a TRSB order parameter.