Phase-sensitive measurements of harmonic response in high-Tc superconducting thin films by means of local microwave microscopy

The microscopic origins of Meissner-state nonlinearities in superconductors are still not clear. Traditionally, microwave nonlinear measurements of superconducting thin films employ a spectrum analyzer to measure the power carried by the harmonic signals (P$_{2f }$and P$_{3f})$. Such measurements have provided strong evidence for the Nonlinear Meissner Effect (NLME) at the critical temperature T$_{c}$ in cuprates [PRB 71, 014507 (2005)]. Investigations of the NLME in underdoped YBa$_{2}$Cu$_{3}$O$_{7-\delta }$ (YBCO) thin films have revealed the existence of an additional nonlinear mechanism that onsets at T$_{c}$ and leads to the persistence of P$_{3f}$ above T$_{c}$, a feature which has not been observed in optimally-doped samples. A possible nonlinear source active at and slightly above T$_{c}$ is the current-dependent normal conductivity, as proposed earlier by Mishonov and co-workers [PRB 65, 064519 (2002)]. The measurements performed with a spectrum analyzer do not provide phase information about the harmonic signals and therefore the nature of the nonlinear source (inductive vs. resistive) remains undetermined. However, nonlinear phase-sensitive measurements can be carried out with a network analyzer in the frequency offset mode and such data are instrumental in disentangling the effects of different types of nonlinear mechanisms. Work supported by NSF-GOALI , grant no. DMR-0201261