Probing the Locally Generated Even and Odd Order Nonlinearity in Y - Ba - Cu - O and Tl - Ba - Ca - Cu - O (2212) Microwave Resonators Around $T_{\rm C}$

Spatial scanning of the synchronously generated second- and third-order intermodulation distortion in superconducting resonators uncovers local nonlinearity hot spots, and possible time reversal symmetry breaking, using a simple probe fashioned from coaxial cable. It is clear that even and odd order nonlinearity in these samples do not share the same physical origins, because their temperature and static magnetic field dependences are quite different. 2nd order intermodulation distortion remains strong in these measurements as the temperature continues to drop below T_C to 77 K even though the 3rd order peaks near T_C and becomes smaller at lower temperature as predicted by the nonlinear Meissner effect. Both YBa₂Cu₃O₇ and Tl₂Ba₂CaCu₂O₈ resonators of the same structure exhibit similar temperature dependence in the second order with second order remaining high at lower temperature. The YBa₂ Cu₃O₇ sample has lower third-order intermodulation distortion with a pronounced peak at T_C.