Even and Odd Order Intermodulation Nonlinearity From Superconductive Microstrip Lines

Abstract

Three-tone intermodulation distortion (IMD) was used to measure the even and odd order microwave nonlinearity of superconducting Tl <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Ba <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> CaCu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> and YBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">7</sub> resonators. By using an off-resonance probe signal, the IMD generation is stimulated locally in the vicinity of the probe. Both 2nd and 3rd order IMD appear at the microwave resonant frequency, providing a synchronous comparison of the local even and odd order nonlinearities and a quantitative determination of the current densities that produce the intermodulation distortion. Comparison of synchronous 2nd and 3rd order IMD provides a characterization of the extent of time reversal symmetry breaking (TRSB) in the superconductor. As the probe is scanned across the resonator, the degree of TRSB is seen to vary in different regions, always exhibiting a significant rise in the 3rd order IMD at the critical temperature, T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , consistent with expectation from the nonlinear Meissner effect. The ratio of 2nd order to 3rd order IMD current drops significantly at T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> , indicating a reduction in TRSB at the phase transition.