Role of non-linear effects and standing waves in microwave spectroscopy: Corbino measurements on superconductors and VO

Broadband microwave spectroscopy can probe material properties in wide spectral and temperature ranges. The quality of such measurements crucially depends on the calibration, which also removes from the obtained spectra signatures of standing waves. Here we consider cryogenic Corbino-type reflection measurements on superconductors close to the critical temperature. We show that the non-linear sample response, which relates to sample heating, can lead to strong signatures of standing waves even in a well-calibrated Corbino spectrometer. We demonstrate our findings with microwave measurements as a function of frequency, power, and temperature and for different lengths of the microwave transmission line. Finally, we note such non-linear effects beyond the case of superconductors by probing a VO