How to distinguish a mixture of two d-Wave States from a Pure d-Wave State of High-Temperature Superconductors

By the study of the spectrum of collective modes in a pure d-wave state and in a mixed d x 2 y 2 + id xy state of high-temperature superconductors, we show that in spite of the fact that spectra in both pure states d x 2 y 2 and d xy are identical, the spectrum in the mixture d x 2 y 2 + id xy state turns out to be quite different from them. Thus, the probe of the spectrum in ultrasound and/or microwave absorption experiments could be used to distinguish a mixture of two d-wave states from pure d-wave states.