Ultrasound attenuation and collective modes in mixed d x2-y2 + id xy state of unconventional superconductors

We discuss two methods used for the study of unconventional superconductors: ultrasound attenuation and collective modes. These two methods, as well as microwave absorption, turn out to be coupled and have become very important now. Within models built by path integration technique we analyze some recent ideas concerning possible realization of the mixture of different d-wave states in high temperature superconductors (HTSC).We specifically consider the mixture of d x2-y2 and d xy states. We study the collective mode spectrum and the ultrasound attenuation in the mixed state, and show that eac...