d_x²-y²-STATE OF HIGH TEMPERATURE SUPERCONDUCTORS WITH A SMALL ADMIXTURE OF d_xy-STATE

It is well known that most of the high temperature superconductors (at least hole-type) are in d-wave state. But it is still an unsolved problem whether it is a pure d-wave state or one has some kind of mixed state. Among the candidates for an admixture, there are s- and d-wave states. Existing experiments could not resolve this issue. New possibilities for experimental resolution of this problem are opened via recent observation of the collective modes in UBe₁₃ (heavy fermion superconductor) by microwave impedance technique experiments and in Sr₂RuO₄ (high temperature superconductor) by ultrasound attenuation experiments.

Some theoretical treatments show that the most likely state is a mixture of two d-wave states: d_x²-y² and d_xy with a small admixture of former state. To create the theoretical basis for investigation of possible mixed superconducting state in unconventional superconductors by sound attenuation and microwave absorption experiments, I derive for the first time a full set of equations for collective modes spectrum in d_x²-y²-state with small admixture of d_xy state. These equations allow to calculate the whole collective mode spectrum in mixed d_x²-y²+iεd_xy state and distinguish this state from pure d-wave states (whose collective mode spectrum has been calculated earlier) by ultrasound attenuation and microwave absorption experiments.