Equations for collective modes spectrum in a mixed d-wave state of unconventional superconductors

Direct observation of the collective modes in unconventional superconductors (USC) by microwave impedance technique experiments has made the very important study of the collective excitations in these systems. One of the problem is still the exact form of the order parameter of unconventional superconductors. Among the possibilities there are extended s-wave pairing, mixture of s- and d-states, as well as of different d-wave states. I consider the mixed (1-gamma)d(x2-y2) + igammad(xy) state in high temperature superconductors (HTSC) and derive for the first time a full set of equations for collective modes spectrum in mixed d-wave state with arbitrary admixture of d(xy) state. Obtained results allow to calculate the whole collective mode spectrum, which could be used for interpretation of the sound attenuation and microwave absorption data as well as for identification of the type of pairing and order parameter in unconventional superconductors. In particular, they allow to estimate the extent of admixture of d(xy) state in a possible mixed state. (C) 2004 Elsevier B.V. All rights reserved.