Collective modes and a theory of response ofd-wave superconductors

We present a theory of the response ofd-wave superconductors to weak applied fields, by taking account of the Coulomb interaction and all the collective degrees of freedom as well as crystal symmetry. We choose two representative phases: the d phase, which has point nodes in the energy gap, and theY _2–1 phase, which has line as well as point nodes. The former is a self-consistent solution for cubic as well as spherical symmetries and the latter is one for spherical, cubic, and hexagonal symmetries. We obtain obviously gauge-invariant expressions for the order-parameter fluctuations and the currents, having forms common not only to thed-wave states, but also to thep-wave states studied earlier. We also investigate the collective excitations; in the long-wavelength limit for spherically symmetric systems, there are, on the frequency-temperature plane, seven branches for eachd-wave phase considered, in addition to the common plasma mode and orbital Goldstone modes resulting from the spontaneous breakdown of the rotational invariance. In theY _2–1-phase two eigenmodes are found to become gapless at a finite temperature, below which they are purely imaginary. This implies instability of the phase. The effect of crystal anisotropy on the collective spectra is also studied.A preliminary report on the present work was published inJpn. J. Appl. Phys. Suppl. 26-3, 167 (1987).