Collective modes and a theory of response of d-wave superconductors

The authors present a theory of the response of d-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. They choose two representative phases: the d γ phase, which has point nodes in the energy gap, and the Y/sub 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. They obtain obviously gauge-invariant expressions for the order-parameter fluctuations and the currents, having forms common not only to the d-wave states, but also to the p-wave states studied earlier. They also investigate the collective excitations; in the long-wavelength limit for spherically symmetric systems, there are, on the frequency-temperature plane, seven branches for each d-wave phase considered, in addition to the common plasma mode and orbital Goldstone modes resulting from the spontaneous breakdown of the rotational invariance. In the Y/sub 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