COLLECTIVE MODES AND A THEORY OF RESPONSE OF D-WAVE SUPERCONDUCTORS

We 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. We choose two representative phases: the dγ phase, which has point nodes in the energy gap, and the Y2-1 phase, which has line as well as point nodes. We obtain obviously gauge-invariant expressions for the order-parameter fluctuations and the currents. 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 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 Y2-1 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.