Quantum phase transitions in d-wave superconductors

Motivated by the strong, low temperature damping of nodal quasiparticles observed in some cuprate superconductors, we study quantum phase transitions in d(x2-y2) superconductors with a spin-singlet, zero momentum, fermion bilinear order parameter. We present a complete, group-theoretic classification of such transitions into seven distinct cases (including cases with nematic order) and analyze fluctuations by the renormalization group. We find that only two, the transitions to d(x2-y2) + is and d(x2-y2) + id(xy) pairing, possess stable fixed points with universal damping of nodal quasiparticles; the latter leaves the gapped quasiparticles along (1,0), (0, 1) essentially undamped.