Damping of Nodal Fermions Caused by a Dissipative Mode

Abstract

Using a $d_{x^2 - y^2}$ superconductor in 2+1 dimensions we show that the Nambu Goldstone fluctuations are replaced by dissipative excitations. We find that the nodal quasi-particles damping is caused by the strong dissipative excitations near the nodal points. As a result we find that the scattering rates are linear in frequency and not cubic as predicted in the literature for the ``d'' wave superconductors. Our results explain the recent angle resolved photoemission spectroscopy and optical conductivity in the BSCCO high $T_c$ compounds.