Understanding the Protected Nodes and the Fermi Arcs in the Cuprate Superconductors*

We address a recent analysis of photoemission data which elucidates the superconducting phase of the underdoped cuprates. We first present a simple phenomenological approach to the spectral function which shows how the $d$-wave order parameter symmetry results in protected nodes, which, above $T_c$ broaden into Fermi arcs; this ``protection'' is associated with superconducting coherence rather than reduced thermal broadening. A microscopic theory, consistent with this phenomenology, is presented. It reconciles the observations that the excitation gap below $T_c$ is temperature independent while the superfluid density necessarily vanishes at $T_c$. \\ Reference: Q.J. Chen, K. Levin, and I. Kosztin, Phys. Rev. B \textbf{63}, 184519 (2001).