Strong correlations lead to protected low energy excitations in disordered d-wave superconductors

We show that strong correlations play a vital role in protecting low energy excitations in disordered high temperature superconductors. The impurity-induced low-energy density of states (DOS) is greatly reduced in the strongly correlated superconductor compared to d-wave Bogoliubov-deGennes theory. The gapless nodal quasiparticles, and the resulting `V' in the low-energy DOS, are much more robust against disorder compared to the large-gap antinodal excitations. We discuss the relevance of our results to angle-resolved photoemission and scanning tunneling spectroscopy experiments.