Strong correlations make high-temperature superconductors robust against disorder

Strong correlations are central to the problem of high-temperature superconductivity in the cuprates(1-4). Correlations are responsible for both the Mott insulating, antiferromagnetic state in the parent compounds and for the d-wave superconducting state that arises on doping with mobile charge carriers. An important experimental fact about the superconducting state is its insensitivity to disorder(5), in marked contrast with conventional theories of d-wave pairing, which predict just the opposite. Here, we generalize the theory of the strongly correlated superconducting ground state based on projected wavefunctions(6-9) to include impurity effects and find the remarkable result that correlations play a central role in making the superconductor robust against disorder. The nodal quasiparticles, which are the low-energy electronic excitations, are protected against disorder leading to characteristic signatures in scanning tunnelling spectroscopy(10-14) and angle-resolved photoemission(15-17).