Effect of non-magnetic impurities on the gap of a $d_{x^2-y^2}$ superconductor as seen by angle-resolved photoemission

Abstract

An analysis of angle-resolved photoemission (ARPES) experiments in the superconducting state of the high \tc copper-oxides is presented. It is based on a phenomenological weak-coupling BCS model which incorporates the experimental normal state dispersion extracted from ARPES, and non-magnetic impurity scattering in the presence of a $d_{x^2-y^2}$ order parameter (OP). It is shown, that already in the pure case, the broadening by finite momentum resolution of the analyzer leads to a finite region of apparent `gaplessness' around the true node of the OP. Non-magnetic impurities further amplify this effect by introducing additional spectral weight around zero frequency. At sufficiently large impurity concentrations $n_i\approx 0.02-0.05$, this results in an extended region of `gaplessness' up to $\delta\phi=\pm7$ ($\phi$ the angle on the Fermi surface) around the true node for a large range of moderate to strong impurity potential strengths. Different ways to identify the presence of impurity scattering in the ARPES spectra are proposed.