Plasmonic performance of Au$_\mathbf{x}$Ag$_\mathbf{y}$Cu$_\mathbf{1-x-y}$ alloys from many-body perturbation theory

We present a detailed appraisal of the optical and plasmonic properties of ordered alloys of the form Au$_{x}$Ag$_{y}$Cu$_{1-x-y}$, as predicted by means of first-principles many-body perturbation theory augmented by a semi-empirical Drude-Lorentz model. In benchmark simulations on elemental Au, Ag, and Cu, we find that the random-phase approximation (RPA) fails to accurately describe inter-band transitions when it is built upon semi-local approximate Kohn-Sham density-functional theory (KS-DFT) band-structures. We show that non-local electronic exchange-correlation interactions sufficient to correct this, particularly for the fully-filled, relatively narrow $d$-bands that which contribute strongly throughout the low-energy spectral range ($0-6$ eV), may be modelled very expediently using band-stretching operators that imitate the effect of a perturbative G$_0$W$_0$ self-energy correction incorporating quasiparticle mass renormalization. We thereby establish a convenient work-flow for carrying out approximated G$_0$W$_0$+RPA spectroscopic calculations on alloys. We develop a pragmatic procedure for calculating the Drude plasmon frequency from first principles, including self-energy effects, as well as a semi-empirical scheme for interpolating the plasmon inverse lifetimes between stoichiometries. A range of optical and plasmonic figures of merit are discussed at three representative solid-state laser wavelengths.