Multiple magnetic impurities on surfaces: Scattering and quasiparticle interference

Abstract

We study systems of multiple interacting quantum impurities deposited on a metallic surface in a three-dimensional host. For the real-space two-impurity problem, using numerical renormalization group calculations, a rich range of behavior is shown to arise due to the interplay between Kondo physics and effective Ruderman-Kittel-Kasuya-Yosida interactions—provided the impurity separation is small. Such calculations allow identification of the minimum impurity separation required for a description in terms of independent impurities, and thereby the onset of the “dilute-impurity limit” in many-impurity systems. A “dilute-cluster” limit is also identified in systems with higher impurity density, where interimpurity interactions are important only within independent clusters. We calculate the quasiparticle interference due to two and many impurities, and explore the consequences of the independent impurity and cluster paradigms. Our results provide a framework to investigate the effects of disorder due to interacting impurities at experimentally relevant surface coverages.