RKKY interaction in topological nanoribons: a DMRG study

Abstract

The study of the two-impurity Anderson model has a prominent position in the attempt to understand the physics of heavy-fermion materials. As in the case with heavy-fermions, a two impurity system may present a competition between the Kondo and the Ruderman- Kittel-Kasuya-Yosida (RKKY) couplings. The first is the coupling between a localized magnetic moment (in a metallic host) and the conduction electrons. The so-called Kondo effect is characterized by the screening (singlet formation) of the impurity magnetic moment by the conduction electrons. The RKKY interaction is an indirect interaction between two magnetic impurities, mediated by the conduction electrons. In this dissertation, we study the RKKY interaction between two impurities that are connected by a topological metallic edge state in a silicene nanoribbon. We use the Lanczos transformation plus DMRG method to treat this problem numerically. Besides finding partial agreement with quantum field theory calculations, we do a thorough examination of the convergence of the results with the DMRG parameters.