On the Localization of Heavy Particles in Metals

Abstract

It has been conjectured that an impurity with charge Z greater or equal to 2 can be localized due to its interaction with electrons in a metal. The simplest case is an impurity free to move between only two sites, which interacts locally with s-wave electrons. For Z greater or equal to 2 the hopping of the impurity is formally irrelevant and this has been argued to lead to localization. In this paper it is shown that other processes, in particular joint hopping of the impurity and one or more electrons between the sites, play an important role and have not been treated properly in the literature. Being relevant in a renormalization group sense, even when Z greater or equal to 2, these terms lead to delocalization of the impurity. Using bosonization, it is shown how these processes are generated from marginal operators that are usually neglected and the dangers of ignoring marginal or irrelevant operators are discussed in detail. Questions about implications for the more general situation of many sites to which the impurity can hop, are also considered.