Localization of heavy particles in metals: reexamined

It has been conjectured [F. Sols and F. Guinea, Phys. Rev. B 36, 7775 (1987); K. Yamada, A. Sakurai, and M. Takeshiga, Prog. Theor. Phys. 70, 73 (1983)] that an impurity with charge Z{≥}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{≥}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{≥}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.