Critical properties of the Fermi-Bose Kondo and pseudogap Kondo models: Renormalized perturbation theory

Magnetic impurities coupled to both fermionic and bosonic baths or to a fermionic bath with pseudogap density of states, described by the Fermi-Bose Kondo and pseudogap Kondo models, display non-trivial intermediate coupling fixed points associated with critical local-moment fluctuations and local non-Fermi liquid behavior. Based on renormalization group together with a renormalized perturbation expansion around the free-impurity limit, we calculate various impurity properties in the vicinity of those intermediate-coupling fixed points. In particular, we compute the conduction electron T matrix, the impurity susceptibility, and the residual impurity entropy, and relate our findings to certain scenarios of local quantum criticality in strongly correlated lattice models.Comment: 16 pages, 5 figs; (v2) large-N results for entropy of Bose-Kondo model added; (v3) final version as publishe

Interplay of quantum magnetic and potential scattering around Zn or Ni impurity ions in superconducting cuprates

To describe the scattering of superconducting quasiparticles from non-magnetic (Zn) or magnetic (Ni) impurities in optimally doped high T$_c$ cuprates, we propose an effective Anderson model Hamiltonian of a localized electron hybridizing with $d_{x^2-y^2}$-wave BCS type superconducting quasiparticles with an attractive scalar potential at the impurity site. Due to the strong local antiferromagnetic couplings between the original Cu ions and their nearest neighbors, the localized electron in the Ni-doped materials is assumed to be on the impurity sites, while in the Zn-doped materials the localized electron is distributed over the four nearest neighbor sites of the impurities with a dominant $d_{x^2-y^2}$ symmetric form of the wave function. With Ni impurities, two resonant states are formed above the Fermi level in the local density of states at the impurity site, while for Zn impurities a sharp resonant peak below the Fermi level dominates in the local density of states at the Zn site, accompanied by a small and broad resonant state above the Fermi level mainly induced by the potential scattering. In both cases, there are no Kondo screening effects. The local density of states and their spatial distribution at the dominant resonant energy around the substituted impurities are calculated for both cases, and they are in good agreement with the experimental results of scanning tunneling microscopy in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ with Zn or Ni impurities, respectively.Comment: 24 pages, Revtex, 8 figures, submitted to Physical Review B for publication. Sub-ject Class: Superconductivity; Strongly Correlated Electron