Localized Correlations in Narrow Conduction Bands. I

Abstract

We have studied the effects of an exchange-enhanced substitutional impurity on a host metal by double-time Green's functions. We have used a simplification of the Wolff model to describe this system, i.e., a one-band model in which Coulomb interactions in the host lattice are neglected, and the impurity is represented by $U{n}_{\sigma }{n}_{\overline{\sigma }}+V(n_{\sigma }+n_{\overline{\sigma }})$, where $n_{\sigma }$ is the electron occupation number for spin $\sigma$ at the impurity site. A decoupling scheme is used in which operators on the exchange-enhanced site are never separated from each other in the process of decoupling. This leads to a singular integral equation for the localized Green's function of the exchange-enhanced site, in terms of which all the one-electron properties of the system are expressible. The integral equation, assuming essentially a Lorentzian density of states for the host lattice, is exactly solvable in the $U$-infinite, $V$-finite limit, as well as for the special case of electron-hole symmetry, $U+2V=0\mathrm{}$. Numerical results for the $U$-infinite, $V$-zero limit for zero temperature are obtained for $n_0$, the number of electrons on the impurity site, and for the one-electron $t$ matrix as a function of energy. $n_0$ has a value of 0.4, which may be compared with the values $n_0=0\mathrm{}$ predicted by the Hartree-Fock theory and $n_0=\frac{2}{3}$ obtained by using a determinantal wave function from which the doubly occupied state is projected out. The $t$ matrix is found to exhibit a characteristic Kondo-like resonance at zero energy, and indicates a resistivity which falls rapidly with increasing temperature, as well as a specific-heat anomaly.