Heavy-hole excitonic effects in rare-earth compounds

Abstract

In order to explain some recent experiments on a variety of rare-earth compounds such as Sm${\mathrm{B}}_{6}$ and the high-pressure phase of SmS, we propose a model consisting of conducting $d$ and $f$ electrons, the latter assumed to be infinitely heavy. They interact with each other by both non-spin-flip (${V}_{0}$) and spin-flip (${V}_{s}$) electron-electron interactions. We find that as far as the first-order renormalization-group method is concerned this system is equivalent to a one-dimensional (1-D) system that has become quite popular recently (the Menyhard-Solyom model). The correspondence has ${V}_{0}={g}_{2}\ensuremath{-}\frac{{g}_{1}}{2}$ and ${V}_{s}=\ensuremath{-}2{g}_{1}$ in the usual notation. Owing to this interaction the system may or may not go through an "excitonic" phase transition. From the 1-D work of Solyom on the density-density response function, we conclude that ${V}_{0}$ will never cause a phase transition at any finite temperature, that only ${V}_{s}$ may cause a phase transition, and that the temperature at which this occurs is unaffected by ${V}_{0}$. We argue that because ${V}_{s}$ is much smaller than ${V}_{0}$, it is not important for the system and the range of temperature that is of interest. Neglecting ${V}_{s}$, we find that the conductivity is given by a formula $\ensuremath{\sigma}=\frac{N{e}^{2}\ensuremath{\tau}}{m}$, where $\ensuremath{\tau}$ is given approximately by the equation ${\ensuremath{\tau}}^{\ensuremath{-}1}={\ensuremath{\tau}}_{0}^{\ensuremath{-}1}{[\frac{(T+\ensuremath{\beta}{\ensuremath{\tau}}^{\ensuremath{-}1})}{{E}_{F}}]}^{\ensuremath{-}\ensuremath{\alpha}}$, $\ensuremath{\beta}$ here is a constant of the order of unity. We also discuss the resistivities of Sm${\mathrm{B}}_{6}$, "metallic" SmS, TmS, and TmSe and find good agreement with the experimental results.