Basic Properties of Conductivity and Normal Hall Effect in the Periodic Anderson Model

TL;DR

This paper derives exact formulas for conductivity and Hall effect in the periodic Anderson model, analyzing their behavior across different regimes and implications for heavy electron systems.

Contribution

It introduces a theoretical framework for conductivity and Hall effect in the periodic Anderson model, highlighting the effects of mass-renormalization and Fermi surface curvature.

Findings

Mass-renormalization imbalance increases conductivity in valence-fluctuation regime.

Cancellation of renormalization factors causes slight increase in Kondo regime.

Hall coefficient remains nearly constant, reflecting Fermi surface properties.

Abstract

Exact formulas of diagonal conductivity $\sigma_{xx}$ and Hall conductivity $\sigma_{xy}$ are derived from the Kubo formula in hybridized two-orbital systems with arbitrary band dispersions. On the basis of the theoretical framework for the Fermi liquid based on these formulas, the ground-state properties of the periodic Anderson model with electron correlation and weak impurity scattering are studied on the square lattice. It is shown that imbalance of the mass-renormalization factors in $\sigma_{xx}$ and $\sigma_{xy}$ causes remarkable increase in the valence-fluctuation regime as the f level increases while the cancellation of the renormalization factors causes slight increase in $\sigma_{xx}$ and $\sigma_{xy}$ in the Kondo regime. The Hall coefficient $R_{\rm H}$ shows almost constant behavior in both the regimes. Near half filling, $R_{\rm H}$ is expressed by the total hole density as $R_{\rm H}=1/(\bar{n}_{\rm hole}e)$ while $R_{\rm H}$ approaches zero near quarter filling, which reflects the curvature of the Fermi surface. These results hold as far as the damping rate for f electrons is less than about $10~\%$ of the renormalized hybridization gap. From these results we discuss pressure dependence of residual resistivity and normal Hall effect in Ce- and Yb-based heavy electron systems.