Semiclassical Solution of One Dimensional Model of Kondo Insulator

TL;DR

This paper analyzes a one-dimensional Kondo chain model with degenerate conduction bands, revealing how the spin excitation spectrum and electronic properties depend on the degeneracy and localized spins, with implications for higher-dimensional Kondo insulators.

Contribution

It provides a semiclassical solution for the one-dimensional Kondo insulator model, connecting the spectrum to the O(3) nonlinear sigma model with a topological term.

Findings

Spin excitation spectrum described by O(3) nonlinear sigma model with topological term

Insulating behavior with massive spin polarons when |M - 2S| is even

Pseudogap in density of states vanishing at Fermi level

Abstract

The model of Kondo chain with $M$-fold degenerate band of conduction electrons of spin 1/2 interacting with localized spins $S$ is studied for the case when the electronic band is half filled. It is shown that the spectrum of spin excitations in the continuous limit is described by the O(3) nonlinear sigma model with the topological term with $\theta = \pi(2S - M)$. For a case $|M - 2S| = $(even) the system is an insulator and single electron excitations at low energies are massive spin polarons. Otherwise the density of states has a pseudogap and vanishes only at the Fermi level. The relevance of this picture to higher dimensional Kondo insulators is discussed.