Nontrivial topology and localization in the double exchange model with possible applications to perovskite manganites

TL;DR

This paper demonstrates that the one-dimensional double exchange model with an incommensurate spiral exhibits topological insulator behavior with protected edge states and localization, revealing new physics relevant to manganites.

Contribution

It uncovers nontrivial topology and localization phenomena in the double exchange model with potential applications to perovskite manganites.

Findings

The model is a topological insulator with Chern number 2Z.

Electronic states can be localized under strong exchange coupling.

Protected edge states enable charge pumping and multiferroic responses.

Abstract

The double exchange model describing the coupling between conduction electrons and localized magnetic moments is relevant for a large family of physical systems including manganites. Here we reveal that the one dimensional double exchange model with an incommensurate magnetic elliptical spiral is a topological insulator with a Chern number $2\mathbb{Z}$ in the two dimensional space with one physical dimension and one ancillary dimension spanned by the Goldstone mode of the spiral. Moreover, the electronic states can be localized for a strong local exchange coupling. The topological protected edge states are responsible for the pumping of electron charge, and give rise to multiferroic response. Our work uncovers hitherto undiscovered nontrivial topology and Anderson localization in the double exchange model with possible applications to perovskite manganites.