Spin Chern number in altermagnets

TL;DR

This paper introduces a new topological invariant called the spin Chern number for classifying altermagnetic materials, revealing their potential as topologically protected insulators and semimetals.

Contribution

It develops a robust $C^z_4 imes ext{T}$ topological invariant using equivariant K-theory to classify 2D and 3D altermagnetic systems, linking altermagnetism with topological phases.

Findings

Spin Chern number acts as a robust topological index.

Predicts topologically protected 2D insulators and 3D Weyl semimetals.

Provides a pathway for exploring topological applications in $d$-wave altermagnetic materials.

Abstract

This work explores the topological properties of altermagnets, a novel class of collinear magnetic materials. We employ equivariant K-theory of magnetic groups and Hamiltonian models to formulate a robust $C^z_4 \mathbb{T}$ topological invariant to classify 2D and 3D altermagnetic systems. Our findings demonstrate that the spin Chern number serves as a robust topological index, corresponding to the half-quantized Chern number of the divided Brillouin zone. This indicator enables the prediction of a topologically protected 2D altermagnetic insulators and 3D Weyl altermagnetic semimetals, highlighting the relationship between altermagnetism and topological phases. Furthermore, our results provide a pathway to the exploration of topological applications in $d$-wave altermagnetic materials.