Mirror Chern Bands and Weyl Nodal Loops in Altermagnets

TL;DR

This paper explores how the magnetic moment orientation in altermagnets influences their topological electronic properties, revealing new Dirac crossings, mirror Chern bands, and Weyl nodal loops, with potential for novel quantum effects.

Contribution

It demonstrates the emergence of new topological phenomena in altermagnets, including Dirac crossings, mirror Chern bands, and Weyl loops, depending on magnetic moment direction and spin-orbit coupling.

Findings

Out-of-plane moments lead to mirror Chern bands enabling Quantum Spin Hall Effect.

SOC gaps Dirac crossings in 2D models, causing topological transitions.

Weyl nodal loops persist in 3D models despite SOC presence.

Abstract

The electronic spectra of altermagnets are a fertile ground for nontrivial topology due to the unique interplay between time-reversal and crystalline symmetries. This is reflected in the unconventional Zeeman splitting between bands of opposite spins, which emerges in the absence of spin-orbit coupling (SOC) and displays nodes along high-symmetry directions. Here, we argue that even for a small SOC, the direction of the magnetic moments in the altermagnetic state has a profound impact on the electronic spectrum, enabling novel topological phenomena to appear. By investigating microscopic models for two-dimensional (2D) and three-dimensional (3D) altermagnets, motivated in part by rutile materials, we demonstrate the emergence of hitherto unexplored Dirac crossings between bands of the same spin but opposite sublattices. The direction of the moments determines the fate of these crossings when the SOC is turned on. We focus on the case of out-of-plane moments, which forbid an anomalous Hall effect and thus ensure that no weak magnetization is triggered in the altermagnetic state. In the 2D model, the SOC gaps out the Dirac crossings, resulting in mirror Chern bands that enable the Quantum Spin Hall Effect and undergo a topological transition to trivial bands upon increasing the magnitude of the magnetic moment. On the other hand, in the 3D model the crossings persist even in the presence of SOC, forming Weyl nodal loops protected by mirror symmetry. Finally, we discuss possible ways to control these effects in altermagnetic material candidates.