Quantum anomalous Hall conductivity in altermagnets under applied magnetic field

TL;DR

This paper explores how an external magnetic field induces quantum anomalous Hall conductivity in a two-dimensional altermagnet on a Lieb lattice, revealing valley-dependent topological phases and magnetic control mechanisms.

Contribution

It demonstrates a novel mechanism for magnetic control of quantum anomalous Hall effects in altermagnets with valley-dependent topology and distinguishes it from other spintronic systems.

Findings

Valley-specific Chern numbers depend on magnetic field strength.

Phase diagram includes normal insulator, spin Chern insulator, and Dirac semimetal phases.

Berry curvature analysis shows fully gapped topological phases with total Chern numbers ±1.

Abstract

We investigate the emergence of quantum anomalous Hall conductivity in a two-dimensional $d$-wave altermagnet on a Lieb lattice under an external magnetic field. Altermagnetic order induces momentum-dependent spin splitting without net magnetization in the relativistic limit, producing distinct spin-resolved bands at the $X$ and $Y$ valleys. The phase diagram features a normal insulator and a spin Chern insulator separated by an accidental Dirac semimetal. The magnetic field breaks rotational symmetry between valleys while maintaining vanishing total magnetization, enabling independent valley contributions to topology. One valley supports Chern numbers $C=-1$ or $0$, while the other hosts $C=0$ or $+1$, governed by field strength and bandwidth. This competition yields valley-dependent topology. Berry curvature analysis reveals fully gapped phases with total Chern numbers $C=\pm1$, separated by valley-selective gap closings. We uncover a mechanism for rapid magnetic control of the quantum anomalous Hall effect near the semimetal phase and highlight key distinctions from ferro-valleytronic and quantum spin Hall systems.