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Quantum Anomalous Hall Conductivity in Altermagnets under Applied Magnetic Field
Meysam Bagheri Tagan1,2, Amar Fakhredine3, Carmine Autieri1
1International Research Centre Magtop, Institute of Physics, Polish Academy of Sciences, Aleja Lotnik'ow 32/46, PL-02668 Warsaw, Poland.
None:
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, whereas the other hosts C = 0 or +1, governed by the field strength and bandwidth. This competition yields valley-dependent topology. Berry curvature analysis reveals fully gapped phases with total Chern numbers C = ±1, 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.
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