Ferroelectric Altermagnetic Chern Insulator in magnetic field: electrical control of the Chern number

Abstract: The quantum anomalous Hall effect in altermagnets is difficult to realize because spin-up and spin-down states remain degenerate at the $Γ$ point in the nonrelativistic limit. We start from the Bernevig-Hughes-Zhang model to incorporate nontrivial band topology. We demonstrate that the combined effects of an external magnetic field, spin canting, and ferroelectric orbital hybridization lift the degeneracy at the $Γ$ point, enabling electric-field control of the Chern number. A minimal two-dimensional d-wave altermagnetic model with band inversion then realizes a ferroelectrically tunable Chern insulator with spontaneous spin canting. The ferroelectric polarization controls the topological phase and the orbital angular momentum, enabling a rich phase diagram with C = $\pm 1$ and C = $\pm 2$ through a Berry-curvature reorganization linked to the spin canting response and ferroelectricity. Our results establish a symmetry-consistent route to electrically tunable Chern insulating phases in altermagnetic materials, opening opportunities for low-power topological and orbitronic devices.