Model Hamiltonian for altermagnetic topological insulators

We present models of topological insulating Hamiltonians exhibiting intrinsic altermagnetic features, protected by combined threefold or fourfold rotational symmetries with time-reversal. We demonstrate that the spin Chern number serves as a robust topological invariant in two-dimensional systems, while for three-dimensional structures, the topological nature is characterized by the spin Chern numbers computed on the ${k}_{z}=0$ and ${k}_{z}=\ensuremath{\pi}$ planes. The resulting phases support symmetry-protected boundary modes, including corner, hinges, and surface states, whose structure is determined by the magnetic symmetry and the local magnetic moments. Our findings bridge the fields of altermagnetism and topological quantum matter, and they establish a theoretical framework for engineering spintronic topological systems without net magnetization.