Band topology and symmetry-driven magneto-optical response in two-dimensional d-wave altermagnets with staggered spin-orbit coupling

Altermagnets combine compensated collinear magnetic order with momentum-dependent spin splitting, providing a route to transverse electronic and optical responses without a net ferromagnetic moment. We develop a strictly periodic four-band tight-binding model for a two-dimensional d-wave altermagnet and distinguish the roles of three spin orbit coupling (SOC) channels: uniform Rashba SOC, a sublattice-staggered Rashba interaction, and bond-staggered SOC. In the absence of SOC, the d-wave kinetic anisotropy produces spin-polarized Dirac points on orthogonal Brillouin-zone boundaries, related by the altermagnetic fourfold spin-group symmetry. Uniform Rashba SOC mixes the spin sectors and shifts these nodes but preserves the antiunitary symmetry that forbids an integrated Hall response. The sublattice-staggered Rashba term breaks this symmetry and activates transverse optical response, whereas the bond-staggered SOC provides the mass that gaps the boundary nodes. Their combined action generates strong Berry-curvature hot spots and, within a narrow parameter window, an isolated lower two-band manifold with Chern number C=-2. For the representative parameters considered here it is possible to stabilize a Chern insulator phase. Using covariant-velocity Kubo calculations, we show that large optical Hall conductivity and circular dichroism extend well beyond the nonzero-Chern region and are controlled by SOC-induced avoided crossings and symmetry breaking. We further find that carrier doping strongly modifies the resonant and dc Hall responses through Pauli blocking and the occupation of Berry-curvature hot spots, enabling gate-controlled sign reversals. These results identify the complementary roles of distinct interfacial SOC mechanisms in producing topology and tunable magneto-optical activity in compensated two-dimensional magnets.