Spin-dependent transport through edge states in 2D semi-Direc materials with Rashba spin-orbit coupling and band inversion

We investigate the bulk-boundary correspondence in two-dimensional type-I semi-Dirac materials with band inversion and Rashba spin-orbit coupling. Employing a dimensional reduction framework, we identify the Zak phase along the quadratically dispersing direction as a topological invariant that captures the presence of edge states. In the non-trivial topological regime, systems with finite width exhibit energy-dependent edge states that are topologically protected only at specific momenta. At kₓ=0, symmetry-protected edge states emerge, analogously to the Rashba-free case. At finite kₓ, the interplay of spin-orbit coupling and band structure gives rise to spin-dependent edge states, localized on specific edges based on its spin and particle-hole character. We computed spin-resolved conductance through these edge channels and observed robust, tunable oscillations—attributable to spin precession induced by the effective Rashba magnetic field. These results reveal how spin-orbit interactions enrich the edge physics of semi-Dirac systems and provide a platform for spintronic control in anisotropic topological materials.