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

Abstract We investigate the bulk-boundary correspondence in two-dimensional type-I semi-Dirac materials with band inversion and Rashba spin–orbit coupling (SOC). 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , symmetry-protected edge states emerge, analogously to the Rashba-free case. At finite <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>x</mml:mi> </mml:msub> </mml:mrow> </mml:math> , the interplay of SOC 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.