We investigate the photonic spin Hall effect (PSHE) and the Goos-Hänchen shift (GH shift) in semi-Dirac materials. Through theoretical modeling, we demonstrate that the anisotropic dielectric function in semi-Dirac materials plays a critical role in determining the magnitude and polarity of these optical displacements. Furthermore, by utilizing the unidirectional drift of massless Dirac electrons in semi-Dirac materials, we systematically reveal how the drift velocity and direction modulate the behavior of optical displacements. The results indicate that the unique electronic properties of semi-Dirac materials—particularly their anisotropic dielectric response and carrier drift dynamics—establish mechanisms for controlling optical displacements and polarization-dependent phenomena. This work opens a new avenue for designing advanced photonic devices with tunable optical responses, particularly with significant application potential in quantum information processing and topological photonics.

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• Transport phenomena
• Two-dimensional electron system
• Tight-binding model