Orientation-dependent crossover from retro to specular Andreev reflections in semi-Dirac materials

Abstract In the framework of Bogoliubov–de Gennes equation, we theoretically study the transport properties in normal-superconducting junctions based on semi-Dirac materials (SDMs). Owing to the intrinsic anisotropy of SDMs, the configuration of Andreev reflection (AR) and the differential conductance are strongly orientation-dependent. For the transport along the linear dispersion direction, the differential conductance exhibits a clear crossover from retro AR to specular AR with increasing the bias-voltage, and the differential conductance oscillates with the interfacial barrier strength without a decaying profile. Conversely, for the transport along the quadratic dispersion direction, the boundary between the retro AR and specular AR becomes ambiguous when the orientation angle increases, and the differential conductance decays with increasing the momentum mismatch or the interfacial barrier strength. We illustrate the pseudo-spin textures to reveal the underling physics behind the anisotropic coherent transport properties. These results enrich the understanding of the superconducting coherent transport in SDMs.