Total reflection and large Goos-Hänchen shift in a semi-Dirac system

Carriers in two-dimensional semi -Dirac materials exhibit massless and massive dispersions along two perpendicular directions. Here, we investigate theoretically their properties of transmission and Goos-Hanchen (GH) shift under an electric barrier. It is found that isolated transmission zeros are allowed (prohibited) when the electric barrier aligns with the parabolic (linear) dispersion direction. Such transmission zeros require the coexistence of evanescent and propagating states in the outgoing region, whose number and position depend on the barrier width and height. Under a wide barrier, huge GH shift can be achieved at a transmission zero close to a reflection zero and at a small incident angle. The polarity of the GH shift depends on the sign of the incident angle and is controlled by the relative position between the barrier height and incident energy. The isolated transmission zeros and enhanced GH shift with tunable polarity could be helpful for potential electron -optics applications of semi -Dirac systems.