Perfect transmission of 3D massive Kane fermions in HgCdTe Veselago lenses

Abstract: The transmission properties of three-dimensional (3D) massive Kane fermions in HgCdTe (MCT) heterojunctions have been studied using the simplified Kane-Mel\'e model. Based on our theoretical calculations, we propose the design of an electronic device, called mass inverter, which consists of the junction of a narrow-gap semiconductor and semimetal. Such a device can be used in electron optics applications, since it operates as a Veselago lens and presents Klein tunneling (KT) of 3D massive Kane fermions under normal incidence. We found that KT and Veselago lensing can also be observed for general MCT heterojunctions with a specific value of doping level. We show that non-resontant perfect transmission of massive Kane fermions persists in a potential barrier for heterojunctions formed by a semimetal between two standard semiconductors. This effect is quite robust when the ideal conditions of a possible experimental test are deviated. Our findings may have important implications in the development of nano-electronic devices using 3D massive Kane fermions, where transmission features of massless particles are recovered.