Abstract
Using an elegant model involving only Γ6c and Γ8v bands, massless Kane fermions were defined as the particles associated with the peculiar band structure of gapless HgCdTe crystals. Although their dispersion relation resembles that of a pseudo-spin-1 Dirac semimetal, these particles were originally considered to be hybrids of pseudospin-1 and -1/2 fermions. Here we unequivocally find that, by considering an additional Γ7c conduction band inherent in HgCdTe crystals, the Kane fermions are ultimately two nested Dirac particles. This observation allows for the direct application of Lorentz transformations to describe the relativistic behavior of these particles in crossed electric and magnetic fields. By studying the relativistic collapse of their Landau levels at different orientations between the crossed fields and the main crystallographic axes, we demonstrate that the Kane fermions strikingly decay into two independent Dirac particles with increase of the electric field. Our results provide insight into semirelativistic effects in narrow-gap semiconductors in crossed electric and magnetic fields.