3D massless Kane fermions observed in a zinc-blende crystal

Solid state physics and quantum electrodynamics with its ultra-relativistic (massless) particles meet, to their mutual beneit, in the electronic properties of one-dimensional carbon nanotubes as well as two-dimensional graphene or surfaces of topological insulators. However, clear experimental evidence for electronic states with conical dispersion relations in all three dimensions, conceivable in certain bulk materials, is still missing. In the present work, we fabricate and study a zinc-blend crystal, HgCdTe, at the point of the semiconductor-to-semimetal topological transition. Three-dimensional massless electrons with a velocity of about 10$^6$ m/s are observed in this material, as testifed by: (i) the dynamical conductivity which increases linearly with the photon frequency, (ii) in a magnetic field $B$, by a $\sqrt{B}$ dependence of dipole-active inter-Landau-level resonances and (iii) the spin splitting of Landau levels, which follows a $\sqrt{B}$ dependence, typical of ultra-relativistic particles but not really seen in any other electronic system so far.