Observation of three-dimensional massless Kane fermions in a zinc-blende crystal

Solid-state physics and quantum electrodynamics, with its ultrarelativistic (massless) particles, meet in the electronic properties of one-dimensional carbon nanotubes, two-dimensional graphene or topological-insulator surfaces. However, clear experimental evidence for electronic states with a conical dispersion relation in all three dimensions, conceivable for certain bulk materials, is still missing. Here, we study a zinc-blende crystal, HgCdTe, at the point of the semiconductor-to-semimetal topological transition. For this compound, we observe three-dimensional massless electrons, as certified from the dynamical conductivity increasing linearly with the photon frequency, with a velocity of about 10(6) m s(-1). Applying a magnetic field B results in a root B-dependence of dipole-active inter-Landau-level resonances and spin splitting of Landau levels also following a root B-dependence-well-established signatures of ultrarelativistic particles but until now not observed experimentally in any solid-state electronic system.