Universal transparency and fine band structure near the Dirac point in HgTe quantum wells

Spin-orbit coupling in thin HgTe quantum wells results in a relativistic-like electron band structure, making it a versatile solid state platform to observe and control non-trivial electrodynamic phenomena. Here we report an observation of universal terahertz (THz) transparency determined by fine-structure constant $\alpha \approx 1\mathrm{/}137$ in 6.5 nm-thick HgTe layer, close to the critical thickness separating phases with topologically different electronic band structure. Using THz spectroscopy in magnetic field we obtain direct evidence of asymmetric spin splitting of the Dirac cone. This particle-hole asymmetry facilitates optical control of edge spin currents in the quantum wells.