Landau levels and spin splitting in the two-dimensional electron gas of a HgTe quantum well near the critical width for the topological phase transition

Abstract

We report a detailed low-temperature study of the two-dimensional (2D) electron gas in a 6.1-nm-wide HgTe quantum well with $\mathrm{H}{\mathrm{g}}_{0.3}\mathrm{C}{\mathrm{d}}_{0.7}\mathrm{Te}$ barriers by terahertz magnetophotoconductivity and magnetotransmission combined with magnetotransport measurements (${R}_{xx}$ and ${R}_{xy}$) in magnetic fields up to 10 T. This well width, close to that at the topological phase transition, corresponds to conventional band ordering, and we probe the ``bulk'' quasi-2D Landau-level (LL) spectrum of the conduction band at high energies $(\ensuremath{\approx}135\ensuremath{-}160\phantom{\rule{0.16em}{0ex}}\mathrm{meV})$ above the Dirac point. The calculated separations between adjacent LLs of the same spin based on published parameters for this structure are in fair agreement with the measured cyclotron resonance energies. However, the very large spin splittings observed $({E}_{\mathrm{spin}}>{E}_{\mathrm{cyclotron}})$ require a significantly larger $g$-parameter ${g}_{e}$ for electrons. Tilted field coincidence experiments are consistent with the large spin splitting showing coincidences at 3/2 and twice the cyclotron energy. This large value of ${g}_{e}$ also leads to interesting crossings of the calculated LLs, and we find direct evidence of these crossings in the ${R}_{xx}$ measurements at lower electron densities (Fermi energies) produced by negative gate bias.