Magnetospectroscopy of two-dimensional HgTe-based topological insulators around the critical thickness

Abstract

Recently, a new class of materials, so-called topological insulators, has emerged. These are systems characterized by the inversion of the electronic band structure and also by a certain strength of the spin-orbit interaction. HgTe/Cd${}_{x}$Hg${}_{1\ensuremath{-}x}$Te quantum wells represent a prominent example. They can change to the topological insulator phase from the conventional insulator phase when the thickness of the quantum well is increased over the critical thickness ${d}_{c}$ = 6.3 nm. Here, we report on a far-infrared magnetospectroscopy study of a set of HgTe/Cd${}_{x}$Hg${}_{1\ensuremath{-}x}$Te quantum wells with different thicknesses from below to above the critical value ${d}_{c}$. In quantizing magnetic fields up to 16 T, both intraband and interband transitions have been clearly observed. In the widest quantum well with inverted band structure, we confirm the avoided crossing of the zero-mode Landau levels observed earlier in similar structures. In both noninverted quantum wells close to the critical thickness, we report unambiguously on the square root dependence of the transition energy on the magnetic field, as expected in the single-particle model of massless Dirac fermions. The obtained results are compared with the allowed transition energies between Landau levels in the valence and conduction bands calculated using the 8 \ifmmode\times\else\texttimes\fi{} 8 Kane model.