Energy spectrum of semimetallic HgTe quantum wells

Quantum wells (QWs) based on mercury telluride (HgTe) thin films provide a large range of unusual physical properties, from an insulator via a two-dimensional Dirac semimetal to a three-dimensional topological insulator. These properties result from the dramatic change in the QW band structure with the HgTe film thickness. Despite being a key property, these energy dispersion relations cannot be reflected in experiments due to the lack of appropriate tools. Here we report an experimental and theoretical study of two HgTe QWs with an inverted energy spectrum in which two-dimensional semimetallic states are realized. Using magneto-optical spectroscopy at subterahertz frequencies we obtain information about electron and hole cyclotron masses at all relevant Fermi level positions and different charge densities. The outcome is also supported by a Shubnikov-de Haas analysis of capacitance measurements, which allows us to obtain information on the degeneracy of the active modes. From these data, it is possible to reconstruct electron and hole dispersion relations. A detailed comparative analysis of the energy dispersion relations with theoretical calculations demonstrates a good agreement, even reflecting several subtle features like band splitting, the second conduction band, and the overlaps between the first conduction and the first valence band. Our study demonstrates that cyclotron resonance experiments can be efficiently used to directly obtain the band structures of semimetallic two-dimensional materials.