Band structure of a two-dimensional Dirac semimetal from cyclotron resonance

Knowing the band structure of materials is one of the prerequisites to understanding their properties. Therefore, angle-resolved photoemission spectroscopy (ARPES) has become a highly demanded experimental tool to investigate the band structure. However, especially in thin film materials with a layered structure and several capping layers, access to the electronic structure by ARPES is limited. Therefore, several alternative methods to obtain the required information have been suggested. Here we directly invert the results by cyclotron resonance experiments to obtain the band structure of a two-dimensional (2D) material. This procedure is applied to the mercury telluride quantum well with a critical thickness which is characterized by a 2D electron gas with linear dispersion relations. The Dirac-like band structure in this material could be mapped both on the electron and on the hole side of the band diagram. In this material, purely linear dispersion of the holelike carriers is in contrast to detectable quadratic corrections for the electrons.

Figure 1

Schematic drawing of the magneto-optical terahertz transmission experiment. $\theta$ is the Faraday rotation angle, $\eta$ is the ellipticity, and $t_p$ and $t_c$ are the transmission amplitudes in the parallel and crossed polarizers, respectively. The inset shows the photograph of the sample with ex situ gate.

Figure 2

Cyclotron resonance in the terahertz range. Three-dimensional (3D) presentation of the measured transmission at 320 GHz (sample 2) in crossed polarizers geometry and in a broad range of magnetic fields and gate voltages. In a simple approximation, the transmission in crossed polarizers is proportional to the Faraday rotation angle $\theta$.

Figure 3

Complex-plane presentation of the cyclotron resonance. Complex presentation of the Faraday rotation $\theta$ and ellipticity $\eta$ at selected gate voltages demonstrating the transition from holelike (a) to electronlike (d) carriers (sample 2, $\nu =320$ GHz). Symbols: experimental data, red lines: model fit using Drude conductivity, Eq. (6), and black lines are a guide to the eyes.

Figure 4

Electrodynamic parameters of the charge carriers. The data are obtained from simultaneous fitting of the magneto-optical spectra using the Drude model in the presence of the external magnetic field [28, 35]. Left panels: sample 1 (340 GHz), $d=6.3$ nm, right panels: sample 2 (320 GHz), $d=6.6$ nm. (a) and (b) Normalized conductivity, (c) and (d) mobility, and (e) and (f) effective mass. Up triangles: increasing gate voltage, down triangles: decreasing voltage, closed green/blue triangles: electrons, and open red/orange triangles: holes. Blue and green lines are a guide to the eyes and red solid lines in (e) and (f) represent the square root behavior expected for Dirac dispersion.

Figure 5

Band structure of the HgTe films with critical thickness. (a) and (c) Sample 1. (b) and (d) Sample 2. Left panels: 2D presentation. The notations are the same as in Fig. 4. Right panels: the data are replotted in a 3D form.

Figure 6

Far-infrared magneto-optical spectra. Symbols: experimental absorption frequencies in the infrared transmission experiment. Solid gray lines: magnetic field dependence of the Landau level energy. Red solid line: calculated position of the absorption frequencies as described in the text. The inset shows examples of the normalized transmission spectra. The curves are shifted for clarity.