We report on optical reflectivity experiments performed on ${\mathrm{Cd}}_3{\mathrm{As}}_2$ over a broad range of photon energies and magnetic fields. The observed response clearly indicates the presence of 3D massless charge carriers. The specific cyclotron resonance absorption in the quantum limit implies that we are probing massless Kane electrons rather than symmetry-protected 3D Dirac particles. The latter may appear at a smaller energy scale and are not directly observed in our infrared experiments.

It has recently been shown that electronic states in bulk gapless HgCdTe offer another realization of pseudo-relativistic three-dimensional particles in condensed matter systems. These single valley relativistic states, massless Kane fermions, cannot be described by any other relativistic particles. Furthermore, the HgCdTe band structure can be continuously tailored by modifying cadmium content or temperature. At critical concentration or temperature, the bandgap collapses as the system undergoes a semimetal-to-semiconductor topological phase transition between the inverted and normal alignments. Here, using far-infrared magneto-spectroscopy we explore the continuous evolution of band structure of bulk HgCdTe as temperature is tuned across the topological phase transition. We demonstrate that the rest mass of Kane fermions changes sign at critical temperature, whereas their velocity remains constant. The velocity universal value of (1.07±0.05) × 10⁶ m s⁻¹ remains valid in a broad range of temperatures and Cd concentrations, indicating a striking universality of the pseudo-relativistic description of the Kane fermions in HgCdTe.

Resistively detected nuclear magnetic resonance measurements have been performed on a high mobility heterostructure in the quantum Hall regime. At millikelvin temperatures the nuclear resonances are observed in the vicinity of various integer and fractional filling factors without previous dynamic nuclear polarization. Near $\nu =1\mathrm{}$, the observed large enhancement of the resonance amplitude accompanied by a reduction of $T_1$ strongly suggests a greatly increased coupling between the electronic and nuclear spin systems. This is consistent with the proposed coupling of the nuclear spin system to the Goldstone mode of the Skyrme crystal.

We report a direct observation of temperature-induced topological phase transition between the trivial and topological insulator states in an HgTe quantum well. By using a gated Hall bar device, we measure and represent Landau levels in fan charts at different temperatures, and we follow the temperature evolution of a peculiar pair of “zero-mode” Landau levels, which split from the edge of electronlike and holelike subbands. Their crossing at a critical magnetic field $B_c$ is a characteristic of inverted band structure in the quantum well. By measuring the temperature dependence of $B_c$, we directly extract the critical temperature $T_c$ at which the bulk band gap vanishes and the topological phase transition occurs. Above this critical temperature, the opening of a trivial gap is clearly observed.

We report on the temperature-dependent magnetospectroscopy of two HgTe/CdHgTe quantum wells below and above the critical well thickness $d_c$. Our results, obtained in magnetic fields up to 16 T and s temperature range from 2 to 150 K, clearly indicate a change in the band-gap energy with temperature. A quantum well wider than $d_c$ evidences a temperature-driven transition from topological insulator to semiconductor phases. At a critical temperature of 90 K, the merging of inter- and intraband transitions in weak magnetic fields clearly specifies the formation of a gapless state, revealing the appearance of single-valley massless Dirac fermions with a velocity of $5.6\times {10}^5\mathrm{m}{\mathrm{s}}^{-1}$. For both quantum wells, the energies extracted from the experimental data are in good agreement with calculations on the basis of the eight-band Kane Hamiltonian with temperature-dependent parameters.

InSe is a promising material in many aspects where the role of excitons is decisive. Here we report the sequential appearance in its luminescence of the exciton, the biexciton, and the P-band of the exciton-exciton scattering while the excitation power increases. The strict energy and momentum conservation rules of the P-band are used to reexamine the exciton binding energy. The new value ≥20 meV is markedly higher than the currently accepted one (14 meV), being however well consistent with the robustness of the excitons up to room temperature. A peak controlled by the Sommerfeld factor is found near the bandgap (~1.36 eV). Our findings supported by theoretical calculations taking into account the anisotropic material parameters question the pure three-dimensional character of the exciton in InSe, assumed up to now. The refined character and parameters of the exciton are of paramount importance for the successful application of InSe in nanophotonics.