We present detailed theoretical analysis of nonradiative Auger recombination in narrow-gap mercury-cadmium-telluride quantum wells (HgCdTe QWs). We suggest a microscopic model to calculate Auger recombination rates in the QWs with different Cd fraction as functions of non-equilibrium carrier density with account to the complex band dispersions and wavefunctions, degenerate carrier statistics, and screening effects. Our model is validated by the comparison of measured photoconductivity kinetics with the simulated curves. Furthermore, we use the developed calculation technique to evaluate different designs of HgCdTe/CdHgTe QWs for the far-IR emitters. In particular, we consider a series of QWs with the fixed bandgap of 40 meV (lasing wavelength about 30 μm) and find out that lasing may be favored in the QWs with moderate (6%–9%) cadmium content and not in the pure binary HgTe QWs, which is in contrast to intuitive expectations within threshold energy concept for Auger recombination. Though cadmium-free QWs do provide the highest possible Auger threshold energies, Cd-containing QWs feature much more efficient screening of Coulomb potential (and so Auger interaction) by free charge carriers. The latter effect contributes decisively into the suppression of Auger processes at low temperatures and high carrier concentrations.

Long-wavelength stimulated emission (SE) is studied in optically pumped HgCdTe quantum well heterostructures with dielectric waveguides. Continuous temperature tuning of the wavelength from 27 to 18 μm is achieved in structures with optimized waveguides. Above 27 μm, SE clamps at 31 μm wavelength, where mode leaking is reduced due to the Reststrahlen effect in the GaAs substrate. The operating temperature is mainly limited by the activation of Auger recombination in quasi-equilibrium conditions, while at low temperatures, we expect that lowering initial carrier heating would enhance the gain considerably. We conclude that exploiting the Reststrahlen effect should allow one to achieve continuous wavelength tuning around 30 μm and operating wavelengths up to 40 μm with technologically attainable epistructure thickness.

Amplified interband emission within the 14–24 μm range is investigated in HgCdTe-based quantum wells under optical pumping. Carrier lifetimes are shown to be marginally limited only by Shockley–Read–Hall recombination, fully realizing the advantage of relativistic energy spectra of 2D HgCdTe in terms of suppressing the Auger processes. By carefully optimizing the waveguides and mitigating carrier heating, we achieve amplification thresholds as low as 1.5–2 W/cm2 at a pulse duration of 20–500 μs. With last generation quantum cascade lasers used for optical pumping, we estimate that continuous-wave HgCdTe lasers can operate in the very long-wavelength range (15–30 μm) and beyond.

For $\nu \in \left[0,1\right]$ , let $D^{\nu }$ be the distinguished self-adjoint realisation of the three-dimensional Coulomb-Dirac operator $-\mathrm{i}\mathbf{\alpha }\cdot \nabla -\nu |\cdot {|}^{-1}$ . For $\nu \in [0,1)$ , we prove the lower bound of the form $|D^{\nu }|⩾C_{\nu }\sqrt{-\mathrm{\Delta }}$ , where $C_{\nu }$ is found explicitly and is better than in all previous studies on the topic. In the critical case $\nu =1$ , we prove that for every $\mathrm{\lambda }\in [0,1)$ , there exists $K_{\mathrm{\lambda }}>0$ such that the estimate $|D^1|⩾K_{\mathrm{\lambda }}{a}^{\mathrm{\lambda }-1}{(-\mathrm{\Delta })}^{\mathrm{\lambda }∕2}-a^{-1}$ holds for all $a>0$ . As applications, we extend the range of coupling constants in the proof of the stability of the relativistic electron-positron field and obtain Cwickel-Lieb-Rozenblum and Lieb-Thirring type estimates on the negative eigenvalues of perturbed projected massless Coulomb-Dirac operators in the Furry picture. We also study the existence of a virtual level at zero for such projected operators.

<!-- *** Custom HTML *** --> Temperature-driven photoconductivity spectra are studied in HgCdTe thin films and quantum well (QW) heterostructures grown by molecular beam epitaxy (MBE). It is shown that the absorption edge steepness in narrow gap HgCdTe epilayers approaches the fundamental limit. The corresponding Urbach energy is 1.5 to 4 meV at 4.2 to 77 K, which is an order of magnitude lower than values reported previously, indicating a significant progress in the quality of structures grown by MBE. Auger-suppressed multi-QW heterostructures that can be used for development of long-wavelength lasers/detectors are shown to have the comparable steepness of the absorption edge. The corresponding “Urbach” energy is much less than the threshold energy of the Auger recombination, which means that furthering the operating wavelengths beyond 20 μm is feasible for optoelectronic devices based on HgCdTe structures.

HgTe/CdHgTe quantum well (QW) heterostructures have attracted a lot of interest recently due to insights they provided towards the physics of topological insulators and massless Dirac fermions. Our work focuses on HgCdTe QWs with the energy spectrum close to the graphene-like relativistic dispersion that is supposed to suppress the non-radiative Auger recombination. We combine various methods such as photoconductivity, photoluminescence and magneto-optical measurements as well as transmission electron microscopy to retrofit growth parameters in multi-QW waveguide structures, designed for long wavelengths lasing in the range of 10–22 μm. The results reveal that the attainable operating temperatures and wavelengths are strongly dependent on Cd content in the QW, since it alters the dominating recombination mechanism of the carriers.