Mercury telluride (HgTe) colloidal Quantum Dots (QDs) combine the inverted bandgap of bulk HgTe with tunable optoelectronic properties, making them ideal for infrared optoelectronic applications. In this work, we study spherical QDs with diameters up to 22 nm to explore their evolution from a conventional positive-gap semiconductor phase to a negative-gap phase at ambient and low temperatures. This transition is characterized by the crossover between conduction and valence levels, as occurs in the topological transition within HgTe quantum wells. We use a semiempirical tight binding model along with advanced solvers to compute the energy levels, wave functions, and oscillator strengths as functions of size. Our analysis reveals the progressive emergence of edge states associated with band inversion, as had already been predicted in HgS QDs. By comparing with predictions for QDs of conventional semiconductors such as CdTe, we highlight many unusual behaviors, such as a strong variation of the $s/p$ components of the wave functions with size, the increase in spin-orbit splitting between quantum levels as QD size increases, or a strong influence of spin-orbit coupling on the spatial shape of QD orbitals. Furthermore, certain optical transitions that are forbidden by symmetry in CdTe QDs become allowed in HgTe QDs. We also simulate absorption spectra for neutral and doped QDs, showing a complex interplay between interband and intraband transitions across the infrared range, the energy order between these different transitions can be reversed depending on the QD size. These effects have a strong influence on radiative recombination rates and their variation with size and temperature. Our results predict that the optical properties of HgTe QDs, when approaching the inverted-gap transition, are of great interest for infrared optoelectronic devices.

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• Electronic structure
• Quantum dots
• Topological materials
• Tight-binding model