HgTe colloidal quantum dots (QDs) are of interest because quantum confinement of semimetallic bulk HgTe allows one to synthetically control the bandgap throughout the infrared. Here, we synthesize highly monodisperse HgTe QDs and tune their doping both chemically and electrochemically. The monodispersity of the QDs was evaluated using small-angle X-ray scattering (SAXS) and suggests a diameter distribution of ∼10% across multiple batches of different sizes. Electron-doped HgTe QDs display an intraband absorbance and bleaching of the first two excitonic features. We see splitting of the intraband peaks corresponding to electronic transitions from the occupied 1Se state to a series of nondegenerate 1Pe states. Spectroelectrochemical studies reveal that the degree of splitting and relative intensity of the intraband features remain constant across doping levels up to two electrons per QD. Theoretical modeling suggests that the splitting of the 1Pe level arises from spin-orbit coupling and reduced QD symmetry. The fine structure of the intraband transitions is observed in the ensemble studies due to the size uniformity of the as-synthesized QDs and strong spin-orbit coupling inherent to HgTe.

In the recent work of Ref.\cite{Vlaic2017-bs}, it has been shown that Pb nanocrystals grown on the electron accumulation layer at the (110) surface of InAs are in the regime of Coulomb blockade. This enabled the first scanning tunneling spectroscopy study of the superconducting parity effect across the Anderson limit. The nature of the tunnel barrier between the nanocrystals and the substrate has been attributed to a quantum constriction of the electronic wave-function at the interface due to the large Fermi wavelength of the electron accumulation layer in InAs. In this manuscript, we detail and review the arguments leading to this conclusion. Furthermore, we show that, thanks to this highly clean tunnel barrier, this system is remarkably suited for the study of discrete electronic levels induced by quantum confinement effects in the Pb nanocrystals. We identified three distinct regimes of quantum confinement. For the largest nanocrystals, quantum confinement effects appear through the formation of quantum well states regularly organized in energy and in space. For the smallest nanocrystals, only atomic-like electronic levels separated by a large energy scale are observed. Finally, in the intermediate size regime, discrete electronic levels associated to electronic wave-functions with a random spatial structure are observed, as expected from Random Matrix Theory.

Colloidal quantum dots (QDs) raise more and more interest as solution-processable and tunable optical gain materials. However, especially for infrared active QDs, optical gain remains inefficient. Since stimulated emission involves multifold degenerate band-edge states, population inversion can be attained only at high pump power and must compete with efficient multi-exciton recombination. Here, we show that mercury telluride (HgTe) QDs exhibit size-tunable stimulated emission throughout the near-infrared telecom window at thresholds unmatched by any QD studied before. We attribute this unique behaviour to surface-localized states in the bandgap that turn HgTe QDs into 4-level systems. The resulting long-lived population inversion induces amplified spontaneous emission under continuous-wave optical pumping at power levels compatible with solar irradiation and direct current electrical pumping. These results introduce an alternative approach for low-threshold QD-based gain media based on intentional trap states that paves the way for solution-processed infrared QD lasers and amplifiers.

Recently, new materials exhibiting exotic band structures characterized by Dirac cones, nontrivial flat bands, and band crossing points have been proposed on the basis of effective two-dimensional lattice Hamiltonians. Here, we showusing atomistic tight-binding calculations that these theoretical predictions could be experimentally realized in the conduction band of superlattices nanolithographed in III-V and II-VI semiconductor ultrathin films. The lithographed patterns consist of periodic lattices of etched cylindrical holes that form potential barriers for the electrons in the quantum well. In the case of honeycomb lattices, the conduction minibands of the resulting artificial graphene host several Dirac cones and nontrivial flat bands. Similar features, but organized in different ways, in energy or in k-space are found in kagome, distorted honeycomb, and Lieb superlattices. Dirac cones extending over tens of meV could be obtained in superlattices with reasonable sizes of the lithographic patterns, for instance in InAs/ AlSb heterostructures. Bilayer artificial graphene could be also realized by lithography of a double quantum-well heterostructure. These new materials should be interesting for the experimental exploration of Dirac-based quantum systems, for both fundamental and applied physics.

The possibility of obtaining optical gain in an ensemble of semiconductor nanocrystals without involvement of multiexcitons is very attractive for low-threshold laser applications. Here, we reexamine theoretically the conditions required to reach this single-exciton gain regime in nanocrystals. We show that the electron-phonon interaction can play a very positive role, in addition to the exciton-exciton interaction. In presence of both interactions, the optical gain regime can be reached even when the population of nanocrystals containing single excitons is below 10%. For these reasons, we suggest that ultrasmall nanocrystals, or nanocrystals with deep defects at their surface, could be promising materials for light amplification.

The cooling dynamics of hot charge carriers in colloidal lead chalcogenide nanocrystals is studied by hyperspectral transient absorption spectroscopy. We demonstrate a transient accumulation of charge carriers at a high energy critical point in the Brillouin zone. Using a theoretical study of the cooling rate in lead chalcogenides, we attribute this slowing down of charge carrier cooling to a phonon scattering bottleneck around this critical point. The relevance of this observation for the possible harvesting of the excess energy of hot carriers by schemes such as multiexciton generation is discussed.

We study theoretically two-dimensional single-crystalline sheets of semiconductors that form a honeycomb lattice with a period below 10 nm. These systems could combine the usual semiconductor properties with Dirac bands. Using atomistic tight-binding calculations, we show that both the atomic lattice and the overall geometry influence the band structure, revealing materials with unusual electronic properties. In rocksalt Pb chalcogenides, the expected Dirac-type features are clouded by a complex band structure. However, in the case of zinc-blende Cd-chalcogenide semiconductors, the honeycomb nanogeometry leads to rich band structures, including, in the conduction band, Dirac cones at two distinct energies and nontrivial flat bands and, in the valence band, topological edge states. These edge states are present in several electronic gaps opened in the valence band by the spin-orbit coupling and the quantum confinement in the honeycomb geometry. The lowest Dirac conduction band has S-orbital character and is equivalent to the pi-pi* band of graphene but with renormalized couplings. The conduction bands higher in energy have no counterpart in graphene; they combine a Dirac cone and flat bands because of their P-orbital character. We show that the width of the Dirac bands varies between tens and hundreds of meV. These systems emerge as remarkable platforms for studying complex electronic phases starting from conventional semiconductors. Recent advancements in colloidal chemistry indicate that these materials can be synthesized from semiconductor nanocrystals.

The interest in 2-dimensional systems with a honeycomb lattice and related Dirac-type electronic bands has exceeded the prototype graphene1. Currently, 2-dimensional atomic2,3 and nanoscale4-8 systems are extensively investigated in the search for materials with novel electronic properties that can be tailored by geometry. The immediate question that arises is how to fabricate 2-D semiconductors that have a honeycomb nanogeometry, and as a consequence of that, display a Dirac-type band structure? Here, we show that atomically coherent honeycomb superlattices of rocksalt (PbSe, PbTe) and zincblende (CdSe, CdTe) semiconductors can be obtained by nanocrystal self-assembly and facet-to-facet atomic bonding, and subsequent cation exchange. We present a extended structural analysis of atomically coherent 2-D honeycomb structures that were recently obtained with self-assembly and facet-to-facet bonding9. We show that this process may in principle lead to three different types of honeycomb structures, one with a graphene type-, and two others with a silicene-type structure. Using TEM, electron diffraction, STM and GISAXS it is convincingly shown that the structures are from the silicene-type. In the second part of this work, we describe the electronic structure of graphene-type and silicene type honeycomb semiconductors. We present the results of advanced electronic structure calculations using the sp3d5s* atomistic tight-binding method10. For simplicity, we focus on semiconductors with a simple and single conduction band for the native bulk semiconductor. When the 3-D geometry is changed into 2-D honeycomb, a conduction band structure transformation to two types of Dirac cones, one for S- and one for P-orbitals, is observed. The width of the bands depends on the honeycomb period and the coupling between the nanocrystals. Furthermore, there is a dispersionless P-orbital band, which also forms a landmark of the honeycomb structure. The effects of considerable intrinsic spin-orbit coupling are briefly considered. For heavy-element compounds such as CdTe, strong intrinsic spin-‐orbit coupling opens a non-trivial gap at the P-orbital Dirac point, leading to a quantum Spin Hall effect10-12. Our work shows that well known semiconductor crystals, known for centuries, can lead to systems with entirely new electronic properties, by the simple action of nanogeometry. It can be foreseen that such structures will play a key role in future opto-electronic applications, provided that they can be fabricated in a straightforward way.

HgTe colloidal quantum dots are synthesized with high monodispersivity with sizes up to ∼15 nm corresponding to a room temperature absorption edge at ∼5 μm. The shape is tetrahedral for larger sizes and up to five peaks are seen in the absorption spectra with a clear size dependence. The size range of the HgTe quantum dots is extended to ∼20 nm using regrowth. The corresponding room temperature photoluminescence and absorption edge reach into the long-wave infrared, past 8 μm. Upon cooling to liquid nitrogen temperature, a photoconductive response is obtained in the long-wave infrared region up to 12 μm. Configuration-interaction tight-binding calculations successfully explain the spectra and the size dependence. The five optical features can be assigned to sets of single hole to single electron transitions whose strengths are strongly influenced by the multiband/multiorbital character of the quantum-dot electronic states.

The electronic structure of recently synthesized square superlattices with atomic coherence composed of PbSe, CdSe, or CdTe nanocrystals (NCs) attached along ${100}$ facets is investigated using tight-binding calculations. In experimental realizations of these systems [W. H. Evers et al., Nano Lett. 13, 2317 (2013)], NC facets are atomically bonded, resulting in single-crystalline sheets, which, due to their nanogeometry, have an effective dimensionality below two. We predict electronic structures composed of successive bands formed by strong coupling between the wave functions of nearest-neighbor NCs. This coupling is mainly determined by the number of atoms at the NC bonding plane. The band structures deviate markedly from that of the corresponding two-dimensional (2D) quantum well; the 2D case can be recovered, however, if the effects of the nanogeometry are gradually reduced. The width of the bands can reach hundreds of meV, ascribing highly promising transport properties to square superlattices. The band edges are located at $k=0$ except for PbSe superlattices, where their position in $k$ space surprisingly depends on the parity of the number of ${100}$ atomic planes in the NCs. Our calculations demonstrate that semiconductors with dimensionality below two have a strong potential for (opto-)electronic, photovoltaic, and spintronic applications.

Se analiza la estructura electrónica de los óxidos GaAsO4, As2O5 y GO3. Se presentan resultados experimentales de fotoemisión (XPS) de la densidad de estados (DOS) de banda de valencia para cada uno de los sistemas, y se comparan con cálculos teóricos de la DOS obtenidos a partir del cómputo de las respectivas estructuras de bandas utilizando un método tight-binding. Se identifican los estados atómicos que contribuyen a cada pico experimental y se correlacionan las diferencias estructurales entre estos óxidos con los diferentes rasgos experimentales exhibidos en los espectros XPS.

The investigation of sub-nanosecond exciton dynamics in HgTe colloidal quantum dots using ultrafast transient absorption spectroscopy is reported. The transmittance change spectrum acquired immediately after pumping is dominated by a bleach blue-shifted by ~200-300 nm from the photoluminescent emission band. Comparison with a tight-binding model of the electronic structure allows this feature to be attributed to the filling of band edge states. The form of the pump-induced transmittance transients is dependent on the excitation rate and the rate of sample stirring. For moderate pumping of stirred samples, the transmittance transients are well-described by a mono-exponential decay associated with biexciton recombination, with a lifetime of 49 ± 2 ps. For samples that are strongly-pumped or unstirred, the decay becomes bi-exponential in form, indicating that trap-related recombination has become significant. We also present a new analysis that enables fractional transmittance changes to be related to band edge occupation for samples with arbitrary optical density at the pump wavelength. This allows us to identify the occurrence of multiple exciton generation, which results in a quantum yield of 1.36 ± 0.04 for a photon energy equivalent to 3.1 times the band gap, in good agreement with the results of the model.

We combined the Maxwell-Garnett effective medium theory with the Kramers-Kronig relations to obtain the complex dielectric function epsilon of colloidal PbS, PbSe, and PbTe quantum dots (Qdots). The method allows extracting both real (epsilon(R)) and imaginary (epsilon(I)) parts of the dielectric function from the experimental absorption spectrum. This enables the quantification of the size-dependent oscillator strength of the optical transitions at different critical points in the Brillouin zone, strongly improving our understanding of quantum confinement effects in these materials. In addition, the static-limit sum rule yields the electronic dielectric constant from the epsilon(I) spectrum. Interestingly, values for lead chalcogenide Qdots remain close to the bulk dielectric constant. To verify these trends, we determined the dielectric constant of thin lead chalcogenide layers by ab initio calculations, and the results agree with the experimental data.

We report on the gradual evolution of the conductivity of spherical CdTe nanocrystals of increasing size from the regime of strong quantum confinement with truly discrete energy levels to the regime of weak confinement with closely spaced hole states. We use the high-frequency (terahertz) real and imaginary conductivities of optically injected carriers in the nanocrystals to report on the degree of quantum confinement. For the smaller CdTe nanocrystals (3 nm < radius < 5 nm), the complex terahertz conductivity is purely imaginary. For nanocrystals with radii exceeding 5 nm, we observe the onset of real conductivity, which is attributed to the increasingly smaller separation between the hole states. Remarkably, this onset occurs for a nanocrystal radius significantly smaller than the bulk exciton Bohr radius aB ∼ 7 nm and cannot be explained by purely electronic transitions between hole states, as evidenced by tight-binding calculations. The real-valued conductivity observed in the larger nanocrystals can be explained by the emergence of mixed carrier-phonon, that is, polaron, states due to hole transitions that become resonant with, and couple strongly to, optical phonon modes for larger QDs. These polaron states possess larger oscillator strengths and broader absorption, and thereby give rise to enhanced real conductivity within the nanocrystals despite the confinement.

In this paper, we present a detailed investigation of the size dependence of the optical transitions of colloidal CdTe QDs ranging in diameter from 2.9 to 14.8 nm. The energy integrated absorption cross section per CdTe unit is investigated in detail for the lowest two exciton transitions (1S3/2(h)–1S(e) and 2S3/2(h)–1S(e)) and shown to increase with decreasing size, although the size dependence of the 2S3/2(h)–1S(e) is less pronounced. The experimental absorption spectra are compared to spectra calculated by using a tight-binding approach. The calculations were carried out with electron–hole configuration interaction (CI) and without (single-particle, SP). The optical absorption spectra calculated by using the CI approach are in excellent agreement with the experiment, as well as the evolution of the optical gap and the optical transitions with nanocrystal size.

Colloidal nanocrystal quantum dots with a band gap in the near infra-red have potential application as the emitters for telecommunications or in vivo imaging, or as the photo-absorbing species in next generation solar cells or photodetectors. However, electro- and photoluminescence yields and the efficiency with which photo-generated charges can be extracted from quantum dots depend on the total rate of recombination, which can be dominated by surface-mediated processes. In this study, we use ultrafast transient absorption spectroscopy to characterise the recombination dynamics of photo-generated charges in InAs/ZnSe nanocrystal quantum dots. We find that recombination is dominated by rapid, sub-nanosecond transfer of conduction band electrons to surface states. For the size of dots studied, we also find no evidence of significant multiple exciton generation for photon energies up to 3.2 times the band gap, in agreement with our theoretical modelling.

We propose a tight-binding model of HgTe which gives an accurate band structure in a wide energy range compared to recent ab initio calculations. The inverted band structure near the Fermi level and its temperature dependence are also very well described. Using this parametrization, we study the effects of the quantum confinement on the electronic structure of HgTe quantum dot nanocrystals. We calculate the optical absorption spectra of quantum dots with various shapes and diameters up to 10 nm. We show, using a configuration interaction approach, that excitonic effects are negligible in this range of sizes. Our predictions for the size dependence of the energy gap and for the optical spectra are consistent with recent experimental data.