Characterization of the Edge States in Colloidal Bi2Se3 Platelets.

The remarkable development of colloidal nanocrystals with controlled dimensions and surface chemistry has resulted in vast optoelectronic applications. But can they also form a platform for quantum materials, in which electronic coherence is key? Here, we use colloidal, two-dimensional Bi2Se3 crystals, with precise and uniform thickness and finite lateral dimensions in the 100 nm range, to study the evolution of a topological insulator from three to two dimensions. For a thickness of 4-6 quintuple layers, scanning tunneling spectroscopy shows an 8 nm wide, nonscattering state encircling the platelet. We discuss the nature of this edge state with a low-energy continuum model and ab initio GW-Tight Binding theory. Our results also provide an indication of the maximum density of such states on a device.

Van Hove Singularities and Trap States in Two-Dimensional CdSe Nanoplatelets.

Semiconductor nanoplatelets, which offer a compelling combination of the flatness of two-dimensional semiconductors and the inherent richness brought about by colloidal nanostructure synthesis, form an ideal and general testbed to investigate fundamental physical effects related to the dimensionality of semiconductors. With low temperature scanning tunnelling spectroscopy and tight binding calculations, we investigate the conduction band density of states of individual CdSe nanoplatelets. We find an occurrence of peaks instead of the typical steplike function associated with a quantum well, that rule out a free in-plane electron motion, in agreement with the theoretical density of states. This finding, along with the detection of deep trap states located on the edge facets, which also restrict the electron motion, provides a detailed picture of the actual lateral confinement in quantum wells with finite length and width.

The Fine-Structure Constant as a Ruler for the Band-Edge Light Absorption Strength of Bulk and Quantum-Confined Semiconductors.

Low-dimensional semiconductors have found numerous applications in optoelectronics. However, a quantitative comparison of the absorption strength of low-dimensional versus bulk semiconductors has remained elusive. Here, we report generality in the band-edge light absorptance of semiconductors, independent of their dimensions. First, we provide atomistic tight-binding calculations that show that the absorptance of semiconductor quantum wells equals mπα (m = 1 or 2 with α as the fine-structure constant), in agreement with reported experimental results. Then, we show experimentally that a monolayer (superlattice) of quantum dots has similar absorptance, suggesting an absorptance quantum of mπα per (confined) exciton diameter. Extending this idea to bulk semiconductors, we experimentally demonstrate that an absorptance quantum equal to mπα per exciton Bohr diameter explains their widely varying absorption coefficients. We thus provided compelling evidence that the absorptance quantum πα per exciton diameter rules the band-edge absorption of all direct semiconductors, regardless of their dimension.

Bias Tunable Spectral Response of Nanocrystal Array in a Plasmonic Cavity.

Nanocrystals (NCs) have gained considerable attention for their broadly tunable absorption from the UV to the THz range. Nevertheless, their optical features suffer from a lack of tunability once integrated into optoelectronic devices. Here, we show that bias tunable aspectral response is obtained by coupling a HgTe NC array with a plasmonic resonator. Up to 15 meV blueshift can be achieved from a 3 µm absorbing wavelength structure under a 3 V bias voltage when the NC exciton is coupled with a mode of the resonator. We demonstrate that the blueshift arises from the interplay between hopping transport and inhomogeneous absorption due to the presence of the photonic structure. The observed tunable spectral response is qualitatively reproduced in simulation by introducing a bias-dependent diffusion length in the charge transport. This work expands the realm of existing NC-based devices and paves the way toward light modulators.

Engineering a Robust Flat Band in III-V Semiconductor Heterostructures.

Electron states in semiconductor materials can be modified by quantum confinement. Adding to semiconductor heterostructures the concept of lateral geometry offers the possibility to further tailor the electronic band structure with the creation of unique flat bands. Using block copolymer lithography, we describe the design, fabrication, and characterization of multiorbital bands in a honeycomb In0.53Ga0.47As/InP heterostructure quantum well with a lattice constant of 21 nm. Thanks to an optimized surface quality, scanning tunnelling spectroscopy reveals the existence of a strong resonance localized between the lattice sites, signature of a p-orbital flat band. Together with theoretical computations, the impact of the nanopatterning imperfections on the band structure is examined. We show that the flat band is protected against the lateral and vertical disorder, making this industry-standard system particularly attractive for the study of exotic phases of matter.

Correlating Structure and Detection Properties in HgTe Nanocrystal Films.

HgTe nanocrystals (NCs) enable broadly tunable infrared absorption, now commonly used to design light sensors. This material tends to grow under multipodic shapes and does not present well-defined size distributions. Such point generates traps and reduces the particle packing, leading to a reduced mobility. It is thus highly desirable to comprehensively explore the effect of the shape on their performance. Here, we show, using a combination of electron tomography and tight binding simulations, that the charge dissociation is strong within HgTe NCs, but poorly shape dependent. Then, we design a dual-gate field-effect-transistor made of tripod HgTe NCs and use it to generate a planar p-n junction, offering more tunability than its vertical geometry counterpart. Interestingly, the performance of the tripods is higher than sphere ones, and this can be correlated with a stronger Te excess in the case of sphere shapes which is responsible for a higher hole trap density.

Electronic properties of atomically coherent square PbSe nanocrystal superlattice resolved by Scanning Tunneling Spectroscopy.

Rock-salt lead selenide nanocrystals can be used as building blocks for large scale square superlattices via two-dimensional assembly of nanocrystals at a liquid-air interface followed by oriented attachment. Here we report Scanning Tunneling Spectroscopy measurements of the local density of states of an atomically coherent superlattice with square geometry made from PbSe nanocrystals. Controlled annealing of the sample permits the imaging of a clean structure and to reproducibly probe the band gap and the valence hole and conduction electron states. The measured band gap and peak positions are compared to the results of optical spectroscopy and atomistic tight-binding calculations of the square superlattice band structure. In spite of the crystalline connections between nanocrystals that induce significant electronic couplings, the electronic structure of the superlattices remains very strongly influenced by the effects of disorder and variability.

Continuous-wave infrared optical gain and amplified spontaneous emission at ultralow threshold by colloidal HgTe quantum dots.

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.

Colloidal nanocrystals as LEGO® bricks for building electronic band structure models.

The synthesis of self-assembled semiconductor nanocrystal (NC) superlattices using oriented attachment recently became a flourishing research topic. This technique already produced remarkable forms of NC superlattices, such as linear chains, mono and multilayer square lattices, and silicene-like honeycomb lattices. In the case of lead chalcogenide semiconductors where NCs are in the form of truncated nanocubes, the attachment mostly occurs via (100) facets. In this work, we show that all these structures can be seen as sub-structures of a simple cubic lattice. From this, we investigate a rich variety of one-dimensional or two-dimensional superlattices that could be built as few lines or few layers taken from the same cubic system following different crystallographic orientations. Each NC can be therefore considered as a LEGO® brick, and any superlattice can be obtained from another one by rearranging the bricks. Moreover, we show that this concept of LEGO® bricks can be extended to the calculation of the electronic band structure of the superlattices. This leads to a simple yet powerful way to build analytical Hamiltonians that present band structures in excellent agreement with more elaborate atomistic tight-binding calculations. This LEGO® concept could guide the synthesis of superlattices and LEGO® Hamiltonians should greatly simplify further studies on the (opto-)electronic properties of such structures.

Minimum Line Width of Surface Plasmon Resonance in Doped ZnO Nanocrystals.

The optical response of ZnO nanocrystals (NCs) doped with Al (Ga) impurities is calculated using a model that incorporates the effects of quantum confinement, dielectric mismatch, surface, and ionized impurity scattering. For dopant concentrations of a few percent, the NC polarizability is dominated by a localized surface plasmon resonance (LSPR) in the infrared (IR) which follows the Drude-Lorentz law for NC diameter above ∼10 nm but is strongly blue-shifted for smaller diameters due to quantum confinement effects. The intrinsic width of the LSPR peak is calculated in order to characterize plasmon losses induced by ionized impurity scattering. Widths below 80 meV are found in the best cases, in agreement with the lowest values recently measured on single NCs. These results confirm that doped ZnO NCs are very promising for the development of IR plasmonics. The width of the LSPR peak strongly increases when dopants are placed near the surface of the NCs or when additional fixed charges are present.

Magnetic-Phase Dependence of the Spin Carrier Mean Free Path in Graphene Nanoribbons.

We show theoretically that the intrinsic (phonon-limited) carrier mobility in graphene nanoribbons is considerably influenced by the presence of spin-polarized edge states. When the coupling between opposite edges switches from antiferromagnetic to ferromagnetic with increasing carrier density, the current becomes spin polarized and the mean free path rises from 10 nm to micrometers. In the ferromagnetic state, the current flows through one majority-spin channel which is ballistic over micrometers and several minority-spin channels with mean free paths as low as 1 nm. These features predicted in technology-relevant conditions could be nicely exploited in spintronic devices.

Nanoscale carrier multiplication mapping in a Si diode.

Carrier multiplication (CM), the creation of electron-hole pairs from an excited electron, has been investigated in a silicon p-n junction by multiple probe scanning tunneling microscopy. The technique enables an unambiguous determination of the quantum yield based on the direct measurement of both electron and hole currents that are generated by hot tunneling electrons. The combined effect of impact ionization, carrier diffusion, and recombination is directly visualized from the spatial mapping of the CM efficiency. Atomically well-ordered areas of the p-n junction surface sustain the highest CM rate, demonstrating the key role of the surface in reaching high yield.

From semiconductor nanocrystals to artificial solids with dimensionality below two.

Two-dimensional films of semiconductors can be patterned into super-lattices with nanoscale periodicity, using top-down (lithography) or bottom-up approaches. In particular, square and honeycomb lattices of semiconductor nanocrystals have been recently synthesized using oriented attachment. We have performed atomistic tight-binding calculations of the conduction bands of super-lattices of CdSe. We consider spherical nanocrystals connected by horizontal cylinders and we investigate the band structure between two extreme limits, the uniform two-dimensional film, and the assembly of disconnected nanocrystals. Using this model system, we explain how rich band structures emerge from the periodic nano-geometry, including Dirac cones and non-trivial flat bands in honeycomb lattices. The possibility to build non-conventional band structures using multi-orbital artificial atoms (nanocrystals) opens up new prospects.

Tight-binding calculations of the optical response of optimally P-doped Si nanocrystals: a model for localized surface plasmon resonance.

We present tight-binding calculations in the random-phase approximation of the optical response of Silicon nanocrystals (Si NCs) ideally doped with large concentrations of phosphorus (P) atoms. A collective response of P-induced electrons is demonstrated, leading to localized surface plasmon resonance (LSPR) when a Si NC contains more than ≈10 P atoms. The LSPR energy varies not only with doping concentration but also with NC size due to size-dependent screening by valence electrons. The simple Drude-like behavior is recovered for NC size above 4 nm. Si NCs containing a large number of deep defects in place of hydrogenic impurities do not give rise to LSPR.

Multiple exciton generation and ultrafast exciton dynamics in HgTe colloidal quantum dots.

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.

Effects of strain on the carrier mobility in silicon nanowires.

We investigate electron and hole mobilities in strained silicon nanowires (Si NWs) within an atomistic tight-binding framework. We show that the carrier mobilities in Si NWs are very responsive to strain and can be enhanced or reduced by a factor >2 (up to 5×) for moderate strains in the ± 2% range. The effects of strain on the transport properties are, however, very dependent on the orientation of the nanowires. Stretched 100 Si NWs are found to be the best compromise for the transport of both electrons and holes in ≈10 nm diameter Si NWs. Our results demonstrate that strain engineering can be used as a very efficient booster for NW technologies and that due care must be given to process-induced strains in NW devices to achieve reproducible performances.

Loosening quantum confinement: observation of real conductivity caused by hole polarons in semiconductor nanocrystals smaller than the Bohr radius.

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 a(B) ∼ 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.

Ultrafast exciton dynamics in InAs/ZnSe nanocrystal quantum dots.

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.

Size and Solvation Effects on Electronic and Optical Properties of PbS Quantum Dots.

PbS quantum dots (QDs), among the most mature nanocrystals obtained by colloidal chemistry, are promising candidates in optoelectronic applications at various operational frequencies. QD device performances are often determined by charge transport, either carrier injection before photoemission or charge detection after photoabsorption, which is significantly influenced by the dielectric environment. Here, we present the electronic structure and the optical gap of PbS QDs versus size for various solvents calculated using ab initio methods including the many-body perturbation approaches. This study highlights the importance of the dielectric environment, pointing out (1) the non-negligible shift of the electronic structure due to the ground state polarization and (2) a substantial impact on the electronic bandgap. The electron-hole binding energy, which varies largely with the QD size and solvent, is well-described by an electrostatic model. This study reveals the fundamental physics of size and solvation effects, which could be useful to design PbS QD-based optoelectronic devices.