Doped colloidal InAs nanocrystals in the single ionized dopant limit

We investigate the electronic properties of individual n-type (Cu) doped and p-type (Ag) doped InAs colloidal nanocrystals (NCs) in the 2–8 nm size range from their charge transfers toward a highly oriented pyrolytic graphite (HOPG) substrate, using ultrahigh vacuum Kelvin probe force microscopy (KPFM) with elementary charge sensitivity at 300 K. The NC active dopant concentration is measured as ND = 8 × 1020 cm–3 and NA > 5 × 1020 cm–3 for n- and p-type doping, respectively. The electrostatic equilibrium between the NC and the HOPG reference substrate is investigated and reveals an enhancement of the Fermi-level mismatch between the NCs and the HOPG substrate at reduced NC sizes, both for n- and p-type doping. It also shows, for n-type doped NCs with smallest sizes (∼2 nm), the existence of a full depletion regime, in which smallest NCs contain single ionized dopants. Results are compared with self-consistent tight-binding calculations of the electronic structure of InAs NCs, including hydrogenoid impurities and the presence of a host substrate, in the case of n-type doped NCs. The observed enhancement of the NC–HOPG Fermi-level mismatch can be understood by considering a size-dependent electrostatic contribution attributed to dipolar effects at the NC–ligand interface. The estimated surface dipole density equals a few Debye/nm2 and is increased at smallest NC sizes, which follows the enhancement of ligand densities at small NC sizes previously reported for metallic or semiconducting NCs. The results put forward the role played by the NC–ligand interface electrostatics for electronic applications

Structure électronique et propriétés de réseaux cohérents de nanocristaux semi-conducteurs

These last years, condensed matter physics has witnessed the emergence of a new trend based on material patterning which allows a fine tuning of their properties. At a nanometer scale, the patterning modifies the electronic properties of the systems. Recently, superlattices of semiconductor nanocrystals have been synthesized using (bottom-up) self-assembly techniques, opening a new road toward electronic properties tuning. In this thesis, we made use of numerical and analytical methods to study the properties of these superlattices. We started by developing a simple analytical model (the LEGO model) that helps us perdict the electronic bandstructures of the superlattices. The model is based on the idea that nanocrystals are identical and hence act like LEGO bricks. The bandstructure is then constructed by building the supperlatice of these elementary bricks. Its results were confronted to more elaborate atomistic calculations and showed good agreement. In addition to this model, we proposed a new top-down approach to synthesize more complex superlattices. The approach is based on the lithographic patterning of semiconductor quantum wells, which provides enhanced parametric control than the bottom-up approach. We showed that the bandstructures of these lithographed superlattices have the same features as their atomic counterparts. This thesis also addresses the behavior of superlattices under the application of a static magnetic field. A preliminary study allowed us to show that the Zeeman splitting of the lowest conduction state in a nanostructure depends only on its energy gap and is independent of its shape, size and dimensionality. A simple analytical formula linking the Landé g-factor to the energy gap was derived. The physical causes of this universal response helped us explain the appearance of large magnetic moments in coherent superlattices of semiconductor nanocrystals. Moreover, we studied the effect of an experimentally observed disorder on the properties of these superlattices. The disorder consists in a random distribution of nanocrystal diameters. In honeycomb superlattices of HgTe (that were predicted to host a quantum spin Hall phase), the disorder destroys those large magnetic moments while keeping those originating from the topological edge states unchanged. This difference in behavior could be used to probe trivial to non-trivial phase transitions. Finally, we showed that this random distribution of diameters in square superlattices of PbSe nanocrystals generates a disorder on the sign of the coupling terms between them. We showed that this disorder can be reduced by gauge transformations and we determined the irreducible (real) disorder felt by electrons. We have found that the localization lengths of the wavefunctions due to the bond-sign disorder are larger than the ones predicted in literature due to Anderson-type disorder. Therefore, the bond-sign disorder can be neglected.Ces dernières années, une nouvelle tendance en physique des solides reposant sur la structuration des matériaux est née, permettant ainsi la modification à souhait de leurs propriétés. Concernant les propriétés électroniques, l’échelle de structuration doit être nanométrique, ce qui représente un défi expérimental. Récemment, des réseaux cohérents de nanocristaux semiconducteurs ont pu être synthétisés par des techniques d’auto-assemblage (bottom-up). Ceci ouvre par conséquent une voie à la manipulation des propriétés électroniques des matériaux. Dans ce travail, nous avons utilisé des approches théoriques numériques et analytiques afin de caractériser certaines propriétés de ces réseaux de nanocristaux semi-conducteurs. Dans un premier temps, nous avons développé un modèle analytique simplifié (modèle LEGO) permettant de prédire les comportements électroniques des différents réseaux construits et dans lesquels les nanocristaux sont considérés identiques et s’apparentent à des briques de LEGO. Ce modèle permet principalement de s’affranchir des lourds calculs numériques atomistiques tout en garantissant des résultats fidèles à ces derniers. Les relations de dispersion obtenues sont analytiques et ainsi facilement exploitables. Outre ce modèle analytique, nous proposons dans cette thèse une nouvelle approche top-down pour la synthèse de ces réseaux artificiels. Cette approche se base sur la lithographie de réseaux de trous dans des puits quantiques permettant ainsi l’augmentation du contrôle sur les structures obtenues. Nous avons montré que des réseaux bidimensionnels exotiques présentant des propriétés électroniques originales pourraient être synthétisés en utilisant cette approche. Au-delà des propriétés électroniques, nous avons étudié la réponse à un champ magnétique de ces super-réseaux. Pour arriver à cela, une étude préliminaire sur la réponse d’un nanocristal isolé s’est montrée nécessaire. Nos calculs prédisent un comportement universel de la séparation Zeeman dans l’état de conduction le plus bas des nanostructures semi-conductrices. Nous avons dérivé une expression simple donnant le facteur g de Landé en fonction du gap de la nanostructure, indépendamment de sa taille, forme et dimensionnalité. Une confrontation avec des résultats expérimentaux présents dans la littérature confirme notre théorie d’universalité. La compréhension des causes physiques générant cette universalité nous a permis d’expliquer l’apparition de grands moments magnétiques dans les réseaux de nanocristaux semi-conducteurs. Ce travail traite également de l’influence du désordre sur ces propriétés. Nous avons considéré un désordre observé expérimentalement se manifestant comme une distribution en taille des nanocristaux. Cette distribution crée un désordre de type Anderson sur les énergies des orbitales des nanocristaux. Nous avons montré que dans les systèmes présentant une phase Hall quantique de spin (tel que le réseau en nid d’abeilles de nanocristaux HgTe), ce désordre influence peu les moments magnétiques issus des états de bords topologiques. Cependant, il détruit facilement les moments magnétiques des états non topologiques. Cette différence de comportement pourrait être exploitée expérimentalement afin de suivre les transitions topologiques. Enfin, nous montrons que dans les réseaux carrés de PbSe, la distribution aléatoire des diamètres de nanocristaux génère un désordre sur les signes des termes de couplage entre eux. Nous montrons que ce désordre est réductible par des transformations de jauge et nous caractérisons le désordre résiduel (réel) ressenti par les électrons. Nous montrons que ce désordre induit des longueurs de localisation plus grandes que celles induites par le désordre d’Anderson étudié dans la littérature. Par conséquent, le désordre de signes peut être négligé

Electronic structure and properties of coherent superlattices of semiconductor nanocrystals

La nanostructuration de matériaux semi-conducteurs permet de modifier le comportement des porteurs de charge. Ces modifications sont causées par les effets de confinement quantique. Dans cette thèse, nous étudions par des approches théoriques (numériques et analytiques) les propriétés de réseaux cohérents de nanocristaux semi-conducteurs. Ces réseaux sont expérimentalement obtenus par des méthodes ascendantes (bottom-up) d’auto-assemblage orienté. Nous montrons que leurs structures de bandes électroniques peuvent être modélisées par un simple Hamiltonien effectif dont les énergies propres sont analytiques. En outre, nous proposons une méthode descendante (top-down) de nano-fabrication consistant en la gravure de puits quantiques semi-conducteurs par des méthodes de lithographie. Cette approche permet de reproduire artificiellement des réseaux bidimensionnels à fort intérêt et comportant des fermions de Dirac tels que le nid d’abeilles, le kagome et le Lieb. Nous étudions ensuite l’effet d’un champ magnétique statique sur un nanocristal isolé, puis sur un réseau de nanocristaux en nid d’abeilles dans lequel nous prédisons l’apparition de grands moments magnétiques. Enfin, nous montrons que dans les réseaux carrés PbSe, un désordre original portant sur les signes des termes de couplage entre nanocristaux apparaît. Nous montrons que ce désordre est réductible par des transformations de jauge, et nous quantifions le désordre réel (résiduel) ressenti par les électrons.Semiconductor nanostructuration methods are a new route leading to the tuning of charge carriers behavior. This tuning is a direct consequence of the quantum confinement effect. In this thesis, we study using numerical and analytical approaches the properties of coherent superlattices of semiconductor nanocrystals. These superlattices are synthesized by bottom-up methods of oriented self-assembly. We show that their electronic band structures can be modeled by a simple effective Hamiltonian with analytical eigenvalues. In addition, we propose a top-down method where a periodic arrangement of holes is etched in semiconductor quantum wells using lithography. We show that it is possible to artificially reproduce two-dimensional lattices of high interest such as the honeycomb, the kagome and the Lieb lattices. Most of these lattices host Dirac fermions that we also recover in the superlattices. In another chapter, we study the effect of a static magnetic field on isolated nanocrystals and on honeycomb superlattices. We predict the presence of large magnetic moments in those systems. Finally, we show that, in PbSe square superlattices, a bond-sign disorder should arise. We find that this disorder is reducible by gauge transformations and we quantify the true (residual) disorder felt by electrons

Topological protection of electronic states against disorder probed by their magnetic moment

International audienceMagnetic moments (MMs) of electrons in topological insulator quantum dots (TI-QDs) are investigated using a model system, namely a multiorbital honeycomb lattice. Their nature and orientation with respect to the spin are studied. We show that large MMs are not specific to edge states in nontrivial gaps, as band states can host even larger MMs. However, we demonstrate that edge-state and band-state MMs have a totally different sensitivity to disorder. Measuring the MMs in TI-QDs is therefore a direct way to probe the nontrivial to trivial topological transition under increasing disorder

Anderson localization induced by gauge-invariant bond-sign disorder in square PbSe nanocrystal lattices

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Robustness of states at the interface between topological insulators of opposite spin Chern number

We study the nature of the states at the interface between two time-reversal symmetric topological insulators characterized by opposite spin Chern numbers. We show using a multi-orbital model that interface states are usually present in the common topological gaps of the materials. The transport in these states is robust against disorder scattering only when the two spin sectors are uncoupled (no Rashba spin-orbit coupling). Otherwise, the topological protection associated with the spin Chern number is lost and back-scattering is allowed, even in the absence of disorder, due to the coupling between states flowing in opposite directions and originating from the two sides of the interface. Conditions that minimize this effect can be found but the interface states remain sensitive to disorder

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

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Universal behavior of electron g -factors in semiconductor nanostructures

International audienceWe combine analytic developments and numerical tight-binding calculations to study the evolution of the electron g-factors in homogeneous nanostructures of III-V and II-VI semiconductors. We demonstrate that the g-factor can be always written as a sum of bulk and surface terms. The bulk term, the dominant one, just depends on the energy gap of the nanostructure but is otherwise isotropic and independent of size, shape, and dimensionality. At the same time, the magnetic moment density at the origin of the bulk term is anisotropic and strongly dependents on the nanostructure shape. The physical origin of these seemingly contradictory findings is explained by the relation between the spin-orbit-induced currents and the spatial derivatives of the electron envelope wave function. The tight-binding calculations show that the g-factor versus energy gap for spherical nanocrystals can be used as a reference curve. In quantum wells, nanoplatelets, nanorods, and nanowires, the g-factor along the rotational symmetry axis can be predicted from the reference curve with a good accuracy. The g-factors along nonsymmetric axes exhibit more important deviations due to surface contributions but the energy gap remains the main quantity determining their evolution. The importance of surface-induced anisotropies of the g-factors is discussed

Setting Carriers Free: Healing Faulty Interfaces Promotes Delocalization and Transport in Nanocrystal Solids

International audienceSuperlattices of epitaxially connected nanocrystals (NCs) are model systems to study electronic and optical properties of NC arrays. Using elemental analysis and structural analysis by in situ X-ray fluorescence and grazing-incidence small-angle scattering, respectively, we show that epitaxial superlattices of PbSe NCs keep their structural integrity up to temperatures of 300 °C; an ideal starting point to assess the effect of gentle thermal annealing on the superlattice properties. We find that annealing such superlattices between 75 and 150 °C induces a marked red shift of the NC band-edge transition. In fact, the post-annealing band-edge reflects theoretical predictions on the impact of charge carrier delocalization in these epitaxial superlattices. In addition, we observe a pronounced enhancement of the charge carrier mobility and a reduction of the hopping activation energy after mild annealing. While the superstructure remains intact at these temperatures, structural defect studies through X-ray diffraction indicate that annealing markedly decreases the density of point defects and edge dislocations. This indicates that the connections between NCs in as-synthesized superlattices still form a major source of grain boundaries and defects, which prevent carrier delocalization over multiple NCs and hamper NC-to-NC transport. Overcoming the limitations imposed by interfacial defects is therefore an essential next step in the development of high-quality optoelectronic devices based on NC solids