Correction: Excitons in metal halide perovskite nanoplatelets: an effective mass description of polaronic, dielectric and quantum confinement effects

[This corrects the article DOI: 10.1039/D3NA00592E.].

Excitons in metal halide perovskite nanoplatelets: an effective mass description of polaronic, dielectric and quantum confinement effects

A theoretical model for excitons confined in metal halide perovskite nanoplatelets is presented. The model accounts for quantum confinement, dielectric confinement, short and long range polaron interactions by means of effective mass theory, image charges and Haken potentials. We use it to describe the band edge exciton of MAPbI3 structures surrounded by organic ligands. It is shown that the quasi-2D quantum and dielectric confinement squeezes the exciton radius, and this in turn enhances short-range polaron effects as compared to 3D structures. Dielectric screening is then weaker than expected from the static dielectric constant. This boosts the binding energies and radiative recombination probabilities, which is a requisite to match experimental data in related systems. The thickness dependence of Coulomb polarization and self-energy potentials is in fair agreement with sophisticated atomistic models.

Beyond Universal Volume Scaling: Tailoring Two-Photon Absorption in Nanomaterials by Heterostructure Design

Colloidal semiconductor nanomaterials present broadband, with large cross-section, two-photon absorption (2PA) spectra, which turn them into an important platform for applications that benefit from a high nonlinear optical response. Despite that, to date, the only means to control the magnitude of the 2PA cross-section is by changing the nanoparticle volume, as it follows a universal volume scale, independent of the material composition. As the emission spectrum is connected utterly to the nanomaterial dimensions, for a given material, the magnitude of the nonlinear optical response is also coupled to the emission spectra. Here, we demonstrate a means to decouple both effects by exploring the 2PA response of different types of heterostructures, tailoring the volume dependence of the 2PA cross-section due to the different dependence of the density of final states on the nanoparticle volume. By heterostructure engineering, one can obtain 1 order of magnitude enhancement of the 2PA cross-section with minimum emission spectra shift.

Two Biexciton Types Coexisting in Coupled Quantum Dot Molecules

Coupled colloidal quantum dot molecules (CQDMs) are an emerging class of nanomaterials, manifesting two coupled emission centers and thus introducing additional degrees of freedom for designing quantum-dot-based technologies. The properties of multiply excited states in these CQDMs are crucial to their performance as quantum light emitters, but they cannot be fully resolved by existing spectroscopic techniques. Here we study the characteristics of biexcitonic species, which represent a rich landscape of different configurations essentially categorized as either segregated or localized biexciton states. To this end, we introduce an extension of Heralded Spectroscopy to resolve the different biexciton species in the prototypical CdSe/CdS CQDM system. By comparing CQDMs with single quantum dots and with nonfused quantum dot pairs, we uncover the coexistence and interplay of two distinct biexciton species: A fast-decaying, strongly interacting biexciton species, analogous to biexcitons in single quantum dots, and a long-lived, weakly interacting species corresponding to two nearly independent excitons. The two biexciton types are consistent with numerical simulations, assigning the strongly interacting species to two excitons localized at one side of the quantum dot molecule and the weakly interacting species to excitons segregated to the two quantum dot molecule sides. This deeper understanding of multiply excited states in coupled quantum dot molecules can support the rational design of tunable single- or multiple-photon quantum emitters.

Biexcitons in CdSe nanoplatelets: geometry, binding energy and radiative rate

Biexciton properties in semiconductor nanostructures are highly sensitive to quantum confinement, relative electron-hole masses, dielectric environment and Coulomb correlations. Here we present a variational Quantum Monte Carlo model which, coupled to effective mass Hamiltonians, takes into account all of the above effects. The model is used to provide theoretical assessment on the biexciton ground state properties in colloidal CdSe nanoplatelets. A number of characteristic features is observed: (i) the finite thickness of these systems makes the biexciton geometry depart from the planar square expected in the two-dimensional (2D) limit, and form a distorted tetrahedron instead; (ii) the strong dielectric confinement enhances not only Coulomb attractions but also repulsions, which lowers the ratio of the biexciton-to-exciton binding energy down to EXXb/EXb = 0.07. (iii) EXXb is less sensitive than EXb to lateral confinement, and yet it can reach values above 30 meV, thus granting room temperature stability; (iv) the ratio of biexciton-to-exciton radiative rates, kradXX/kradX, decreases from 3.5 to ∼1 as the platelet area increases. These results pave the way for the rational design of biexciton properties in metal chalcogenide nanoplatelets.

Dielectric Confinement Enables Molecular Coupling in Stacked Colloidal Nanoplatelets

We show theoretically that carriers confined in semiconductor colloidal nanoplatelets (NPLs) sense the presence of neighbor, cofacially stacked NPLs in their energy spectrum. When approaching identical NPLs, the otherwise degenerate energy levels red-shift and split, forming (for large stacks) minibands that are several millielectronvolts in width. Unlike in epitaxial structures, the molecular behavior does not result from quantum tunneling but from changes in the dielectric confinement. The associated excitonic absorption spectrum shows a rich structure of bright and dark states, whose optical activity and multiplicity can be understood from reflection symmetry and Coulomb tunneling. We predict spectroscopic signatures that should confirm the formation of molecular states, whose practical realization would pave the way for the development of nanocrystal chemistry based on NPLs.

CdSe/CdS/CdTe Core/Barrier/Crown Nanoplatelets: Synthesis, Optoelectronic Properties, and Multiphoton Fluorescence Upconversion

Colloidal two-dimensional (2D) nanoplatelet heterostructures are particularly interesting as they combine strong confinement of excitons in 2D materials with a wide range of possible semiconductor junctions due to a template-free, solution-based growth. Here, we present the synthesis of a ternary 2D architecture consisting of a core of CdSe, laterally encapsulated by a type-I barrier of CdS, and finally a type-II outer layer of CdTe as so-called crown. The CdS acts as a tunneling barrier between CdSe- and CdTe-localized hole states, and through strain at the CdS/CdTe interface, it can induce a shallow electron barrier for CdTe-localized electrons as well. Consequently, next to an extended fluorescence lifetime, the barrier also yields emission from CdSe and CdTe direct transitions. The core/barrier/crown configuration further enables two-photon fluorescence upconversion and, due to a high nonlinear absorption cross section, even allows to upconvert three near-infrared photons into a single green photon. These results demonstrate the capability of 2D heterostructured nanoplatelets to combine weak and strong confinement regimes to engineer their optoelectronic properties.

Chloride-Induced Thickness Control in CdSe Nanoplatelets

Current colloidal synthesis methods for CdSe nanoplatelets (NPLs) routinely yield samples that emit, in discrete steps, from 460 to 550 nm. A significant challenge lies with obtaining thicker NPLs, to further widen the emission range. This is at present typically achieved via colloidal atomic layer deposition onto CdSe cores, or by synthesizing NPL core/shell structures. Here, we demonstrate a novel reaction scheme, where we start from 4.5 monolayer (ML) NPLs and increase the thickness in a two-step reaction that switches from 2D to 3D growth. The key feature is the enhancement of the growth rate of basal facets by the addition of CdCl₂, resulting in a series of nearly monodisperse CdSe NPLs with thicknesses between 5.5 and 8.5 ML. Optical characterization yielded emission peaks from 554 nm up to 625 nm with a line width (fwhm) of 9-13 nm, making them one of the narrowest colloidal nanocrystal emitters currently available in this spectral range. The NPLs maintained a short emission lifetime of 5-11 ns. Finally, due to the increased red shift of the NPL band edge photoluminescence excitation spectra revealed several high-energy peaks. Calculation of the NPL band structure allowed us to identify these excited-state transitions, and spectral shifts are consistent with a significant mixing of light and split-off hole states. Clearly, chloride ions can add a new degree of freedom to the growth of 2D colloidal nanocrystals, yielding new insights into both the NPL synthesis as well as their optoelectronic properties.

Piezoelectric Control of the Exciton Wave Function in Colloidal CdSe/CdS Nanocrystals

Using multiband k·p calculations, we show that strain-engineered piezoelectricity is a powerful tool to modulate the electron-hole spatial separation in a wide class of wurtzite CdSe/CdS nanocrystals. The inherent anisotropy of the hexagonal crystal structure leads to anisotropic strain and, consequently, to a pronounced piezoelectric field along the c axis, which can be amplified or quenched through a proper design of the core-shell structure. The use of large cores and thick shells promotes a gradual departure from quantum confined nanocrystals to a regime dominated by piezoelectric confinement. This allows excitons to evolve from the usual type-I and quasi-type-II behavior to a type-II behavior in dot-in-dots, dot-in-rods, rod-in-rods, and dot-in-plates. Piezoelectric fields explain experimental observations for giant-shell nanocrystals, whose time-resolved photoluminescence reveals long exciton lifetimes for large cores, contrary to the expectations of standard quantum confinement models. They also explain the large differences in exciton lifetimes reported for different classes of CdSe/CdS nanocrystals.

Hole spin relaxation in InAs/GaAs quantum dot molecules

We calculate the spin-orbit induced hole spin relaxation between Zeeman sublevels of vertically stacked InAs quantum dots. The widely used Luttinger-Kohn Hamiltonian, which considers coupling of heavy- and light-holes, reveals that hole spin lifetimes (T1) of molecular states significantly exceed those of single quantum dot states. However, this effect can be overcome when cubic Dresselhaus spin-orbit interaction is strong. Misalignment of the dots along the stacking direction is also found to be an important source of spin relaxation.

Magnetic field implementation in multiband k⋅p Hamiltonians of holes in semiconductor heterostructures

We propose an implementation of external homogeneous magnetic fields in k⋅p Hamiltonians for holes in heterostructures, in which we make use of the minimal coupling prior to introducing the envelope function approximation. Illustrative calculations for holes in InGaAs quantum dot molecules show that the proposed Hamiltonian outperforms the standard Luttinger model (Luttinger 1956 Phys. Rev. 102 1030) describing the experimentally observed magnetic response. The present implementation culminates our previous proposal (Planelles et al 2010 Phys. Rev. B 82 155307).

A new parametric model for fitting fertility curves

What is the optimum way of describing the age-specific fertility pattern by mathematical functions? We propose a parametric fitting model, based on a mixture of Weibull functions, which performs well for countries where the fertility curve shows a non-traditional pattern. We also consider a simplified version of this model with a reduced number of parameters that can be applied to fit fertility curves in countries where the fertility pattern exhibits a classical shape. To test the new model, fertility curves for a range of countries and years are fitted empirically. The results show that both versions of the new model outperform existing procedures in most cases.

Magnetic modulation of the tunnelling between defect states in antidot superlattices

We show theoretically that the tunnelling between properly designed defects in periodic antidot lattices can be strongly modulated by applied magnetic fields. Further, transport channels made up of linear arrangements of tunnel-coupled defects can accommodate Aharonov-Bohm cages, suggesting a magnetic control of the transport through the system. Evidence supporting an unusual robustness of the caging effect against electron-electron interactions is also provided.

Valence band mixing of cubic GaN/AlN quantum dots

We study the spin purity of the hole ground state in nearly axially symmetric GaN/AlN quantum dots (QDs). To this end, we develop a six-band Burt-Foreman Hamiltonian describing the valence band structure of zinc blende nanostructures with cylindrical symmetry and calculate the effects of eccentricity variationally. We show that the aspect ratio is a key factor for spin purity. In typical QDs with small aspect ratio the ground state is essentially a heavy hole (HH) whose spin purity is even higher than that of InGaAs QDs of similar sizes. When the aspect ratio increases, mixing with light-hole (LH) and split-off (SO) subbands becomes important and, additionally, the ground state becomes sensitive to QD anisotropy, which further enhances the mixing. We finally show that, despite the large GaN hole effective mass, an efficient magnetic modulation is feasible in QDs with aspect ratio ~1, which can be used to modify the ground state symmetry and hence the optical spectrum properties.

Auger recombination suppression in nanocrystals with asymmetric electron-hole confinement

Type II and quasi-type II nanocrystals with thick shells exhibit reduced blinking. However, after a number of monolayers, the influence of the shell thickness is found to vanish. Using a two-band Kane Hamiltonian, it is shown that this behavior is a consequence of interband coupling and asymmetric confinement of electrons and holes. Interface alloying provides an additional, order-of-magnitude contribution to the Auger suppression, in agreement with recent experiments. The existence is predicted of critical shell thicknesses that strongly quench Auger processes for any core size.

Dielectric confinement of excitons in type-I and type-II semiconductor nanorods

We theoretically study the effect of the dielectric environment on the exciton ground state of CdSe and CdTe/CdSe/CdTe nanorods. We show that insulating environments enhance the exciton recombination rate and blueshift the emission peak by tens of meV. These effects are particularly pronounced for type-II nanorods. In these structures, the dielectric confinement may even modify the spatial distribution of the electron and hole charges. A critical electric field is required to separate electrons from holes, whose value increases with the insulating strength of the surroundings.

Correlation in narrow nanorods: a variational potential-configuration interaction scheme

Full configuration interaction calculations for two electrons in narrow semiconductor nanorods are carried out employing different orbital basis sets. It is shown that the usual configurations built from single-particle states cannot yield a correct singlet-triplet energetic order regardless of the basis size, as they miss the correlation energy. Mean-field optimized orbitals partially correct this drawback. A new approach is introduced, based on a simple variational procedure, which yields robust results.

Theoretical characterization of triangular CdS nanocrystals: a tight-binding approach

We provide theoretical modeling of the optical spectrum of recently synthesized triangular CdS nanocrystals by means of atomistic tight-binding theory. Both zinc blende and wurtzite structures are considered. Optical properties predicted for triangular prisms are very different from the ones obtained for tetrahedral quantum dots when z-polarized light is employed. In particular, the ground transition is dim for triangular prisms, whereas it is bright and highly intense for tetrahedra. The high sensitivity of the fine optical properties on the quantum dot shape allows us to discriminate between truncated tetrahedra and triangular prisms and also to estimate the thickness of the nanocrystals.

Simple technique for the intraoperative detection of Crohn's strictures with a calibration sphere

Several methods have been used to detect and evaluate small-bowel strictures in Crohn's disease. We describe a simple technique for the calibration of strictures using a 2.5-cm medical plastic sphere. This method provides an aseptic, safe, and effective calibration of the entire small bowel.