Toward Bright Red-Emissive Carbon Dots through Controlling Interaction among Surface Emission Centers.

Relatively weak red photoluminescence of carbon dots (CDots) is a major challenge on the way to their successful implementation in biological and optoelectronic devices. We present a theoretical analysis of the interaction among the surface emission centers of CDots, showing that it may determine efficiency of the red photoluminescence of CDots. Based on the previous experimental studies, it is assumed that the optical response of the CDots is determined by the molecule-like subunits of polycyclic aromatic hydrocarbons (PAHs) attached to the CDots' surface. Three characteristic types of coupling of these PAH subunits are considered: non-interacting monomers, noncovalently bound dimers, and covalently bound dimers with two, three, or four carbon linkers. We demonstrate that the CDots' photoluminescence broadens, redshifts, and weakens by 2 orders of magnitude when the free monomers are substituted by the covalently bridged centers. These and other results of our study show that the realization of CDots with many weakly interacting surface emission centers may constitute an efficient way to achieve their efficient red photoluminescence, which is highly desirable for biological and optoelectronic applications.

Band Structure and Intersubband Transitions of Three-Layer Semiconductor Nanoplatelets.

This paper presents the first general theory of electronic band structure and intersubband transitions in three-layer semiconductor nanoplatelets. We find a dispersion relation and wave functions of the confined electrons and use them to analyze the band structure of core/shell nanoplatelets with equal thicknesses of the shell layers. It is shown that the energies of electrons localized inside the shell layers can be degenerate for certain electron wave vectors and certain core and shell thicknesses. We also show that the energies of intersubband transitions can be nonmonotonic functions of the core and shell thicknesses, exhibiting pronounced local minima and maxima which can be observed in the infrared absorption spectra. Our results will prove useful for the design of photonic devices based on multilayered semiconductor nanoplatelets operating at infrared frequencies.

Amino Functionalization of Carbon Dots Leads to Red Emission Enhancement.

The availability of carbon dots (CDots) with bright red photoluminescence (PL) would significantly broaden the range of their biological and optoelectronic applications. We present a theoretical model that predicts that amino functionalization of CDots not only shifts their PL to longer wavelengths but also preserves large oscillator strengths of the fundamental radiative transitions of CDots. The model considers the optical response of amino-functionalized CDots determined by molecule-like subunits of polycyclic aromatic hydrocarbons with one, two, or three -NH2 groups at the CDots' surface; the excited state of those subunits is characterized by strong charge separation between the amino groups and CDots' carbon core. Such a separation determines the Stokes shift of the CDots' emission, which increases with the growing amount of the amino functional groups at the CDot surface. Our model explains the experimentally observed dependence of the PL spectra of CDots on the excitation wavelength, the phenomenon well documented in the literature for nitrogen-containing CDots.

sp2-sp3-Hybridized Atomic Domains Determine Optical Features of Carbon Dots.

Carbon dots (CDots) are a promising biocompatible nanoscale source of light, yet the origin of their emission remains under debate. Here, we show that all the distinctive optical properties of CDots, including the giant Stokes shift of photoluminescence and the strong dependence of emission color on excitation wavelength, can be explained by the linear optical response of the partially sp2-hybridized carbon domains located on the surface of the CDots' sp3-hybridized amorphous cores. Using a simple quantum chemical approach, we show that the domain hybridization factor determines the localization of electrons and the electronic bandgap inside the domains and analyze how the distribution of this factor affects the emission properties of CDots. Our calculation data fully agree with the experimental optical properties of CDots, confirming the overall theoretical picture underlying the model. It is also demonstrated that fabrication of CDots with large hybridization factors of carbon domains shifts their emission to the red side of the visible spectrum, without a need to modify the size or shape of the CDots. Our theoretical model provides a useful tool for experimentalists and may lead to extending the applications of CDots in biophysics, optoelectronics, and photovoltaics.

Electric-field-enhanced circular dichroism of helical semiconductor nanoribbons.

In this Letter, we analyze circular dichroism (CD) enhancement of a helical semiconductor nanoribbon exposed to a weak homogenous electric field. By creating a periodic superlattice for the confined electrons, the electric field splits the electronic sub-bands into minibands and gives rise to critical points in the electronic density of states. We show that the modification of the electronic energy spectrum results in the appearance of new optically active transitions in the CD and absorption spectra, and that the CD signal of the nanoribbon is significantly enhanced at the critical points. The ability to dynamically control the chiroptical response of semiconductor nanoribbons by an external electric field makes them promising for the next-generation nanophotonic devices.

Excitonic phenomena in perovskite quantum-dot supercrystals.

Quantum confinement and collective excitations in perovskite quantum-dot (QD) supercrystals offer multiple benefits to the light emitting and solar energy harvesting devices of modern photovoltaics. Recent advances in the fabrication technology of low dimensional perovskites has made the production of such supercrystals a reality and created a high demand for the modelling of excitonic phenomena inside them. Here we present a rigorous theory of Frenkel excitons in lead halide perovskite QD supercrystals with a square Bravais lattice. The theory shows that such supercrystals support three bright exciton modes whose dispersion and polarization properties are controlled by the symmetry of the perovskite lattice and the orientations of QDs. The effective masses of excitons are found to scale with the ratio of the superlattice period and the number of QDs along the supercrystal edge, allowing one to fine-tune the electro-optical response of the supercrystals as desired for applications. We also calculate the conductivity of perovskite QD supercrystals and analyze how it is affected by the optical generation of the three types of excitons. This paper provides a solid theoretical basis for the modelling of two- and three-dimensional supercrystals made of perovskite QDs and the engineering of photovoltaic devices with superior optoelectronic properties.

Optically Active Semiconductor Nanosprings for Tunable Chiral Nanophotonics.

The search for the optimal geometry of optically active semiconductor nanostructures is making steady progress and has far-reaching benefits. Yet the helical springlike shape, which is very likely to provide a highly dissymmetric optical response, remains somewhat understudied theoretically. Here we comprehensively analyze the optical activity of semiconductor nanosprings using a fully quantum-mechanical model of their electronic subsystem and taking into account the anisotropy of their interaction with light. We show that the circular dichroism of semiconductor nanosprings can exceed that of ordinary semiconductor nanocrystals by a factor of 100 and be comparable to the circular dichroism of metallic nanosprings. It is also demonstrated that nanosprings can feature a total dissymmetry of optical response for certain ratios between their length and coil height. The magnitude and sign of the circular dichroism signal can be controlled by stretching or compressing the nanosprings, which makes them a promising material base for optomechanical sensors, polarization controllers, and other types of optically active nanophotonic devices.

Optical Activity of Semiconductor Gammadions beyond Planar Chirality.

We present rigorous analysis of optical activity of chiral semiconductor gammadions whose chirality in three dimensions is caused by the nonuniformity of thickness in the transverse plane. It is shown that such gammadions not only distinguish between the two circular polarizations upon scattering and reflection of light, like all two-dimensional semiconductor nanostructures with planar chirality do, but also exhibit circular dichroism and circularly polarized luminescence. Chiral semiconductor gammadions whose charge carriers are mostly confined to the arms are found to feature both high dissymmetry of optical response and a constant-sign circular dichroism signal over a wide frequency range. It is also shown that the strength of the gammadion's chiroptical response is determined solely by two geometric factors: the variation range of the gammadion's thickness and the arms' curvature. Our seminal theoretical study is intended to lay the foundation for future applications of semiconductor gammadions in chiral nanophotonics and nanotechnology.

Analytical theory of real-argument Laguerre-Gaussian beams beyond the paraxial approximation.

We study the propagation of real-argument Laguerre-Gaussian beams beyond the paraxial approximation using the perturbation corrections to the complex-argument Laguerre-Gaussian beams derived earlier by Takenaka et al. [J. Opt. Soc. Am. A2, 826 (1985)JOAOD60740-323210.1364/JOSAA.2.000826]. Each higher-order correction to the amplitude of the real-argument beam (l, m) is represented as a superposition of the same-order corrections to the amplitudes of the complex-argument beams (l, q) with q=0,1,2,…,m. We derive explicit expressions for the electric and magnetic fields of transversely and longitudinally polarized real-argument beams and calculate the chirality densities of these beams up to the fourth order of the smallness parameter. For the first time to the best of our knowledge, we show that essentially achiral Gaussian beams (corresponding to l=m=0) possess nonzero chirality density due to the wavefront curvature. The obtained corrections to the paraxial beams may prove useful for precise laser beam shaping and in studies of optomechanical forces.

Excitons in gyrotropic quantum-dot supercrystals.

We use quantum theory of molecular crystals to study collective excitations (excitons) of gyrotropic quantum-dot (QD) supercrystals with complex lattices consisting of two or more sublattices of semiconductor QDs. We illustrate the potentials of our approach by applying it to analytically calculate the linear permittivity tensor of supercrystals with two QDs per unit cell. The spatial dispersions of exciton energy bands and permittivity tensor components are examined in detail for two-dimensional supercrystals with a square lattice, which are relatively easy to fabricate in practice. Our results provide a systematic and versatile framework for the engineering of dispersion properties of gyrotropic QD supercrystals and for the analysis of their absorption and circular dichroism spectra.

Optical Anisotropy of Topologically Distorted Semiconductor Nanocrystals.

Engineering nanostructured optical materials via the purposeful distortion of their constituent nanocrystals requires the knowledge of how various distortions affect the nanocrystals' electronic subsystem and its interaction with light. We use the geometric theory of defects in solids to calculate the linear permittivity tensor of semiconductor nanocrystals whose crystal lattice is arbitrarily distorted by imperfections or strains. The result is then employed to systematically analyze the optical properties of nanocrystals with spatial dispersion caused by screw dislocations and Eshelby twists. We demonstrate that Eshelby twists create gyrotropy in nanocrystals made of isotropic semiconductors whereas screw dislocations can produce it only if the nanocrystal material itself is inherently anisotropic. We also show that the dependence of circular dichroism spectrum on the aspect ratio of dislocation-distorted semiconductor nanorods allows resonant enhancing their optical activity (at least by a factor of 2) and creating highly optically active nanomaterials.

Chiral Optical Properties of Tapered Semiconductor Nanoscrolls.

Large surface-to-volume ratio, one-dimensional quantum confinement, and strong optical activity make chiral nanoscrolls ideal for the detection and sensing of small chiral molecules. Here, we present a simple physical model of chiroptical phenomena in multilayered tapered semiconductor nanoscrolls. Our model is based on a linear transformation of coordinates, which converts nanoscrolls into flat but topologically distorted nanoplatelets whose optical properties can then be treated analytically. As an illustrative application example, we analyze absorption and circular dichroism spectra of CdSe nanoscrolls using an eight-band model of CdSe. We show that the optical activity of the nanoscrolls originates from the chiral distortion of their crystal lattice and determine selection rules for the optically active interband transitions. The results of our study may prove useful for the modeling and design of semiconductor nanoscrolls and nanoscroll-based materials.

Quantum theory of electroabsorption in semiconductor nanocrystals.

We develop a simple quantum-mechanical theory of interband absorption by semiconductor nanocrystals exposed to a dc electric field. The theory is based on the model of noninteracting electrons and holes in an infinitely deep quantum well and describes all the major features of electroabsorption, including the Stark effect, the Franz-Keldysh effect, and the field-induced spectral broadening. It is applicable to nanocrystals of different shapes and dimensions (quantum dots, nanorods, and nanoplatelets), and will prove useful in modeling and design of electrooptical devices based on ensembles of semiconductor nanocrystals.

Level anticrossing of impurity states in semiconductor nanocrystals.

The size dependence of the quantized energies of elementary excitations is an essential feature of quantum nanostructures, underlying most of their applications in science and technology. Here we report on a fundamental property of impurity states in semiconductor nanocrystals that appears to have been overlooked--the anticrossing of energy levels exhibiting different size dependencies. We show that this property is inherent to the energy spectra of charge carriers whose spatial motion is simultaneously affected by the Coulomb potential of the impurity ion and the confining potential of the nanocrystal. The coupling of impurity states, which leads to the anticrossing, can be induced by interactions with elementary excitations residing inside the nanocrystal or an external electromagnetic field. We formulate physical conditions that allow a straightforward interpretation of level anticrossings in the nanocrystal energy spectrum and an accurate estimation of the states' coupling strength.

Phonon-assisted photoluminescence from a semiconductor quantum dot with resonant electron and phonon subsystems.

We present a theory of phonon-assisted photoluminescence from a semiconductor quantum dot (QD) whose electron and phonon subsystems are resonantly coupled via the polar electron-phonon interaction. We show that the resonance-induced renormalization of the QD energy spectrum, leading to the formation of the polaron-like states, can be performed exactly in terms of the arbitrarily degenerate states of electron-hole pairs and the phonon modes of equal energies. Using the model of QDs with finite potential barriers for electron and holes leads to new selection rules of interband optical transitions and the three-particle interaction describing simultaneous absorption and/or emission of a photon and a phonon. We also derive a simple expression for the differential cross section of the stationary, low-temperature photoluminescence, which allows the fundamental parameters of the polaron-like excitations to be readily extracted from the frequency-resolved experimental spectra. In particular, the energies of the excitations and the coherence relaxation rates of the optical transitions resulting in their generation and recombination are shown to be directly given by the positions and widths of the photoluminescence peaks. The developed theory complements the existing experimental techniques of studying the phonon-assisted photoluminescence from individual nanocrystals.

Electroabsorption by 0D, 1D, and 2D nanocrystals: a comparative study of CdSe colloidal quantum dots, nanorods, and nanoplatelets.

This work presents a comprehensive study of electroabsorption in CdSe colloidal quantum dots, nanorods, and nanoplatelets. We experimentally demonstrate that the exposure of the nanoplatelets to a dc electric field leads to strong broadening of their lowest-energy heavy-hole absorption band and drastically reduces the absorption efficiency within the band. These are results of the quantum-confined Stark and Franz­Keldysh effects. The field-induced change in the nanoplatelets' absorption is found to be more than 10 times the change in the absorption by the quantum dots. We also demonstrate that the electroabsorption by the nanorods is weaker than that by the quantum dots and nanoplatelets and reveal an unusual dependence of the differential absorption changes on the nanoplatelet thickness: the thicker the nanoplatelet, the smaller the change.

Kinetics of pulse-induced photoluminescence from a semiconductor quantum dot.

Optical methods, which allow the determination of the dominant channels of energy and phase relaxation, are the most universal techniques for the investigation of semiconductor quantum dots. In this paper, we employ the kinetic Pauli equation to develop the first generalized model of the pulse-induced photoluminescence from the lowest-energy eigenstates of a semiconductor quantum dot. Without specifying the shape of the excitation pulse and by assuming that the energy and phase relaxation in the quantum dot may be characterized by a set of phenomenological rates, we derive an expression for the observable photoluminescence cross section, valid for an arbitrary number of the quantum dot's states decaying with the emission of secondary photons. Our treatment allows for thermal transitions occurring with both decrease and increase in energy between all the relevant eigenstates at room or higher temperature. We show that in the general case of N states coupled to each other through a bath, the photoluminescence kinetics from any of them is determined by the sum of N exponential functions, whose exponents are proportional to the respective decay rates. We illustrate the application of the developed model by considering the processes of resonant luminescence and thermalized luminescence from the quantum dot with two radiating eigenstates, and by assuming that the secondary emission is excited with either a Gaussian or exponential pulse. Analytic expressions describing the signals of secondary emission are analyzed, in order to elucidate experimental situations in which the relaxation constants may be reliably extracted from the photoluminescence spectra.