Some basic radiative and non-radiative processes taking place in semiconductor nanocrystals are discussed, and rates of these processes are calculated. In particular, in the present review we explore both intra-crystallite processes, such as the photon emission, Auger recombination, phonon-assisted exciton relaxation, capture on surface defects, multi-exciton generation, and inter-crystallite processes realized through the exciton migration in ensembles of nanocrystals. Exciton transitions, creation, and annihilation accompanied by the photon and (or) phonon emission or absorption are considered from the point of view of their influence on the optical properties of nanocrystals.
The use of ultrafast gating techniques allows us to resolve both spectrally and temporally the emission from short-lived neutral and negatively charged biexcitons in ultrasmall (sub-10 nm) CdSe nanocrystals (nanocrystal quantum dots). Because of forced overlap of electronic wave functions and reduced dielectric screening, these states are characterized by giant interaction energies of tens (neutral biexcitons) to hundreds (charged biexcitons) of meV. Both types of biexcitons show extremely short lifetimes (from sub-100 picoseconds to sub-picosecond time scales) that rapidly shorten with decrea…
In a recent paper [E. P. Pokatilov et al, PRB 65, 075316 (2002) the Raman selection rules in spherical nanocrystals with a degenerate valence band are analyzed. Some precisions are given here.
The dependences of the fundamental transition on the semiconductor quantum dot size obtained experimentally at various temperatures using different measuring methods are analyzed and compared. The possibility to extrapolate the results for the case of arbitrary temperature is discussed.
The combined effect of finite potential barriers and dielectric mismatch between dot and matrix on excitonic properties of semiconductor quantum dots has been studied. To avoid the unphysical divergence in the self-polarization energy which arises for the simplest and profusely adopted step-like model of the dielectric interface, we proposed a realistic (finite size) smooth profile for the dielectric interface. We have found that the excitonic binding energy can be either higher than the corresponding one to complete confinement by infinite barriers or essentially zero for a wide range of dot …
In this review we discuss several fundamental processes taking place in semiconductor nanocrystals (quantum dots, QDs) when their electron subsystem interacts with electromagnetic (EM) radiation. The physical phenomena of light emission and EM energy transfer from a QD exciton to other electronic systems such as neighbouring nanocrystals and polarisable 3D (semi-infinite dielectric or metal) and 2D (graphene) materials are considered. The cases of direct (II-VI) and indirect (silicon) band gap semiconductors are compared. We also cover the relevant non-radiative mechanisms such as the Auger pr…
We calculate the rate of non-radiative, Forster-type energy transfer (ET) from an excited epitaxial quantum well (QW) to a proximal monolayer of semiconductor nanocrystal quantum dots (QDs). Different electron-hole configurations in the QW are considered as a function of temperature and excited electron-hole density. A comparison of the theoretically determined ET rate and QW radiative recombination rate shows that, depending on the specific conditions, the ET rate is comparable to or even greater than the radiative recombination rate. Such efficient Forster ET is promising for the implementat…
We review the existing and present the new results of $\bf kp$ calculations of the electron, hole, and exciton effective $g$-factors in semiconductor nanocrystals of different shape and symmetry. We propose a simple yet accurate method for calculation of electron $g$-factor size dependence in bare nanocrystals within the eight-band Kane model. Using the spherical approximation for Luttinger Hamiltonian we find the dependence of hole $g$-factor on light to heavy hole effective mass ratio in semiconductor nanostructures with spherical, axial, and cubically symmetric shape. We show that the non-e…
In our recent paper [Phys. Rev. B 65, 075316 (2002)], the selection rules for the Raman scattering in spherical nanocrystals are analyzed. Here we show, that a physically expedient choice of the coordinate system, related to the polarization vector of the incoming or scattered light, simplifies and clarifies the analysis.
Zero-dimensional nanocrystals, as obtained by chemical synthesis, offer a broad range of applications, as their spectrum and thus their excitation gap can be tailored by variation of their size. Additionally, nanocrystals of the type ABC can be realized by alloying of two pure compound semiconductor materials AC and BC, which allows for a continuous tuning of their absorption and emission spectrum with the concentration x. We use the single-particle energies and wave functions calculated from a multiband sp^3 empirical tight-binding model in combination with the configuration interaction schem…
Using previously developed exciton scattering model accounting for the interband, i.e., exciton-biexciton, Coulomb interactions in semiconductor nanocrystals (NCs), we derive a closed set of equations for 2D double-quantum coherence signal. The signal depends on the Liouville space pathways which include both the interband scattering processes and the inter- and intraband optical transitions. These processes correspond to the formation of different cross-peaks in the 2D spectra. We further report on our numerical calculations of the 2D signal using reduced level scheme parameterized for PbSe N…
Multi-phonon Raman scattering in semiconductor nanocrystals is treated taking into account both adiabatic and non-adiabatic phonon-assisted optical transitions. Because phonons of various symmetries are involved in scattering processes, there is a considerable enhancement of intensities of multi-phonon peaks in nanocrystal Raman spectra. Cases of strong and weak band mixing are considered in detail. In the first case, fundamental scattering takes place via internal electron-hole states and is participated by s- and d-phonons, while in the second case, when the intensity of the one-phonon Raman…
In this letter, we propose a new model to determine the recombination oscillator strength of trions and biexcitons for bound and unbound cases in the effective mass approximation. The validity of our model has been confirmed by the radiative lifetime of the trion and biexciton in a spherical quantum dot. The results show that the model works sufficient accuracy in comparison with results of more complex methods such as quantum monte carlo techniques and atomistic calculations.
Nonradiative processes limit optoelectronic functionality of nanocrystals and curb their device performance. Nevertheless, the dynamic structural origins of nonradiative relaxations in nanocrystals are not understood. Here, femtosecond electron diffraction measurements corroborated by atomistic simulations uncover transient lattice deformations accompanying radiationless electronic processes in semiconductor nanocrystals. Investigation of the excitation energy dependence shows that hot carriers created by a photon energy considerably larger than the bandgap induce structural distortions at nan…
The influence of the tip-substrate bias induced electric field in a scanning-tunneling-spectroscopy experiment on charged InAs nanocrystals is studied. Calculating the ground and first excited many-particle state for five electrons occupying the quantum dot reveals a Stark-induced reordering of states by increasing the electric field strength. It is shown that this reordering of states is accompanied by a symmetry change of the local density of states (LDOS), which in principal is observable in a wave-function mapping experiment. Since in the usually performed experiments the electric field ca…
Time-resolved Faraday rotation is used to study both transverse and longitudinal spin relaxation in chemically-synthesized CdSe nanocrystals (NCs) 22-80 Angstroms in diameter. The precession of optically-injected spins in a transverse magnetic field occurs at distinct frequencies whose assignment to electron and exciton spins is developed through systematic studies of the size-dependence and theoretical calculations. It is shown that the transverse spin lifetime is limited by inhomogeneous dephasing to a degree that cannot be accounted for by the NC size distribution alone. Longitudinal spin r…
We study the dependence of the quantum yield of photoluminescence of a dense, periodic array of semiconductor nanocrystals (NCs) on the level of doping and NC size. Electrons introduced to NCs via doping quench photoluminescence by the Auger process, so that practically only NCs without electrons contribute to the photoluminescence. Computer simulation and analytical theory are used to find a fraction of such empty NCs as a function of the average number of donors per NC and NC size. For an array of small spherical NCs, the quantization gap between 1S and 1P levels leads to transfer of electro…
Semiconductor nanocrystals are being used as hosts to trap and manipulate single spins. Spins in nanocrystals can have different properties than their bulk counterparts, owing both to quantum confinement and surface effects. We will show that spins can be generated in nanocrystals by the insertion of impurities, either magnetic or not, or by magnetic polarons present at dangling bonds at their surfaces. This chapter reports theoretical contributions to this field, where the Density Functional Theory is used to simulate these functionalized nanocrystals.
We investigated CdTe nanocrystal tetrapods of different sizes by resonant inelastic light scattering at room temperature and under cryogenic conditions. We observe a strongly resonant behavior of the phonon scattering with the excitonic structure of the tetrapods. Under resonant conditions we detect a set of phonon modes that can be understood as confined longitudinal-optical phonons, surface-optical phonons, and transverse-optical phonons in a nanowire picture.
Spin-selective tunneling of holes in SiGe nanocrystals contacted by normal-metal leads is reported. The spin selectivity arises from an interplay of the orbital effect of the magnetic field with the strong spin-orbit interaction present in the valence band of the semiconductor. We demonstrate both experimentally and theoretically that spin-selective tunneling in semiconductor nanostructures can be achieved without the use of ferromagnetic contacts. The reported effect, which relies on mixing the light and heavy holes, should be observable in a broad class of quantum-dot systems formed in semic…
Excitonic properties in the Kagome lattice system, which is produced by quantum wires on semiconductor surfaces, are investigated by using the exact diagonalization of a tight binding model. It is shown that due to the existence of flat bands the binding energy of exciton becomes remarkably large in the two-dimensional Kagome lattice compared to that in one-dimensional lattice, and the exciton Bohr radius is quite small as large as a lattice constant. We also discuss the magnetic field effects on the exciton binding energy and the stability of exciton against the creation of charged exciton an…
The effect of carrier multiplication (CM) in semiconductor nanocrystals is systematically treated by employing an exciton scattering approach. Using projection operators, we reduce the Coulomb coupled multi-exciton dynamics to scattering dynamics in the space spanning both single- and bi-exciton states. We derive a closed set of equations determining the scattering matrix elements. This allows us to interpret CM dynamics as a series of odd-order interband scattering events. Using the time-dependent density matrix formalism, we provide a rigorous description of the CM dynamics induced by a fini…
We study the surface conductivity of a field-effect transistor (FET) made of periodic array of spherical semiconductor nanocrystals (NCs). We show that electrons introduced to NCs by the gate voltage occupy one or two layers of the array. Computer simulations and analytical theory are used to study the array screening and corresponding evolution of electron concentrations of the first and second layers with growing gate voltage. When first layer NCs have two electrons per NC the quantization energy gap between its 1S and 1P levels induces occupation of 1S levels of second layer NCs. Only at a …
We investigate theoretically the effects of interaction between an optical dipole (semiconductor quantum dot or molecule) and metal nanoparticles. The calculated absorption spectra of hybrid structures demonstrate strong effects of interference coming from the exciton-plasmon coupling. In particular, the absorption spectra acquire characteristic asymmetric lineshapes and strong anti-resonances. We present here an exact solution of the problem beyond the dipole approximation and find that the multipole treatment of the interaction is crucial for the understanding of strongly-interacting exciton…
We present a scheme to realize the chiral topological excitonic insulator in semiconductor heterostructures which can be experimentally fabricated with a coupled quantum well adjacent to twoferromagnetic insulating films. The different mean-field chiral topological orders, which are due to the change in the directions of the magnetization of the ferromagnetic films, can be characterized by the TKNN numbers in the bulk system as well as by the winding numbers of the gapless states in the edged system. Furthermore, we propose an experimental scheme to detect the emergence of the chiral gapless e…
We analyze the many-particle correlations that affect the optical properties of two-dimensional semiconductors. These correlations manifest themselves through the specific optical resonances such as excitons, trions, etc. Starting from the generic electron-hole Hamiltonian and employing the microscopic Heisenberg equation of motion the infinite hierarchy of differential equations can be obtained. In order to decouple the system we address the cluster expansion technique which provides a regular procedure of consistent accounting of many-particle correlation contributions into the interband pol…
Electron-phonon and exciton-phonon interactions in nanoclusters are formulated and computed under the framework of GW-BSE (Bethe-Salpeter equation) approach. The phonon effect is modeled with the two-particle representation for the first time. The nonradiative relaxation rates of electrons and excitons are calculated. It is uncovered that both single-phonon relaxation and multiple-phonon relaxation are significant in nanocrystals, and correspond to two types of physical processes that have totally different spectral lineshapes. Furthermore, the multiple-phonon relaxation always occurs and its …
The potential of semiconductors assembled from nanocrystals (NC semiconductors) has been demonstrated for a broad array of electronic and optoelectronic devices, including transistors, light emitting diodes, solar cells, photodetectors, thermoelectrics, and phase charge memory cells. Despite the commercial success of nanocrystals as optical absorbers and emitters, applications involving charge transport through NC semiconductors have eluded exploitation due to the inability for predictive control of their electronic properties. Here, we perform large-scale, ab-initio simulations to understand …
We derive the matrix elements of Coulomb interaction between states with different number of electrons and holes in a semiconductor nanocrystal within the 8-band $\mathbf{k}\cdot\mathbf{p}$ theory. These matrix elements are responsible for multiple exciton generation which may contribute to the enhancement of the efficiency of solar cells. Our calculations are performed within the multi band envelope function formalism based on the states resulting from diagonalization of the 8-band $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian. We study in detail and compare two contributions to the inter-band Coul…
To fully deploy the potential of semiconductor nanocrystal films as low-cost electronic materials, a better understanding of the amount of dopants required to make their conductivity metallic is needed. In bulk semiconductors, the critical concentration of electrons at the metal-insulator transition is described by the Mott criterion. Here, we theoretically derive the critical concentration $n_c$ for films of heavily doped nanocrystals devoid of ligands at their surface and in direct contact with each other. In the accompanying experiments, we investigate the conduction mechanism in films of p…
We investigate theoretically the effect of injection of plasmonic carriers from an optically-excited metal nanocrystal to a semiconductor contact or to attached molecules. The distributions of optically-excited hot carriers are dramatically different in metal nanocrystals with large and small sizes. In large nanocrystals, most carriers have very small energies and the hot carrier distribution resembles the case of a plasmon wave in bulk. In nanocrystals smaller than 20nm, the carrier distribution extends to larger energies and occupies the whole region E_{F}<E<omega. The physical reason for th…
We develop a generalized framework based on a Green's function formalism to calculate the efficiency of multiexciton gen-eration in nanocrystal quantum dots. The direct/indirect absorption and coherent/incoherent impact ionization mechanisms, often used to describe multiexciton generation in nanocrystals, are reviewed and rederived from the unified theory as certain approximations. In addition, two new limits are described systematically - the weak Coulomb coupling limit and the semi-wide band limit. We show that the description of multiexciton generation in nanocrystals can be described as in…
We present a comprehensive theoretical description of quantum well exciton-polaritons imbedded in a planar semiconductor microcavity. The exact non-local dielectric response of the quantum well exciton is treated in detail. The 4-spinor structure of the hole subband in the quantum well is considered, including the pronounced band mixing effect. The scheme is self-contained and can be used to treat different semiclassical aspects of the microcavity properties. As an example, we analyze the "selection" rules for the exciton-cavity mode coupling for different excitons.
Heavily-doped semiconductor nanocrystals characterized by a tunable plasmonic band have been gaining increasing attention recently. Herein, we introduce this type of materials focusing on their structural and photo physical properties. Beside their continuous-wave plasmonic response, depicted both theoretically and experimentally, we also review recent results on their transient, ultrafast response. This was successfully interpreted by adapting models of the ultrafast response of gold nanoparticles.
One of the most striking features of novel 2D semiconductors (e.g., transition metal dichalcogenide monolayers or phosphorene) is a strong Coulomb interaction between charge carriers resulting in large excitonic effects. In particular, this leads to the formation of multi-carrier bound states upon photoexcitation (e.g., excitons, trions and biexcitons), which could remain stable at near-room temperatures and contribute significantly to optical properties of such materials. In the present work we have used the Path Integral Monte Carlo methodology to numerically study properties of multi-carrie…
The population dynamics of single- and bi-exciton states in semiconductor nanocrystals is modeled numerically in the presence of Coulomb coupling between single- and two-exciton states and a dissipation channel in order to study the transient bi-exciton population that occurs in an optically excited semiconductor nanocrystal. The results show that the system evolution strongly changes if the dissipation is included. In a certain range of parameters, the growth of the exciton number (MEG process) is fast (on picosecond time scale) and the following decay (Auger process) is much slower (hundreds…
We present theoretical and experimental investigations of the magnetism of paramagnetic semiconductor CdSe:Mn nanocrystals and propose an efficient approach to the exposure and analysis of the underlying anti-ferromagnetic interactions between magnetic ions therein. A key advance made here is the build-up of an analysis method with the exploitation of group theory technique that allows us to distinguish the anti-ferromagnetic interactions between aggregative Mn2+ ions from the overall pronounced paramagnetism of magnetic ion doped semiconductor nanocrystals. By using the method, we clearly rev…
A configuration space approach is developed to uncover generic stability peculiarities for the lowest energy neutral and charged exciton complexes (biexciton and trion) in quasi-one-dimensional semiconductors. Trions are shown to be more stable than biexcitons in strongly confined structures with small reduced electron-hole masses. Biexcitons are more stable in less confined structures with large reduced electron-hole masses. In semiconducting carbon nanotubes, in particular, the trion binding energy is shown to be greater than that of the biexciton by a factor ~1.4 decreasing with diameter, t…
We use a configuration interaction approach within the envelope function approximation to study the nature of the excitonic resonance in nano-hybrids, composite nanoparticles (NPs) combining a semiconducting and a metallic segment in contact. With reference to recent experimental reports, we specifically study CdS-based nanorods with metallic NPs deposited at the tips (matchstick) or metallic coatings (core-shell). The excitonic states are computed taking into account both the renormalization of the electron-hole interaction and self-energy effects induced by the the metallic segment on the el…
The interaction of optically excited excitons in atomically thin semiconductors with residual doping densities leads to many-body effects which are continuously tunable by external gate voltages. Here, we develop a fully microscopic theory to describe the doping-dependent manipulation of the excitonic properties in atomically thin transition metal dichalcogenides. In particular, we establish a diagonalization approach for the Schrödinger equation which characterizes the interaction of a virtual exciton with the Fermi sea of dopants. Solving this many-body Schrödinger equation provides access t…
We have explored the influence of different matrices on the emission line shape of individual homogeneously coated CdSe/CdS/ZnS nanocrystals. The results obtained corroborate previous observations of a correlation between blinking events and spectral diffusion but in addition we have found that the extent of spectral diffusion is almost independent of the dielectric environment of the NC. Additionally, we report the observation of a correlation between the line width and emission energy which is not expected to occur in the spherical - symmetric NCs employed in this work. The implications of t…
A microscopic approach is developed to compute the excitonic properties and the corresponding terahertz response for semiconductors characterized by anisotropic effective masses. The approach is illustrated for the example of germanium where it is shown that the anisotropic electron mass in the L-valley leads to two distinct terahertz absorption resonances separated by 0.8 meV.
The epitaxial growth of germanium on silicon leads to the self-assembly of SiGe nanocrystals via a process that allows the size, composition and position of the nanocrystals to be controlled. This level of control, combined with an inherent compatibility with silicon technology, could prove useful in nanoelectronic applications. Here we report the confinement of holes in quantum-dot devices made by directly contacting individual SiGe nanocrystals with aluminium electrodes, and the production of hybrid superconductorsemiconductor devices, such as resonant supercurrent transistors, when the dot …
The optical spectra of CdSe nanocrystals up to 55 A in diameter are analyzed in a wide range of energies from the fine structure of the low-energy excitations to the so-called high-energy transitions. We apply a symmetry-based method in two steps. First we take the tight-binding (TB) parameters from the bulk sp^{3}s^{*} TB model, extended to include the spin-orbit interaction. The full single-particle spectra are obtained from an exact diagonalization by using a group-theoretical treatment. The electron-hole interaction is next introduced: Both the Coulomb (direct) and exchange terms are consi…
This paper is focused on the the variable-range hopping of electrons in semiconductor nanocrystal (NC) films below the critical doping concentration $n_c$ at which it becomes metallic. The hopping conductivity is described by the Efros-Shklovskii law which depends on the localization length of electrons. We study how the localization length grows with the doping concentration $n$ in the film of touching NCs. For that we calculate the electron transfer matrix element $t(n)$ between neighboring NCs for two models when NCs touch by small facets or just one point. We study two sources of disorder:…
It is widely accepted that the properties of most semiconductor nanocrystals can be tuned by their core size, shape and material. In covalent semiconductor nanocrystal materials, such as silicon, germanium or carbon, certain degree of tunability of the properties can be also achieved by the surface ligands. In particular, covalently bonded ligand species on the surface of such a nanocrystal (i) contribute to the density of states of the core via orbital delocalization; (ii) might introduce strain via ligand-to-ligand steric hindrance and (iii) will cause charge transfer from/to the core. In th…
We present a new exciton-based formalism for calculating the coherent response of asymmetric semiconductor multiple quantum well structures to ultra-short optical pulses valid to infinite order in the optical field and including the self-generated intraband fields. We use these equations to calculate and explain the oscillations with time delay of peaks in the spectrally-resolved degenerate four wave mixing signals from biased semiconductor superlattices, obtaining good agreement with experiment.
Strain engineering is a powerful tool for tuning physical properties of 2D materials, including monolayer transition metal dichalcogenides (TMD) -- direct bandgap semiconductors with strong excitonic response. Here, we demonstrate an approach for local characterization of strain-induced modification of excitonic photoluminescence in TMD-based materials. We reversibly stress a monolayer of MoSe$_2$ with an AFM tip and perform spatio-spectral mapping of the excitonic photoluminescence in the vicinity of the indentation point. To fully reproduce the experimental data, we introduce the linear depe…
We present quantum yield measurements of single layer $\textrm{WSe}_2$ (1L-$\textrm{WSe}_2$) integrated with high-Q ($Q>10^6$) optical microdisk cavities, using an efficient ($η>$90%) near-field coupling scheme based on a tapered optical fiber. Coupling of the excitonic emission is achieved by placing 1L-WSe$_2$ to the evanescent cavity field. This preserves the microresonator high intrinsic quality factor ($Q>10^6$) below the bandgap of 1L-WSe$_2$. The nonlinear excitation power dependence of the cavity quantum yield is in agreement with an exciton-exciton annihilation model. The cavity quant…
This letter assigns the Faraday rotation in photoexcited semiconductors to ``Pauli interactions'', \emph{i}. \emph{e}., carrier exchanges, between the real excitons present in the sample and the virtual excitons coupled to the $σ_{\pm}$ parts of a linearly polarized light. While \emph{direct Coulomb} interactions scatter bright excitons into bright excitons, whatever their spins are, \emph{Pauli} interactions do it for bright excitons \emph{with same spin only}. This makes these Pauli interactions entirely responsible for the refractive index difference, which comes from processes in which the…
In semiconductors, exciton or charge carrier diffusivity is typically described as an inherent material property. Here, we show that the transport of excitons (i.e., bound electron-hole pairs) in CsPbBr3 perovskite nanocrystals (NCs) depends markedly on how recently those NCs were occupied by a previous exciton. Using fluence- and repetition-rate-dependent transient photoluminescence microscopy, we visualize the effect of excitation frequency on exciton transport in CsPbBr3 NC solids. Surprisingly, we observe a striking dependence of the apparent exciton diffusivity on excitation laser power t…
The exciton states in strained (In,Ga)As nanorings embedded in a GaAs matrix are computed. The strain distribution is extracted from the continuum mechanical model, and the exact diagonalization approach is employed to compute the exciton states. Weak oscillations of the ground exciton state energy with the magnetic field normal to the ring are an expression of the excitonic Aharonov-Bohm effect. Those oscillations arise from anticrossings between the ground and the second exciton state and can be enhanced by increasing the ring width. Simultaneously, the oscillator strength for exciton recomb…
