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We present analytical results which describe the properties of the exciton ground state in a single semiconductor quantum dot (QD). Calculations are performed within the Luttinger–Kohn and Bir–Pikus Hamiltonian theory. We show in an explicit form that an interplay of the exchange interaction and the heavy hole–light hole coupling, which is due to the in-plane asymmetries of the dot shape and the strain distribution, plays an essential role. For both the bright and dark exciton, this combined effect leads to a dependence of the fine structure splitting and polarizations on the main anisotropy axis direction relative to the dot orientation. Basing on the obtained analytical expressions, we discuss some special cases in details.

We report measurements of dynamic (a.c.) electrical conductivity in borosilicate glasses doped with cadmium sulfoselenide and copper and silver iodides in a wide temperature range below the glass transition temperature T g and at different frequencies. The concentration of the mobile dopant ions is governed by specific heat treatment conditions of the glass samples leading to a creation of the CdSSe, AgI and CuI semiconductor nanocrystals. Investigations include different cases from a full solution of the dopant ions coming from a dissociation of the dopants during the glass preparation to their almost complete incorporation into the nanocrystals in the glass matrix. At temperatures higher than 150 °C–200 °C the a.c. conductivity in all the examined glasses exhibits the Arrhenius behavior. In this temperature range the mixed mobile ion effect is detected: the doped glasses have the low values of the conductivity compared to the undoped ones. In the low temperature range only weak temperature dependence is detected for all the samples. The mixed mobile ion effect is still presented for the CdSSe-doped glasses, whereas the AgI- and CuI-doped glasses exhibit the classical MMIE which is essentially absent at low temperatures.

The phonon-induced flip of the exciton spin in single flat semiconductor quantum dots with a light-hole exciton ground state is studied. The corresponding quartet, split by the exchange interaction, consists of three bright states and a dark state located energetically below the bright exciton. The two in-plane polarized bright states contribute to single-phonon transitions to the dark state and also to the upper bright state polarized in the $z$ growth direction of the dot. For these processes, the presented analytical results are calculated for the relaxation driven by the spin-orbit interaction in the conduction and the light-hole valence subbands. The estimated spin-relaxation times at low temperature are (at least) one order of magnitude lower than the bright exciton lifetime. Two other possible transitions, within the in-plane polarized doublet and between the $z$-polarized bright and dark states as well, proceed via intermediate states with a contribution from two acoustic phonons. These processes are strongly suppressed at low temperature, whereas they appear to be of the same intensity as single-phonon transitions at high enough temperatures.

In weakly confining quantum structures such as interfacial islands or quantum disks the exciton-spin relaxation is governed by two independent electron and hole spin flip processes between the optically active and dark states. A microscopic theory for these transitions is presented which is based on second order spin-orbit and corrier-phonon interaction processes. We found that the sequential relaxation between bright and -dark states leads to much faster exciton-spin relaxation than for strongly confining ("small") quantum dots where the dominant process stems from electron-hole exchange interaction plus hole deformation potential coupling. In addition, the fast exciton spin relaxation implies that the (exciton-bound) electron spin flip time is also much shorter than for a single electron.

We report on the injection of electron spins into InGaAs quantum dots with an efficiency of up to 60%. This injection is observed in p-i-n light-emitting diode structures using the diluted magnetic semiconductor ZnMnSe as spin aligner (spin-LED). The degree of spin polarization is deduced from the circular polarization degree of the photons emitted when the injected electrons recombine in the quantum dots with unpolarized holes. We observe a strong energy dependence of the polarization degree with a strong increase starting from zero to a high value on the high energy side of the emission spectrum. To study the origin of this dependence, we compare results of two quantum-dot samples with emission peaks at 1.2 eV and 1.33 eV, respectively. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We study the relaxation of the exciton spin (longitudinal spin–relaxation time T1) in single asymmetrical quantum dots (QD) at low temperatures. The main relaxation mechanism is due to the exciton spin–acoustic phonon coupling via the strain–dependent exchange interaction; piezoelectric coupling is less efficient. For zero magnetic field, relaxation within the radiative exciton–doublet for typical QDs is very slow compared to the exciton lifetime. Relaxation to nonradiative states becomes important for QDs with large singlet–triplet splitting of a few meVs. The calculated relaxation times strongly decrease in high magnetic fields. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

We study the phonon-assisted relaxation processes (longitudinal relaxation time T1) within the radiative doublet of the heavy-hole-exciton in asymmetrical quantum dots. Two different relaxation mechanisms are considered: the exciton spin–acoustic phonon coupling via the strain-dependent short-range exchange interaction and the second-order quasielastic interaction between charge carriers and LO phonons. For zero magnetic fields and low temperatures, the calculated relaxation times for typical QDs are very long compared to the exciton lifetime yet they are strongly reduced in high magnetic fields (of the order of a few Tesla) and high temperatures T ≥ 100 K.

In a differential absorption experiment the induced infrared transitions from the excitonic 1s to the 2p levels in Cu 2 O have been investigated. Intermediate densities of 1s excitons were created by cw-laser excitation while the interexcitonic 1s to 2p transitions were probed simultaneously, using Fourier spectroscopy. Our data give evidence for a surprisingly large splitting of the 2p level (3,7 meV) the origin of which is a matter of speculation. An analysis of lineshape and width of the transitions results in a ratio of the effective masses m 1s /m 2p which deviates from the literature value.

The absorption spectra of CuBr, CuCl, CuI, and AgI nanocrystals (NC) embedded in a glass matrix have been investigated in a wide temperature range between T =6 and 860 K. The change of the absorption in the vicinity of the exciton resonance for CuBr and CuCl reveals a pronounced reduction of the melting temperature of NCs compared to the bulk value and shows a strong hysteresis between melting and solidification temperatures. The melting temperature and the hysteresis width depend on the sizes of NCs. For CuBr NCs a second hysteresis around the bulk melting point is observed. For large NCs the temperature dependence of the exciton peak energies is analogous to its counterpart in bulk crystals. For CuI NCs the shrinkage effect of the gap for both cubic and hexagonal modifications is observed and the temperature coefficients of the energy gaps are deduced. For AgI NCs a rather unusual temperature dependence of energy gap is observed. This dependence is nonmonotonic and shows a change of the energy gap slope from positive to negative.

Infrared transitions of excitons in Cu 2 O from the 1s to 2p levels have been investigated with a pump-probe experiment. 1s densities around 10 15 /cm 3 have been created by pumping with a cw-laser and the induced 1s M 2p absorption has been probed simultaneously. The main experimental finding is that there is a splitting of , 3.7 v meV in the 2p level scheme, which has not been reported so far. Analyzing the linewidth and shape of the transitions, we find that the effective mass of the 1s state might have been overestimated in earlier studies.

The excitonic ground state in single quantum dots with structural anisotropy is studied in dependence on the magnitude of the electron-hole short-range exchange interaction. Structural anisotropy is described phenomenologically by lattice deformation. The fine structure of the exciton levels is due to an interplay of the deformations and exchange interaction and is the more pronounced the smaller the quantum dots are. The lattice deformations are the reason for optical anisotropy in strained quantum dots. The exchange interaction, however, suppresses the polarization effects which are much more significant in large quantum dots. An additional decrease of the optical anisotropy arises from the coexistence of structural and epitaxial deformations.

We report the fabrication, transmission electron microscopy investigation and linear optical properties of silver iodide quantum dots in an aluminaborosilicate host network structure. The nearly spherical quantum dots with radii ranging from 1.7 to 2 nm exhibit a pronounced excitonic absorption and intensive intrinsic photoluminescence in the intermediate confinement regime. The selective photoluminescence and photoluminescence excitation measurements revealed the fine structure in the spectra due to the splitting of the lowest exciton state by the electron-hole exchange interaction. A considerable enhancement of the exchange energy with decreasing quantum dot size is observed.

We calculate the scattering rate of a test electron, due to the Auger process between Landau levels, for two-dimensional electrons in a random potential. The random potential is assumed to be smooth, and its correlation length is large compared to the magnetic length. Two Auger processes were considered. The first one is the Auger process in which two photoelectrons in the same Landau level are scattered, deexciting one to a lower level, losing energy, and exciting the second to a higher level, gaining energy. The second Auger process is the inverse one. In that case a photoelectron from an upper level and a thermal electron from a lower level are scattered, and both are transferred to the same intermediate level. It is shown that the scattering rate is largest for those Auger transitions in which the change in the Landau-level number is equal to 1. The dependence of the scattering rate on the test electron energy and the magnetic field are discussed. As an example, the Auger process in which the interacting electrons are in the second Landau level is considered. Numerical results of the dependence of the Auger scattering rate on the test electron energy and the magnetic field for this case are presented. Simplified formulas for the scattering rate are also suggested.

The optical anisotropy in quantum wires of cubic crystals is calculated analytically on the basis of the effective-mass theory. It is shown that the anisotropy depends strongly on the ratio of the widths of the wire, on the orientation of the wire with respect to the crystallographic directions, and on the material parameters. Quantitative calculations for quantum wires of GaAs are also given.

The optical transition energies have been determined for the lowest electron-hole pair states of CdSe quantum dots embedded in glass. The data obtained by photoluminescence, differential absorption and photoluminescence excitation spectroscopy have been compared and a general size dependence could be established. Based on theoretical calculations, the dominant features in the spectra have been assigned to the different transitions from the ground state to the one-pair states. Within the lowest one pair transition, a fine structure due to exchange interaction has been observed. The change in the optical properties with increasing intensity has been studied and the two-pair states identified in luminescence. Spectrally broad optical gain has been found due to stimulated transitions involving both one- and two-pair states.

The results on the selective photoluminescence (PL), photoluminescence excitation (PLE) and the degree of linear polarization (DLP) for the PL spectrum in AgI nanocrystals (NC) embedded in a glass host matrix are presented. The measurements indicate a fine structure of the exciton ground state due to the electron–hole exchange interaction: the PL originates from the lowest triplet state (“dark” exciton) when the higher singlet state (“bright” exciton) is excited. The obtained negative DLP confirms that the emitting state is not directly excited by the pump light, but is created through the virtual interaction with a higher excitonic state of different polarization features and subsequent relaxation. The corresponding red shift of the PL spectrum with respect to the PLE spectrum has been studied in dependence on the NC size. The exchange splitting shows a pronounced size dependence strongly increasing with a restriction of the dot radii. The value of the exchange energy of the exciton for AgI bulk crystals is determined. Both the short- and long-range contributions to the exchange splitting are discussed.

The temperature dependence of exciton peak energies in large CuI quantum dots embedded in a glass matrix has been measured. The gap shrinkage effect for both cubic and hexagonal CuI phases was observed. The temperature coefficients of the energy gaps and the effective phonon energies are deduced.

We study the phonon-induced flip of the exciton spin in single strongly confining quantum dots. The considered two-phonon process contributes to the exciton spin relaxation (longitudinal relaxation time ${T}_{1}$) within the radiative doublet of the exciton ground state. The respective effective matrix element is driven by an interplay of the short-range exchange interaction and the lattice deformation induced by acoustic phonons. The two-phonon process involves the participation of the dipole-forbidden dark states. The here considered relaxation channel is of paramount importance for symmetrical dots and may be several orders of magnitude faster than the previously studied transition between bright states in asymmetrical quantum dots. The calculated relaxation rates depend on the dot composition and shape, and decrease very strongly upon reduction in the dot size. For various individual dots belonging to a large quantum-dot ensemble the respective relaxation times may differ by a several orders of magnitude. For a typical ensemble of InAs/GaAs self-organized quantum dots at low temperatures, the numerical estimates range from few hundreds of microseconds for the largest dots to few tens of nanoseconds for the smallest dots involved.

We have calculated the characteristic time for the direct heating of the Mn spin system by spin-polarized photoexcited holes as well as the relaxation time for a single hole in semimagnetic quantum wells in an external longitudinal magnetic field. This spin-conserving heating process is due to the $p\text{\ensuremath{-}}d$ exchange interaction-induced scattering of the holes with the Mn ions within the first heavy-hole subband. The relaxation time for a single hole determines the maximum relative change of the magnetization in the case of short (femtosecond) pulse excitation. Numerical calculations are given for the example of (Zn,Mn)Se-based quantum wells. Due to the strong spin-orbit and exchange interactions within the valence band, the photoexcited hole gas heats the Mn spin system on a nanosecond time scale. This is much more effective than for an electron gas under similar conditions, for which the corresponding characteristic time lies in microsecond range. For a single hole, the relaxation time is much smaller than the characteristic heating time and, for typical experimental conditions, lies in the picosecond range. In the frame of the developed theoretical model, we analyze the details of the dependence of the Mn heating on the hole concentration and temperature on the Mn content and on magnetic field.

We have studied temperature dependence of the signals of optical orientation of excitons at resonant excitation of the ensemble of planar self‐assembled CdSe/ZnSe quantum dots and show that spin memory in this system survives up to 100K. To describe the experimental results we apply the model that considers explicitly the effect of multi‐phonon processes on the broadening of bright‐exciton‐phonon sublevels and demonstrate that calculated temperature dependences of spin relaxation rates are in good agreement with obtained experimental data.

We report results of calculations on the spin-flip scattering rate of heavy holes and excitons in semimagnetic quantum wells in an external magnetic field due to the $sp\text{\ensuremath{-}}d$ exchange interaction. Numerical estimates are given for the example of $\mathrm{CdMnTe}$ quantum wells with magnetic wells and nonmagnetic barriers. Due to a giant spin splitting induced by the magnetic field in a semimagnetic quantum well, the heavy hole at zero momentum contributes significantly to spin-flip scattering processes, in marked contrast to the zero-field case. For single (free) heavy holes, the spin-flip scattering rate shows a fast increase with magnetic field which turns to saturation at fields exceeding $1\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. The larger the thickness of a quantum well, the stronger is such an acceleration of the heavy-hole spin relaxation. Still the maximum values of the scattering rate (on the order of ${10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}\mathrm{s}$) are largest for narrow wells. For the exciton-bound carriers (electron and holes), the electron-hole correlation effects get important, particularly, in the presence of an external magnetic field. As a result, the scattering rate for the spin-flip transitions within the states of the (heavy-hole) bright exciton, shows a pronounced maximum at low fields $(\ensuremath{\lesssim}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{T})$. The scattering rate saturates at moderate fields of about $2\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ at a magnitude on the order of a few tens of picoseconds.

We present theoretical results for the spin relaxation of exciton-bound electrons and holes in weakly confining quantum dots. The relaxation is driven by the spin-orbit interaction in the conduction band and the linear in the momentum term in the valence band, respectively. The relaxation occurs between the optically active (bright) and inactive (dark) exciton states due to acoustic-phonon-assisted spin flips. The exchange splitting between the bright and dark states acts as a constant external magnetic field. A sequential flip of the (exciton-bound) electron and hole spins results in the spin-flip transition between the bright exciton states (i.e., an exciton-spin relaxation). We find that the spin relaxation time for an exciton-bound electron is several orders of magnitude faster than for a single electron. The resulting exciton spin-relaxation time is also several orders of magnitude faster than the one in small dots which is driven by the electron hole exchange interaction. We obtain the dependence of the exciton-spin relaxation time on dot size and temperature.

Theoretical results are given for spin relaxation in semimagnetic semiconductor quantum wells due to longitudinal optical (LO) phonon-induced flips of exciton spins at zero temperature and modest magnetic fields. Relaxation in this scenario is due to spin-flip transitions within the heavy-hole exciton subbands which are mediated by the coupling of excitonic spin states via the electron-hole exchange interaction. Relaxation rates are found to depend strongly on a magnetic field, exciton momentum, and size of the quantum well. Results are illustrated by evaluations for the ZnSe-based semimagnetic quantum wells. In longitudinal magnetic fields (Faraday geometry) a maximum in the relaxation rate is found for zero-momentum excitons at a Zeeman splitting of $\ensuremath{\sim}60\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. In transverse magnetic fields (Voigt geometry) the LO-induced spin relaxation is strongly suppressed.

We present an analytic solution to the problem of the Rashba spin-orbit coupling in semiconductor quantum dots. We calculate the exact energy spectrum, wave-functions, and spin--flip relaxation times. We discuss various effects inaccessible via perturbation theory. In particular, we find that the effective gyromagnetic ratio is strongly suppressed by the spin-orbit coupling. The spin-flip relaxation rate has a maximum as a function of the spin-orbit coupling and is therefore suppressed in both the weak- and strong coupling limits., 5 pages, 4 figs, reference added

We present a quantitative interpretation of the anomalous temperature behavior-the so-called "S-shape dependence"-of the photoluminescence (PL) in quantum films containing nanoislands. Experimental data for CdSe/ZnSe samples are modeled using Monte Carlo simulations of the involved relaxation mechanisms and thus providing a realistic picture of the exciton kinetics. We are able to reproduce simultaneously the temperature dependence of the PL maximum and of the full width at half maximum of the PL with good accuracy. We deduce information about the distribution of the localization centers and identify hopping processes between spatially separated states within one island.

We study the relaxation of the exciton spin (longitudinal relaxation time $T_{1}$) in single asymmetrical quantum dots due to an interplay of the short--range exchange interaction and acoustic phonon deformation. The calculated relaxation rates are found to depend strongly on the dot size, magnetic field and temperature. For typical quantum dots and temperatures below 100 K, the zero--magnetic field relaxation times are long compared to the exciton lifetime, yet they are strongly reduced in high magnetic fields. We discuss explicitly quantum dots based on (In,Ga)As and (Cd,Zn)Se semiconductor compounds., Comment: accepted for Phys. Rev. B

Optical anisotropy is the dependence of the optical properties of crystals on the polarization state of the light field. A brief overview is given on the description of the anisotropic optical effects in bulk semiconductor crystals and in low-dimensional semiconductor structures.

The decay time of the linear polarization degree of the luminescence in strongly confined semiconductor quantum dots with asymmetrical shape is calculated in the frame of second-order quasielastic interaction between quantum dot charge carriers and LO phonons. The phonon bottleneck does not prevent significantly the relaxation processes and the calculated decay times can be of the order of a few tens picoseconds at temperature $T \simeq 100$K, consistent with recent experiments by Paillard et al. [Phys. Rev. Lett. {\bf86}, 1634 (2001)]., 4 pages, 4 figures

Commensurability oscillations in the magnetoresistivity of a two-dimensional electron gas in a two-dimensional lateral superlattice are studied in the framework of quasiclassical transport theory. It is assumed that the impurity scattering is of small-angle nature characteristic for currently fabricated high-mobility heterostructures. The shape of the modulation-induced magnetoresistivity $\ensuremath{\Delta}{\ensuremath{\rho}}_{\mathrm{xx}}$ depends on the value of the parameter $\ensuremath{\gamma}\ensuremath{\equiv}{\ensuremath{\eta}}^{2}ql/4,$ where \ensuremath{\eta} and q are the strength and the wave vector of the modulation, and l is the transport mean free path. For $\ensuremath{\gamma}\ensuremath{\ll}1,$ the oscillations are described, in the regime of not too strong magnetic fields B, by perturbation theory in $\ensuremath{\eta}$ as applied earlier to the case of one-dimensional modulation. At stronger fields, where $\ensuremath{\Delta}{\ensuremath{\rho}}_{\mathrm{xx}}$ becomes much larger than the Drude resistivity, the transport takes the advection-diffusion form (Rayleigh-B\'enard convection cell) with a large P\'eclet number, implying a much slower $(\ensuremath{\propto}{B}^{3/4})$ increase of the oscillation amplitude with B. If $\ensuremath{\gamma}\ensuremath{\gg}1,$ the transport at low B is dominated by the modulation-induced chaos (rather than by disorder). The magnetoresistivity drops exponentially and the commensurability oscillations start to develop at the magnetic fields where the motion takes the form of the adiabatic drift. Conditions of applicability, the role of the type of disorder, and the feasibility of experimental observation are discussed.

An analytical study of the low-field magnetoresistance of a two-dimensional electron gas subject to a weak periodic modulation is presented. We assume small-angle impurity scattering characteristic for high-mobility semiconductor heterostructures. It is shown that the condition for existence of the strong low-field magnetoresistance induced by so-called channeled orbits is $\eta^{3/2}ql\gg 1$, where $\eta$ and $q$ are the strength and the wave vector of the modulation, and $l$ is the transport mean free path. Under this condition, the magnetoresistance scales as $\eta^{7/2}$., Comment: 8 pages, 3 figures included

The nature and the relaxation properties of the localized electronic states responsible for the radiative recombination in the ensemble of self-organized CdSe/ZnSe quantum dots (QDs) are studied and discussed. It has been found that due to the complicated topological relief of the localizing potential in the lateral plane of the QDs, both ground and metastable states of dots contribute to the emission at helium temperatures. The metastable states are subjected to further energy relaxation, with the rate being dependent on the temperature. The temperature dependence of the relaxation rate is responsible for the anomalous temperature shift of the luminescence band maximum. By the study of polarization properties of the emission at resonant excitation by linearly or circularly polarized light we have shown that, in the samples studied, the photoluminescence (PL) of quantum dots arises due to the radiative recombination of both excitons and trions formed in the charged dots. The exciton emission comes mostly from the metastable states responsible for the high-energy part of the PL band, whereas the trion emission corresponds to the ground states of the quantum dots and forms the low-energy wing of the PL band. The main attention is given to the theoretical and experimental study of the spin-relaxation processes of the electronic states in QDs. We have demonstrated that the broadening of localized electronic levels caused by multi-phonon processes strongly influences the spin relaxation. Such broadening removes the limitations on the energy of phonons assisting the one-phonon transitions between spin sublevels. Taking into account the multi-phonon broadening of spin sublevels we were able to describe theoretically the temperature dependence of the polarization degree of PL spectra of CdSe/ZnSe quantum dots and to restore from experimental data the characteristic function, describing the interaction of localized electronic states with phonons.

Intrinsic birefringence in single crystals of CuBr has been measured in the vicinity of the absorption edge at 300 K. The strong enhancement of the birefringence in the direction \(\vec q\) //[110] near the gap is caused by the spatial dispersion of the dielectric function. An attempt is made to deduce band-parameters from the experimental data.