Optical gain and entanglement through dielectric confinement and electric field in InP quantum dots.

Quantum dots are widely recognized for their advantageous light-emitting properties. Their excitonic fine structure along with the high quantum yields offers a wide range of possibilities for technological applications. However, especially for the case of colloidal QDs, there are still characteristics and properties which are not adequately controlled and downgrade their performance for applications which go far beyond the simple light emission. Such a challenging task is the ability to manipulate the energetic ordering of exciton and biexciton emission and subsequently control phenomena such as Auger recombination, optical gain and photon entanglement. In the present work we attempt to engineer this ordering for the case of InP QDs embedded in polymer matrix, by means of their size, the dielectric confinement and external electric fields. We employ well tested, state of the art theoretical methods, in order to explore the conditions under which the exciton-biexciton configuration creates the desired conditions either for optical gain or photon entanglement. Indeed, this appears to be feasible for QDs with small diameters (1 nm, 1.5 nm) embedded in a host material with high dielectric constant and additional external electric fields. These findings offer a new design principle which might be complementary to the well-established type II core-shell QDs approach for achieving electron-hole separation.

Optical Properties of Conical Quantum Dot: Exciton-Related Raman Scattering, Interband Absorption and Photoluminescence.

The current work used the effective mass approximation conjoined with the finite element method to study the exciton states in a conical GaAs quantum dot. In particular, the dependence of the exciton energy on the geometrical parameters of a conical quantum dot has been studied. Once the one-particle eigenvalue equations have been solved, both for electrons and holes, the available information on energies and wave functions is used as input to calculate exciton energy and the effective band gap of the system. The lifetime of an exciton in a conical quantum dot has been estimated and shown to be in the range of nanoseconds. In addition, exciton-related Raman scattering, interband light absorption and photoluminescence in conical GaAs quantum dots have been calculated. It has been shown that with a decrease in the size of the quantum dot, the absorption peak has a blue shift, which is more pronounced for quantum dots of smaller sizes. Furthermore, the interband optical absorption and photoluminescence spectra have been revealed for different sizes of GaAs quantum dot.

Exciton States and Optical Absorption in CdSe and PbS Nanoplatelets.

The exciton states and their influence on the optical absorption spectrum of CdSe and PbS nanoplatelets (NPLs) are considered theoretically in this paper. The problem is discussed in cases of strong, intermediate, and weak size quantization regimes of charge carrier motion in NPLs. For each size quantization regime, the corresponding potential that adequately describes the electron-hole interaction in this mode of space quantization of charge carriers is chosen. The single-particle energy spectra and corresponding wave functions for strong intermediate and weak size quantization regimes have been revealed. The dependence of material parameters on the number of monolayers in the sample has been considered. The related selection rules and the dependence of the absorption coefficient on the frequency and polarization direction of the incident light wave were obtained. The interband transition threshold energy dependencies were obtained for each size quantization regime. The effect of dielectric coefficient mismatch and different models of electron-hole interaction potentials have been studied in CdSe and PbS NPLs. It is also shown that with an increase in the linear dimensions of the structure, the threshold frequency of absorption decreases. The binding energies and absorption coefficient results for NPL with different thicknesses agree with the experimental data. The values of the absorption exciton peaks measured experimentally are close to our calculated values for CdSe and PbS samples.

Non-Linear Optical Properties of Biexciton in Ellipsoidal Quantum Dot.

We have presented a theoretical investigation of exciton and biexciton states for the ground and excited levels in a strongly oblate ellipsoidal quantum dot made from GaAs. The variational trial wave functions for the ground and excited states of the exciton and biexciton are constructed on the base of one-particle wave functions. The energies for the ground and excited levels, depending on the ellipsoidal quantum dot's geometrical parameters, are depicted in the framework of the variational method. The oscillator strength of the transition from exciton to biexciton states for ground and excited levels is investigated as a function of the ellipsoidal quantum dot's small and large semiaxes. The third-order optical susceptibilities of ground and excited biexcitons around one-photon and two-photon resonances are calculated as a function of the photon energy. The dependences of third-order optical susceptibilities for the ground and excited levels on the photon energy for different values of the ellipsoidal quantum dot's semiaxis are revealed. The absorption coefficients in the ellipsoidal quantum dot, both for ground and excited states of exciton and biexciton, are calculated. The absorption coefficients for the ground level of exciton and biexciton for the fixed value of the large semiaxis and for the different values of the small semiaxis are determined. Finally, the two-photon absorption coefficient of the biexciton in the GaAs ellipsoidal quantum dot is computed.

Impurity effects on binding energy, diamagnetic susceptibility and photoionization cross-section of chalcopyrite AgInSe2nanotadpole.

Recently the interest in chalcopyrite semiconductor nanostructures has increased because of their non-toxicity and their wide direct bandgap. Likewise, structures with non-trivial geometry are particularly interesting because of their electronic, optical, and magnetic properties. In the current article, the finite element method was used in conjunction with the effective mass approximation to theoretically investigate the properties of a chalcopyrite AgInSe2nanotadpole in the presence of an hydrogen like shallow off-center impurity. The morphology of the nanotadpole gives it excellent hydrodynamic properties and is ideal for a wide range of applications. The probability densities for various impurity positions and energy levels were obtained. The results suggested a strong dependence of the behavior of the electron on the impurity positions and the orientation of the wave function. The investigation of the nanotadpole's energy spectra and their comparison with the cylindrical and spherical quantum dots suggest that the spectrum has degenerate states similar to the spherical case, however at some ranges, the levels behave similarly to the cylindrical case. The binding energy's dependence on the nanotadpole's size and the impurity position was obtained. The dependence of the diamagnetic susceptibility on the impurity position was calculated. An extensive investigation of the photoionization cross-section was carried out for the ground and the first two excited states as the initial states and the first twenty excited states as the final states.

Exciton-Related Raman Scattering, Interband Absorption and Photoluminescence in Colloidal CdSe/CdS Core/Shell Quantum Dots Ensemble.

By using the numerical discretization method within the effective-mass approximation, we have theoretically investigated the exciton-related Raman scattering, interband absorption and photoluminescence in colloidal CdSe/CdS core/shell quantum dots ensemble. The interband optical absorption and photoluminescence spectra have been revealed for CdSe/CdS quantum dots, taking into account the size dispersion of the ensemble. Numerical calculation of the differential cross section has been presented for the exciton-related Stokes-Raman scattering in CdSe/CdS quantum dots ensemble with different mean sizes.

Effects of an External Magnetic Field on the Interband and Intraband Optical Properties of an Asymmetric Biconvex Lens-Shaped Quantum Dot.

The theoretical investigation of interband and intraband transitions in an asymmetric biconvex lens-shaped quantum dot are considered in the presence of an external magnetic field. The selection rules for intraband transitions are obtained. The behaviors of linear and nonlinear absorption and photoluminescence spectra are observed for different temperatures and magnetic field strengths. The second and third harmonic generation coefficients as a function of the photon energy are examined both in the absence and presence of an external magnetic field.

Long-wave Absorption of Few-Hole Gas in Prolate Ellipsoidal Ge/Si Quantum Dot: Implementation of Analytically Solvable Moshinsky Model.

In this paper, the behavior of a heavy hole gas in a strongly prolate ellipsoidal Ge/Si quantum dot has been investigated. Due to the specific geometry of the quantum dot, the interaction between holes is considered one-dimensional. Based on the adiabatic approximation, it is shown that in the z-direction, hole gas is localized in a one-dimensional parabolic well. By modeling the potential of pair interaction between holes in the framework of oscillatory law, the problem is reduced to a one-dimensional, analytically solvable Moshinsky model. The exact energy spectrum of the few-hole gas has been calculated. A detailed analysis of the energy spectrum is presented. The character of long-wave transitions between the center-of-mass levels of the system has been obtained when Kohn theorem is realized.

Realization of the Kohn's Theorem in Ge/Si Quantum Dots with Hole Gas: Theory and Experiment.

This article discusses specific quantum transitions in a few-particle hole gas, localized in a strongly oblate lens-shaped quantum dot. Based on the adiabatic method, the possibility of realizing the generalized Kohn theorem in such a system is shown. The criteria for the implementation of this theorem in a lens-shaped quantum dot, fulfilled in the experiment, is presented. An analytical expression is obtained for the frequencies of resonant absorption of far-infrared radiation by a gas of heavy holes, which depends on the geometric parameters of the quantum dot. The results of experiments on far-infrared absorption in the arrays of p-doped Ge/Si quantum dots grown by molecular beam epitaxy (MBE) with gradually increasing average number of holes in dot are presented. Experimental results show that the Coulomb interaction between the holes does not affect the resonant frequency of the transitions. A good agreement between the theoretical and experimental results is shown.

Electronic States and light absorption in a cylindrical quantum dot having thin falciform cross section.

Energy level structure and direct light absorption in a cylindrical quantum dot (CQD), having thin falciform cross section, are studied within the framework of the adiabatic approximation. An analytical expression for the energy spectrum of the particle is obtained. For the one-dimensional "fast" subsystem, an oscillatory dependence of the wave function amplitude on the cross section parameters is revealed. For treatment of the "slow" subsystem, parabolic and modified Pöschl-Teller effective potentials are used. It is shown that the low-energy levels of the spectrum are equidistant. In the strong quantization regime, the absorption coefficient and edge frequencies are calculated. Selection rules for the corresponding quantum transitions are obtained.

Electron States and light absorption in strongly oblate and strongly prolate ellipsoidal quantum dots in presence of electrical and magnetic fields.

In framework of the adiabatic approximation the energy states of electron as well as direct light absorption are investigated in strongly oblate and strongly prolate ellipsoidal quantum dots (QDs) at presence of electric and magnetic fields. Analytical expressions for particle energy spectrum are obtained. The dependence of energy levels' configuration on QD geometrical parameters and field intensities is analytically obtained. The energy levels of electrons are shown to be equidistant both for strongly oblate and prolate QDs. The effect of the external fields on direct light absorption of a QD was investigated. The dependence of the absorption edge on geometrical parameters of QDs and intensities of the electric and magnetic fields is obtained. Selection rules are obtained at presence as well as absence of external electric and magnetic fields. In particular, it is shown that the presence of the electric field cancels the quantum numbers selection rules at the field direction, whereas in radial direction the selection rules are preserved. Perspectives of practical applications for device manufacturing based on ellipsoidal quantum dots are outlined.