Selection rules for the excitation of quantum dots by spatially structured light beams -- Application to the reconstruction of higher excited exciton wave functions
M. Holtkemper, G. F. Quinteiro, D. E. Reiter, T. Kuhn
Spatially structured light fields applied to semiconductor quantum dots yield fundamentally different absorption spectra than homogeneous beams. In this paper, we theoretically discuss the resulting spectra for different light beams using a cylindrical multipole expansion. For the description of the quantum dots we employ a model based on the effective mass approximation including Coulomb and valence band mixing. The combination of a single spatially structured light beam and state mixing allows all exciton states in the quantum dot to become optically addressable. Furthermore, we demonstrate that the beams can be tailored such that single states are selectively excited, without the need of spectral separation. Using this selectivity, we propose a method to measure the exciton wave function of the quantum dot eigenstate. The measurement goes beyond electron density measurements by revealing the spatial phase information of the exciton wave function. Thereby polarization sensitive measurements are generalized by including the infinitely large spatial degree of freedom.
Dielectric screening is greatly important to an accurate calculation of the exciton binding energies in two-dimensional materials. In this work, we calculate the dielectric function and 2D polarizability of multilayer (up to three) phosphorene sheets using Density Functional Theory. The 2D polarizabilities are then used in the dielectric screening of the excitonic interaction in multilayer phosphorene quantum dots. In the limit of large quantum dots, excitonic gaps are shown to exhibit very good agreement with state-of-the-art measurements of the optical gaps of multilayer phosphorene sheets d…
With the ever-growing interest in quantum computing, understanding the behaviour of excitons in monolayer quantum dots has become a topic of great relevance. In this paper, we consider a Wannier exciton confined in a triangular quantum dot of hexagonal Boron Nitride. We begin by outlining the adequate basis functions to describe a particle in a triangular enclosure, analyzing their degeneracy and symmetries. Afterwards, we discuss the excitonic hamiltonian inside the quantum dot and study the influence of the quantum dot dimensions on the excitonic states.
Excitons in alloyed nanowire quantum dots have unique spectra as shown here using atomistic calculations. The bright exciton splitting is triggered solely by alloying and despite cylindrical quantum dot shape reaches over $15~μ$eV, contrary to previous theoretical predictions, however, in line with experimental data. This splitting can however be tuned by electric field to go below $1$~$μ$eV threshold. The dark exciton optical activity is also strongly affected by alloying reaching notable $1/3500$ fraction of the bright exciton and having large out-of-plane polarized component.
We study the effect of Coulomb correlation on the emission properties of the ground state exciton in zincblende CdSe/ZnS core-shell and in wurtzite ZnO quantum dots. We validate our theory model by comparing results of computed exciton energies of CdSe/ZnS quantum dots to photoluminescence and scanning near-field optical microscopy measurements. We use that to estimate the diameter of the quantum dots using a simple model based on infinitely deep quantum well and compare the results with the statistics of the atomic force microscopy scans of CdSe/ZnS dots, obtaining excellent agreement. Therea…
We use an atomistic model to consider the effect of shape symmetry breaking on the optical properties of self-assembled InAs/GaAs quantum dots. In particular, we investigate the energy level structure and optical activity of the lowest energy excitons in these nanostructures. We compare between quantum dots with two-fold rotational and two reflections (C2v) symmetry and quantum dots in which this symmetry was reduced to one reflection only (Cs) by introducing a facet between the quantum dots and the host material. We show that the symmetry reduction mostly affects the optical activity of the d…
We present numerical investigations based on the Luttinger-Kohn four-band $k \cdot p$ theory and, accordingly, establish a quantitatively valid model of the excitonic fine structures of droplet epitaxial GaAs/AlGaAs quantum dots under uni-axial stress control. In the formalisms, stressing a photo-excited quantum dot is equivalent creating a pseudo-magnetic field that is directly coupled to the pseudo-spin of the exciton doublet and tunable to tailor the polarized fine structure of exciton. The latter feature is associated with the valence-band-mixing of exciton that is especially sensitive to …
So far in the literature the terms "charged exciton" and "trion" are often confused with each other and mostly considered as the same. In this work we show this is not the case in 2D quantum dots with a parabolic confinement. By using the unrestricted Hartree-Fock method the energy and binding energy of both charged excitons and trions in 2D parabolic quantum dots are calculated in dependence on the confinements of charge carriers in quantum dot. It is shown that the binding energies of the charged exciton and the trion behave differently in regard to the ratios of the confinements between the…
Within the Floquet theory of periodically driven quantum systems, we demonstrate that a high-frequency electromagnetic field can be used as an effective tool to control excitonic properties of semiconductor quantum dots (QDs). It is shown, particularly, that the field both decreases the exciton binding energy and dynamically stabilizes the exciton, increasing its radiative lifetime. The developed theory can serve as a basis for the ultrafast method to tune spectral characteristics of the QD-based photon emitters by a high-frequency field.
We propose the concept of valley coherence and superradiance in the reciprocal space and show that it leads to an $N$-fold decrease of the bright exciton radiative lifetime in quantum dots (QDs) of an $N$-valley semiconductor. Next we explain why, despite this, the exciton radiative lifetimes in PbX (X = S, Se, Te) QDs, measured from the photoluminescence decay, are in the microsecond range. We also address peculiarities of the light-matter interaction in nanostructures made of narrow-gap materials with strong inter-band coupling.
Quantum dots are arguably one of the best platforms for optically accessible spin based qubits. The paramount demand of extended qubit storage time can be met by using quantum-dot-confined dark exciton: a longlived electron-hole pair with parallel spins. Despite its name the dark exciton reveals weak luminescence that can be directly measured. The origins of this optical activity remain largely unexplored. In this work, using the atomistic tight-binding method combined with configuration-interaction approach, we demonstrate that atomic-scale randomness strongly affects oscillator strength of d…
Excitonic fine structure splitting in quantum dots is closely related to the lateral shape of the wave functions. We have studied theoretically the fine structure splitting in InAs quantum dots with a type-II confinement imposed by a GaAsSb capping layer. We show that very small values of the fine structure splitting comparable with the natural linewidth of the excitonic transitions are achievable for realistic quantum dot morphologies despite the structural elongation and the piezoelectric field. For example, varying the capping layer thickness allows for a fine tuning of the splitting energy…
We theoretically model the electronic dynamics of a coupled quantum dot pair in a static electric field. We then investigate the possibility of polarization-entangled photon emission from the radiative cascade of the molecular biexciton state. Through numerical simulations, we analyze the dependence of entanglement fidelity on temperature and electric field, as well as tunnel coupling. We establish a regime of direct-indirect exciton detunings for which coupled quantum dots are superior to single dots for entangled photon generation, yielding near-unit fidelity over a larger range of exchange …
We study the dynamics of excitons in GaAs/(Al,Ga)As core-shell nanowires by continuous-wave and time-resolved photoluminescence and photoluminescence excitation spectroscopy. Strong Al segregation in the shell of the nanowires leads to the formation of Ga-rich inclusions acting as quantum dots. At 10 K, intense light emission associated with these shell quantum dots is observed. The average radiative lifetime of excitons confined in the shell quantum dots is 1.7 ns. We show that excitons may tunnel toward adjacent shell quantum dots and nonradiative point defects. We investigate the changes in…
Single and multi-band (Burt-Foreman) k.p Hamiltonians for GaAs crystal phase quantum dots are developed and used to assess ongoing experimental activity on the role of such factors as quantum confinement, spontaneous polarization, valence band mixing and exciton Coulomb interaction. Spontaneous polarization is found to be a dominating term. Together with the control of dot thickness [Vainorious Nano Lett. 15, 2652 (2015)] it enables wide exciton wavelength and lifetime tunability. Several new phenomena are predicted for small diameter dots [Loitsch et al. Adv. Mater. 27, 2195 (2015)], includin…
We propose correlated yet extremely simple single-parameter-dependent wave-functions with a Slater-type correlation factor, to describe excitons in 0D, quasi-1D and quasi-2D semiconductor quantum dots. We provide closed-form formulas for the wave-function normalization factor, electron/hole single-particle density and the expectation value of the kinetic energy. We additionally supply fast integration procedures for the Coulomb interaction in the presence of dielectric mismatch with the surrounding medium for nanoplatelets (quasi-2D systems), and for the bare-Coulomb integral in long nanorods …
Multiple exciton generation is a process in which more than one electron hole pair is generated per absorbed photon. It allows us to increase the efficiency of solar energy harvesting. Experimental studies have shown the multiple exciton generation yield of 1.2 in isolated colloidal quantum dots. However real photoelectric devices require the extraction of electron hole pairs to electric contacts. We provide a systematic study of the corresponding quantum coherent processes including extraction and injection and show that a proper design of extraction and injection rates enhances the yield sig…
The structure of the ground state exciton of Cd(Se,Te) quantum dots embedded in ZnTe matrix is studied experimentally using photoluminescence spectroscopy and theoretically using ${\bf k}\cdot{\bf p}$ and configuration interaction methods. The experiments reveal a considerable reduction of fine-structure splitting energy of the exciton with increase of Se content in the dots. That effect is interpreted by theoretical calculations to originate due to the transition from spatially direct (type-I) to indirect (type-II) transition between electrons and holes in the dot induced by increase of Se. T…
We study the exciton dynamics in an optically excited nanocrystal quantum dot. Multiple exciton formation is more efficient in nanocrystal quantum dots compared to bulk semiconductors due to enhanced Coulomb interactions and the absence of conservation of momentum. The formation of multiple excitons is dependent on different excitation parameters and the dissipation. We study this process within a Lindblad quantum rate equation using the full many-particle states. We optically excite the system by creating a single high energy exciton $E_{SX}$ in resonance to a double exciton $E_{DX}$. With Co…
The exciton recombination and spin dynamics in (In,Al)As/AlAs quantum dots (QDs) with indirect band gap and type-I band alignment are studied. The negligible (less than $0.2~μ$eV) value of the anisotropic exchange interaction in these QDs prevents a mixing of the excitonic basis states with pure spin and allows for the formation of spin polarized bright excitons for quasi-resonant circularly polarized excitation. In a longitudinal magnetic field, the recombination and spin dynamics of the excitons are controlled by the hyperfine interaction between the electron and nuclear spins. A QD blockade…
In this work we study theoretically and experimentally the multi-particle structure of the so-called type-II quantum dots with spatially separated electrons and holes. Our calculations based on customarily developed full configuration interaction approach reveal that exciton complexes containing holes interacting with two or more electrons exhibit fairly large antibinding energies. This effect is found to be the hallmark of the type-II confinement. In addition, an approximate self-consistent solution of the multi-exciton problem allows us to explain two pronounced phenomena: the blue-shift of …
