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TitleElectric and Magnetic Interaction between Quantum Dots and Light
LanguageEnglish
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Total Pages178
Table of Contents
                            Preface
Abstract
Resumé
List of publications
Introduction
Fundamental Properties of Semiconductor Quantum Dots
	Quantum mechanics of semiconductors
		From a huge multi-body system to a single-particle problem
		Band structure of III-V semiconductors
	Basic structural, electronic and optical properties of quantum dots
		Electronic models of quantum dots. Effective-mass theory
		Strain
		Excitons. Weak- and strong-confinement regimes
		Heavy-hole excitons
		Light-hole excitons
	Density of states of confined systems
	The electromagnetic quantum-vacuum field
	Fundamental light-matter interaction with quantum dots
		Spontaneous emission
		The dipole approximation
		Decay dynamics of quantum dots
	Summary
Single-Photon Dicke Superradiance from a Quantum Dot
	Theory of single-photon superradiance from quantum dots
		Strong-confinement regime
		Weak-confinement regime
		Relation between the giant oscillator strength of quantum dots and single-photon Dicke superradiance
	Sample and experimental setup
	Deterministic preparation of superradiant excitons
	Previous work on the giant oscillator strength of quantum dots
	Extracting the impact of nonradiative processes
	Experimental demonstration of single-photon superradiance
	Microscopic insight into the exciton wavefunction
	Results on all measured quantum dots
	Summary
Decay dynamics and Exciton Localization in Large GaAs Quantum Dots Grown by Droplet Epitaxy
	Sample growth and experimental procedure
	Spectral measurements
	Oscillator strength and quantum efficiency
	Temperature dependence of the effective transition strength
	Acoustic-phonon broadening and exciton size
	Summary
Multipolar Theory of Spontaneous Emission from Quantum Dots
	Multipole expansion
		Zeroth order: electric-dipole moment
		First order: electric-quadrupole and magnetic-dipole moments
		Second-order: electric-octupole and magnetic-quadrupole moments
		Summary of the multipole transition moments
	Origin dependence of the multipole transition moments
	Radiative decay rate
	Green's Tensor and derivatives in the vicinity of an Interface
		Homogeneous part of the Green tensor
		Scattering part of the Green tensor
	Origin (in)dependence of the radiative decay rate
		Spontaneous decay in a homogeneous medium
		Spontaneous decay in an arbitrary environment
	Decay dynamics of In(Ga)As quantum dots in the vicinity of an interface
		Zeroth-order contribution
		First-order contribution
		Second-order contribution
	Summary
Unraveling the Mesoscopic Character of Quantum Dots in Nanophotonics
	Microscopic model for mesoscopic quantum dots
	The quantum-mechanical current density
	Breakdown of the dipole theory at nanoscale proximity to a dielectric interface
	Lattice-distortion effects beyond the multipolar theory
	Summary
Probing Electric and Magnetic Vacuum Fluctuations with Quantum Dots
	Electric and magnetic light-matter interaction
	Probing the parity symmetry of nanophotonic environments
	Summary
Conclusion & Outlook
Appendices
Operator Matrices for the Theory of Invariants
Length and Velocity Representation
Evaluation of the First-Order Mesoscopic Moment zx
Evaluation of the Second-Order Mesoscopic Moment zzx
The Unit-Cell Dipole Approximation
Quantum Dots as Building Blocks for Quantum Metamaterials
	Polarizability of split-ring resonators
	Polarizability of quantum dots
	Quantum metamaterial with quantum dots
Bibliography
                        
Document Text Contents
Page 1

Electric and Magnetic Interaction

between Quantum Dots and Light

A dissertation

submitted to the Niels Bohr Institute

at the University of Copenhagen

in partial ful�llment of the requirements

for the degree of

philosophiae doctor

Petru Tighineanu

February 12, 2015

Page 89

Acoustic-phonon broadening and exciton size

σe,ρ (nm) σg,ρ (nm) f

QD A 2.4 2.4 16.6

QD C 3.6 1.9 9.4

Table 4.2: Fitted sizes (HWHM) of the electron and hole wavefunctions and the resulting oscil-

lator strength f .

Φ(t) = C

∞∫
0

kdk

1∫
0

dy

∣∣∣∣Dee−σ2e4 k2(1−ξey2) −Dge−σ2g4 k2(1−ξgy2)
∣∣∣∣2

× [i sin(ωkt) + [1− cos(ωkt)] (2nk + 1)] ,

(4.15)

where C = 1/4π2dc3s~ and ξν = 1− σ2ν,z/σ2ν,ρ. The integration over y is performed analytically,
and the integral over k is evaluated numerically. Finally, the emission spectrum is evaluated by

Fourier transforming the phonon-contribution function [155]

S(ω) =

+∞∫
−∞

dte−i(ω−ω0−iΓrad/2)te−Φ(t), (4.16)

where ω0 is the emission frequency of the QD.

We �t the acquired spectra with the independent-boson model using a least-square approach

so that the sum of the squared residuals is minimized. Following the observations from AFM

measurements, we �x the ratio between the wavefunction height and radius σν,ρ = ασν,z with α =

3. This assumption is needed to avoid over�tting the data. We thus have only two independent

�tting parameters, namely the size of the hole and electron wavefunctions. For QD C, the

spectrum is �tted at the highest recorded temperature (40 K) because the signal coming from the

phonon sidebands increases with temperature and enhances the accuracy of the �tted parameters.

For QD A, the �tting is performed at 30 K because at higher temperatures there is an additional

line in the vicinity of the exciton line, see Fig. 4.5(a), which renders the �t di�cult to realize. For

the data at lower temperatures we do not �t but simply plot the evaluated emission spectrum.

Figure 4.7 shows the spectra of QDs A and C with very good agreement between theory and

experiment. The extracted sizes (HWHM of 2�4 nm) are well below the exciton Bohr radius

(11.2 nm). This independent analysis therefore con�rms the observations from time-resolved

measurements, namely that ground-state excitons are strongly con�ned in droplet-epitaxy QDs.

We can give an estimate of the oscillator strength using Eq. (4.4), which agrees reasonably well

with experiment, compare Tables 4.1 and 4.2.

71

Page 90

Chapter 4. Decay dynamics and Exciton Localization in Large GaAs Quantum Dots Grown by Droplet

Epitaxy

4.6 Summary

In this chapter we have presented an extensive study of the optical properties and decay dy-

namics of large strain-free droplet-epitaxy GaAs QDs. From the measurements, we draw several

important conclusions:

(1) The droplet-epitaxy QDs exhibit an oscillator strength and quantum e�ciency of about

9 and 75 %, respectively.

(2) Ground-state excitons are strongly con�ned despite the large size of the droplet-epitaxy

QDs observed in AFM measurements. This is caused by material inter-di�usion occurring be-

tween the QDs and the surrounding matrix, which creates a localized potential minimum that

traps carriers in a region of space smaller than the exciton Bohr radius. This physical picture

is supported by two independent analyses: the oscillator strength extracted from time-resolved

measurements, and the sizes of electron and hole wavefunctions obtained from the analysis of

the spectral phonon sidebands.

(3) For some QDs, the bright exciton is thermally activated to parity-dark eigenstates with

temperature. As a consequence, the radiative lifetime of bright excitons is substantially prolonged

and the e�ective transition strength decreases from 10 to 4 as the temperature is raised from

10 K to 40 K. Additionally, the nonradiative recombination rate is increased by almost a factor

of two in the same temperature range. Both a�ect the quantum e�ciency, which attains a value

of only 40 % at 40 K.

Our �ndings show that droplet-epitaxy GaAs QDs, similarly to the commonly used self-

assembled In(Ga)As QDs, exhibit non-negligible nonradiative processes. This is likely due to the

low-temperature growth of the QDs and of the capping layer forming a crystalline structure of

low quality, which is not fully restored by thermal annealing. Although we have not found a giant

oscillator strength in these QDs, we believe that better growth techniques have the capability of

improving this aspect owing to the lack of strain in these structures.

Finally, we mention that the general conclusion that the actual exciton size can be signi�cantly

smaller than the QD size has also been reached for other material systems. By analyzing phonon-

broadened spectra, Rol et al. [127] found that the excitons con�ned in GaN/AlN QDs are much

smaller than the spatial extent of the QD. Stobbe et al. [106] extracted a small oscillator strength

of large In(Ga)As QDs of about 10 by controllably modifying the LDOS at the position of the

emitter. The latter work points to the same physical situation, namely that the induced material

inhomogeneities during growth create a non-uniform potential pro�le, which strongly con�nes

excitons. Engineering large QDs with large excitons and giant oscillator strength represents a

future challenge for the droplet-epitaxy growth technique.

72

Page 177

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159

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