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Quantum dots embedded in photonics nanostructures provide unprecedented control over the interaction between light and matter. This review gives an overview of the theoretical principles involved, as well as applications ranging from high-precision quantum electrodynamics experiments to quantum-information processing.

Interfacing single photons and single quantum dots with photonic nanostructures

The properties of quasi-two-dimensional semiconductor quantum dots are reviewed. Experimental techniques for measuring the electronic shell structure and the effect of magnetic fields are briefly described. The electronic structure is analyzed in terms of simple single-particle models, density-functional theory, and "exact" diagonalization methods. The spontaneous magnetization due to Hund's rule, spin-density wave states, and electron localization are addressed. As a function of the magnetic field, the electronic structure goes through several phases with qualitatively different properties. The formation of the so-called maximum-density droplet and its edge reconstruction is discussed, and the regime of strong magnetic fields in finite dot is examined. In addition, quasi-one-dimensional rings, deformed dots, and dot molecules are considered. (Less)

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Electronic structure of quantum dots

We review some electron transport experiments on few-electron, vertical quantum dot devices. The measurement of current versus source–drain voltage and gate voltage is used as a spectroscopic tool to investigate the energy characteristics of interacting electrons confined to a small region in a semiconducting material. Three energy scales are distinguished: the single-particle states, which are discrete due to the confinement involved; the direct Coulomb interaction between electron charges on the dot; and the exchange interaction between electrons with parallel spins. To disentangle these energies, a magnetic field is used to reorganize the occupation of electrons over the single-particle states and to induce changes in the spin states. We discuss the interactions between small numbers of electrons (between 1 and 20) using the simplest possible models. Nevertheless, these models consistently describe a large set of experiments. Some of the observations resemble similar phenomena in atomic physics, such as shell structure and periodic table characteristics, Hund’s rule, and spin singlet and triplet states. The experimental control, however, is much larger than for atoms: with one device all the artificial elements can be studied by adding electrons to the quantum dot when changing the gate voltage.

https://iopscience.iop.org/article/10.1088/0034-4885/64/6/201/pdf

Few-electron quantum dots

The electronic properties of graphene, a two-dimensional crystal of carbon atoms, are exceptionally novel. For instance, the low-energy quasiparticles in graphene behave as massless chiral Dirac fermions which has led to the experimental observation of many interesting effects similar to those predicted in the relativistic regime. Graphene also has immense potential to be a key ingredient of new devices, such as single molecule gas sensors, ballistic transistors and spintronic devices. Bilayer graphene, which consists of two stacked monolayers and where the quasiparticles are massive chiral fermions, has a quadratic low-energy band structure which generates very different scattering properties from those of the monolayer. It also presents the unique property that a tunable band gap can be opened and controlled easily by a top gate. These properties have made bilayer graphene a subject of intense interest. In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene f...

Properties of graphene: a theoretical perspective

New information on the electron-hole wave functions in InAs-GaAs self-assembled quantum dots is deduced from Stark effect spectroscopy. Most unexpectedly it is shown that the hole is localized towards the top of the dot, above the electron, an alignment that is inverted relative to the predictions of all recent calculations. We are able to obtain new information on the structure and composition of buried quantum dots from modeling of the data. We also demonstrate that the excited state transitions arise from lateral quantization and that tuning through the inhomogeneous distribution of dot energies can be achieved by variation of electric field.

https://epubs.surrey.ac.uk/2702/1/inverted_electron-hole_BARKER_00.pdf

Inverted Electron-Hole Alignment in InAs-GaAs Self-Assembled Quantum Dots

Elastic Reflection High Energy Electron Diffraction (RHEED) by solid surfaces is studied theoretically. First, the problem of finding the electron reflection and transmission coefficients of a crystal slab is formally solved. Following this, it is shown how the formal solution may be used in a practical computation of the diffracted beam intensities. These two results are applied to a study of high energy (20 keV) electron diffraction by the Ag(001) surface. Rocking curves are computed to illustrate the dependence of the reflection coefficients on the glancing angle of the incident beam, the incident beam azimuth being in the [110] direction. The curves are shown to have several features in common with a typical set of LEED I - V plots: primary Bragg peaks, secondary Bragg peaks and resonance peaks are all present. The dependence of the reflection coefficients on the deviation of the incident beam azimuth from the [110] direction is also described. Additional computations are made to illustrate the sensitivity of the RHEED pattern to the details of the surface structure: the relative heights of the peaks in the rocking curves are shown to be quite sensitive to the spacing of the topmost atomic layers.

A theory of rheed

The low-temperature magnetization of parabolic quantum dots is calculated and is shown to be a sensitive probe of interaction effects. The interaction causes the ground state to occur at certain magic values of the total angular momentum, the strength of the magnetic field determining which of them is selected. Increasing the mangetic field causes the ground-state angular momentum to jump from one magic value to another and this causes the discontinuities in the magnetization. The effects of spin lead to extra discontinuities at low magnetic field. The magic angular momenta for the spin-polarized case are derived by a simple physical argument.

Effect of electron-electron interactions on the magnetization of quantum dots.

Charged ${(X}^{*})$ and neutral (X) exciton recombination is reported in the photoluminescence spectra of single In(Ga)As quantum dots. Photoluminescence excitation (PLE) spectra show that the charged excitons are created only for excitation in the barrier or cladding layers of the structure, consistent with their charged character, whereas the neutral excitons in addition show well-defined excitation features for resonant excitation of the dots. The PLE spectra for X and ${X}^{*}$ exhibit a clear anticorrelation in the region of the wetting layer transition, showing that they compete for photocreated carriers.

Charged and neutral exciton complexes in individual self-assembled In(Ga)As quantum dots

A transformation to a moving frame (the Eckardt frame) is used to study the quantum states of interacting electrons in parabolic quantum dots in the presence of a perpendicular magnetic field. The approach is motivated by examining ground-state pair-correlation functions obtained by exact diagonalization. The main results concern the physical nature of the electron states and the origin of magic numbers. Some of the states are found to be localized about a single minimum of the potential energy. They have well-defined symmetry and are physically analogous to molecules. They are treated approximately by antisymmetrizing Eckardt frame rotational-vibrational states. This approach leads to selection rules that predict all the magic angular momentum and spin combinations found in previous numerical work. In addition, it enables the ground-state energy and low-lying excitations of the molecular states to be calculated to high accuracy. Analytic results for three electrons agree very well with the results of exact diagonalization. States that are not localized about a single minimum are also studied. They do not have distinct spatial symmetry and occur only when selection rules and conservation laws allow tunneling between states localized on different minima. These states appear to be small system precursors of fractional quantum Hall liquids. \textcopyright{} 1996 The American Physical Society.

P.A. Maksym

Papers

Inverted Electron-Hole Alignment in InAs-GaAs Self-Assembled Quantum Dots

A theory of rheed

Effect of electron-electron interactions on the magnetization of quantum dots.

Charged and neutral exciton complexes in individual self-assembled In(Ga)As quantum dots

Eckardt frame theory of interacting electrons in quantum dots