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A semiconductor microcavity is an optical resonator, where the mirrors consist of alternating layers of two different semiconductors with different refractive indices, e.g., GaAs and AlAs, which have thicknesses of a quarter wavelength each. The resonator itself is called spacer, and has a thickness of a few half wavelengths. The electric fields of the light waves, and hence the light-matter interaction can be modified significantly inside a microcavity. In the past decades, a number of sophisticated experiments have been reported that took advantage of the strongly enhanced electric field inside the spacer of a planar semiconductor microcavity. A prominent example is the enhanced exciton-photon coupling, resulting in an enlarged Rabi splitting, in planar microcavities containing undoped quantum wells [1]. Subsequently, a wealth of theoretical and experimental work on exciton polaritons in semiconductor microcavities, e.g., about the influence of a magnetic field [2], or coupling between different microcavities [3], followed. [ABSTRACT FROM AUTHOR]

The plasmon spectrum of spatially separated two-component plasmas without tunneling has been studied for quite some time (see, e.g., [1]). For finite Coulomb coupling between the layers, the intrasubband charge-density excitation spectrum consists of two modes: The optical plasmon (OP) where both layers oscillate in phase parallel to the layers (see Fig. 7.1a), and, the acoustic plasmon (AP) where the carriers in both layers oscillate out of phase (see Fig. 7.1b). At long wavelengths, the energy of the OP is proportional to √q and the energy of the AP goes linear in q, where q is the wave vector parallel to the layers. It was shown [1] that at large spatial separation of the two layers, the AP can move outside of the continua of possible intraband single-particle transitions. The first experimental observation of coupled- layer plasmons by inelastic light scattering was reported by Fasol et al. [2] on GaAs-AlGaAs samples containing five layers in parallel. In Coulomb-coupled double quantum wells, the observation of AP and OP was reported by Kainth et al. [3]. [ABSTRACT FROM AUTHOR]

In 1989, the first inelastic light scattering experiments on electronic excitations in quantum wires were reported [1, 2]. Since then, a number of experimental papers appeared about, e.g., many-particle interactions and selection rules in those systems [3, 4, 5, 6, 7, 8, 9] and investigations with applied external magnetic field [10, 11, 12]. All these experiments were performed on lithographically-defined GaAs-AlGaAs structures. Consequently, the lateral sizes of these structures were on the order of 100 nm, or at least not much below [8, 9]. Unlike for the case of quantum dots, there is no well- established method of self-organized growth of modulation-doped quantum wires. During the past few years, Carbon nanotubes have evolved as new and alternative quantum-wire structures. So far, the main focus in the investigation of those very promising quantum structures by optical experiments has been on phonon excitations [13]. Phonon Raman spectroscopy has greatly helped in unveiling the topological structure of Carbon nanotubes [13]. An interesting further method to produce very narrow wires with atomic-layer precision is the so called cleaved-etched overgrowth (CEO) [14]. However, with CEO it is difficult to grow very large arrays of wires, which would be necessary to get enough signal strength in inelastic light scattering experiments. Hence, there are so far no reports of inelastic light scattering experiments on CEO wires, though these might be promising structures for high-sensitivity experiments. As mentioned, most of the existing experimental reports are on lithographically-defined GaAs-AlGaAs quantum wires with rather mesoscopic widths. Hence, in those experimental structures, typically several Q1D subbands are occupied with electrons. In this chapter we will discuss both, experiments and calculations on such samples. The main focus will be on the microscopic origin of confined plasmons and interesting internal interaction effects in a magnetic field. These experimental results are described well within the RPA, i.e., a Fermi-liquid theory, as we will see later. [ABSTRACT FROM AUTHOR]

Semiconductor quantum dots are fascinating objects, since, in some respect, they can be regarded as artificial atoms [1]. Figure 5.1 shows a very schematic comparison of a real three-dimensional atom and a disc-shaped quantum dot. The structure of real atoms is three-dimensional, while most of the artificial quantum dots can be regarded as large Q2D atoms, since the lateral dimensions are in most cases much larger than the vertical extension. Of course, a crucial difference between the two systems is the shape of the confining potentials, which, for real atoms is essentially the Coulomb potential of the nucleus, and, for quantum-dot atoms in some approximation a two-dimensional parabolic potential. [ABSTRACT FROM AUTHOR]

Inelastic light scattering - or Raman scattering - is the scattering of light by a medium, where in the scattering process excitations are created (Stokes process) or annihilated (Antistokes process) within the medium. In solids, these excitations can be various types of elementary excitations, like phonons, magnons, or - as considered in this book - electronic excitations. Historically, the scattering by optical phonons, or by internal vibrations of molecules, is called Raman scattering, and the scattering by acoustic phonons Brillouin scattering. For electronic Raman scattering, often the term inelastic light scattering is used, so in this book. Figure 4.1 shows schematically the Stokes and Antistokes processes, where a photon with energy ħωI and momentum kI is scattered by the creation or annihilation of an elementary excitation with energy ħω and momentum q. The scattered photon has an energy ħωS and momentum ks. This means, each scattered photon in the Stokes component is associated with a gain in energy ħω by the sample. Similarly, the sample loses energy ħω for each scattered photon in the Antistokes component [ABSTRACT FROM AUTHOR]

In inelastic light scattering experiments on semiconductor nanostructures, electronic excitations are created or annihilated in the low -dimensional electron systems under investigation. Thus, the main body of this book will deal with the physics of those electronic elementary excitations in various systems and under various conditions. Before we elaborate on the basic concepts of the inelastic light scattering processes themselves in the following chapter, the electronic elementary excitations shall be introduced and discussed here. We will do this by the - most prominent - example of the excitations of Q2D electron systems, realized in modulation-doped GaAs-AlxGa1-xAs quantum wells. These excitations can be categorized into so called spin-density excitations (SDE) and charge-density excitations(CDE), which both are collective plasma oscillations of the Q2D system, and, single-particle excitations (SPE). In particular, the observation of intersubband SPE [1] - which are thought to be electronic excitations, which are not affected by the Coulomb interaction - has posed a puzzle, and has been controversially discussed. We will come to this discussion at various places later in this book, when considering the resonant scattering in quantum wells and in quantum dots. In particular in Chap. 5 we will see that - at least for quantum dots - the SPE's are actually collective excitations: SDE's and CDE's. However, the many-particle interaction effects partly cancel under specific conditions so that the energies are close to single-particle energies of a noninteracting system. Historically, in 1979, intersubband CDE and SDE in GaAs-AlGaAs quantum wells [2] and heterojunctions [3] were the first electronic excitations, which were observed in semiconductor nanostructures by inelastic light scattering by A. Pinczuk et al. and G. Abstreiter et al., respectively. [ABSTRACT FROM AUTHOR]

The majority of experiments of inelastic light scattering on semiconductor nanostructures has been performed on III-V semiconductors, like GaAs, as the most prominent example. In this chapter, an introduction into the basic properties of these materials is given. The first section gives a summary of the crystal and electronic band structure of the bulk material. After a short survey into the properties of electrons in different dimensions in the second section, growth methods for so called vertical nanostructures, i.e., layered heterostructures consisting of two different materials, are described in the third section. In these vertical nanostructures, quasi two-dimensional (Q2D) electron systems can be realized. This section is finalized by the description of commonly used concepts for theoretical calculations of the ground state of such systems. The second last section introduces the most important methods for the preparation of lateral micro and nanostructures. In those structures, the dimensionality of charge carriers or of quasi particles is reduced further by lithography and etching processes, or by self-organized growth methods, resulting in quasi one-dimensional (Q1D) or quasi zero-dimensional (Q0D) quantum structures. The section is finalized by an overview over methods for the calculation of the electronic ground state of lateral nanostructures. Readers who are already familiar with semiconductors and the fabrication and physics of nanostructures may skip this tutorial chapter and directly continue with Chap. 3. [ABSTRACT FROM AUTHOR]

Charge carriers in modulation-doped semiconductor quantum systems are a field of enormous and still growing research interest since they allow, in specially tailored systems, the investigation of fundamental properties, such as many-particle interactions, of electrons in reduced dimensions. Over the past decades, the experimental investigation of interacting electrons in low dimensions has led to many new and sometimes unexpected insights into many-particle physics in general. Famous examples are unique electronic transport properties as the integer and fractional quantum-Hall effects in quasi two-dimensional (Q2D) systems. Quasi one-dimensional (Q1D) electron systems, realized in semiconductor quantum wires, have been the subject of intense theoretical and experimental debates concerning the character - Fermi-liquid or Luttinger-liquid - of the interacting Q1D quantum liquid. During the past few years, tunneling-coupled electronic double-layer structures have been revisited as very interesting candidates for the realization of new quantum phases in an interacting many-particle system. A new quality came into the physics of semiconductor nanostructures by the development of quantum systems, embedded in microresonators, also called microcavities. This new inventions allowed one to investigate the light-matter interaction from an advanced point of view. [ABSTRACT FROM AUTHOR]

Electron transport through a quantum-dot in the Coulomb blockade regime is modeled by a Kondo-type hamiltonian describing spin-dependent tunneling and exchange interaction with the local spin. We consider the regime of large transport voltage V and magnetic field B with max(V, B) ≫ Tk, the Kondo temperature, and show that a renormalized perturbation theory can be formulated describing the local magnetization M and the differential conductance G quantitatively. Based on the structure of leading logarithmic corrections in bare perturbation theory we argue that the perturbative renormalization group has to be generalized to allow for frequency dependent coupling functions. We simplify the full RG equations in the spirit of poor man's scaling and calculate M and G in leading order of 1/ln[(V, B)/Tk]. [ABSTRACT FROM AUTHOR]

We outline a theoretical framework that allows qualitative as well as quantitative analysis of the optical properties of Photonic Crystals (PCs) derived from solid state theoretical concepts. Starting from advances in photonic band structure computations which we apply to structures containing dispersive components, we show how defect structures can be efficiently treated with the help of photonic Wannier functions. In addition, nonlinear PCs may be investigated by an appropriate multi-scale analysis utilizing Bloch waves as carrier waves together with an adaptation of k·p-perturbation theory. This leads to a natural generalization of the slowly varying envelope approximation to the case of nonlinear wave propagation in PCs. [ABSTRACT FROM AUTHOR]

Investigations of the physical and chemical properties of transition-metal oxides have a long history in solid-state and surface physics owing to the wide range of technical applications of these compounds. They have been used in lasers and catalysis for decades; their use in various sensors — e.g. for gases, high pressures, and magnetic fields — followed more recently. Not least a copper oxide is responsible for the occurrence of high-temperature superconductivity in various perovskites. For understanding and optimizing these applications, a detailed knowledge of the electronic structure of the bulk and also the surface of the transition-metal oxides is indispensable. [ABSTRACT FROM AUTHOR]

In this chapter, the results of our spin-polarized electron energy-loss measurements of the dipole-forbidden d-d excitations CoO, and NiO are presented and discussed. Measurements of some transitions across the optical gap and of some dipole-allowed and dipole-forbidden excitations from upper core levels are also included. Most of the results and conclusions presented here have already been published [50, 51, 52, 53, 54, 55, 56]. References to these publications are often omitted in this chapter for simplicity. [ABSTRACT FROM AUTHOR]

The setup of our SPEELS experiment is shown in Fig. 4.1. It is described in this section briefly; a more detailed description of some parts of the apparatus is given in the following sections. The numbers in parentheses in the text correspond to the numbers in Fig. 4.1. The significant experimental parameters, such as energy resolution, primary polarization, and scattering angle, are summarized in Table 4.1. [ABSTRACT FROM AUTHOR]

Electron energy-loss spectroscopy (EELS) is a widely used experimental technique for investigation of the excitation spectra of atoms, molecules, and solids. In this method, advantage is taken of the possibility of excitation by electron impact: incident electrons of fixed primary energy are inelastically scattered at the target, and the energy distribution of the scattered electrons is measured with respect to the incident electron energy. This energy distribution - the electron energy-loss spectrum - directly reflects the target excitations, because an excitation leads to the appearance of electrons in the scattered beam which have suffered a characteristic energy loss corresponding to the excitation energy. If other properties of the scattered electron beam (such as the angular distribution or polarization) are measured additionally (Sect. 3.2, 3.3), the kind of interaction between the incident electrons and the target that is responsible for the target excitation and the inelastic scattering process, can be inferred. [ABSTRACT FROM AUTHOR]

Investigations of the electronic structure of transition-metal oxides with incompletely filled 3d shells have a long history [15]. With the discovery of their insulating behavior, presented at a conference in Bristol in 1937 [27], they were among the first highly correlated systems found, where band theory fails to describe a wide range of physical properties. For the monoxides it is mainly the large size of the insulating gap and often the occurrence of a gap at all which cannot be explained adequately in one-particle band-structure formalisms such as the local-density approximation (LDA). Determined attempts have been made during the last sixty years to understand the origin of the insulating gaps, and it were the ingenious ideas of Peierls, Wilson, and Mott [137] at the Bristol conference and the later work of Mott [138] and Hubbard [81] which brought the problems closer to a solution. According to these ideas, which led to the development of the concepts of Mott-Hubbard and charge-transfer insulators later on, a strong Coulomb correlation between the d electrons is responsible for the insulating nature of the monoxides. Briefly, the d electrons remain localized at the metal ions, because their Coulomb correlation prevents them from forming an incompletely filled 3d band. They do not behave like a gas of easily movable electrons, because an energy of several electron volts is needed for the transport of electrons through the crystal lattice, and the conductivity is therefore very low. [ABSTRACT FROM AUTHOR]

Transition-metal oxides form a fascinating class of compounds with a wide range of technological applications. They are used in catalysis, lasers, and magnetic recording tapes, as well as in sensors for very high pressures and for gases, for example. New applications in magnetic-field sensors, based on the principle of giant magnetoresistance [67], and in transparent transistors, applicable as on-screen electronic devices in displays or cameras [165], were added recently. In addition, they are responsible for the occurrence of high-temperature superconductivity. [ABSTRACT FROM AUTHOR]

At the fundamental bandgap E0 we have for Q2D systems generally a mixing of heavy and light-hole states. In this case, the dipole matrix elements between a valence-band state ψhi,k∥ (r) and a conduction-band state ψcj,k∥ (r) is given by [ABSTRACT FROM AUTHOR]

In this chapter, Kronecker products corresponding to dipole matrix elements of Bloch functions of the Γ6 conduction-band edge and the Γ7 split-off valence-band edge are calculated. The corresponding band-edge Bloch functions are listed in Table 4.29 on page 71. The calculation shall be explained by the following example: [ABSTRACT FROM AUTHOR]