Current research into semiconductor clusters is focused on the properties of quantum dots-fragments of semiconductor consisting of hundreds to many thousands of atoms-with the bulk bonding geometry and with surface states eliminated by enclosure in a material that has a larger band gap. Quantum dots exhibit strongly size-dependent optical and electrical properties. The ability to join the dots into complex assemblies creates many opportunities for scientific discovery.

Semiconductor Clusters, Nanocrystals, and Quantum Dots

This paper reviews recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near-Feshbach resonances in the BCS-BEC crossover.

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Many-Body Physics with Ultracold Gases

We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

Semiconductor nanocrystals exhibit a wide range of size-dependent properties. Variations in fundamental characteristics ranging from phase transitions to electrical conductivity can be induced by controlling the size of the crystals. The present status and new opportunities for research in this area of materials physical chemistry are reviewed.

Perspectives on the Physical Chemistry of Semiconductor Nanocrystals

The last decade witnessed significant progress in angle-resolved photoemission spectroscopy (ARPES) and its applications. Today, ARPES experiments with 2-meV energy resolution and $0.2\ifmmode^\circ\else\textdegree\fi{}$ angular resolution are a reality even for photoemission on solids. These technological advances and the improved sample quality have enabled ARPES to emerge as a leading tool in the investigation of the high-${T}_{c}$ superconductors. This paper reviews the most recent ARPES results on the cuprate superconductors and their insulating parent and sister compounds, with the purpose of providing an updated summary of the extensive literature. The low-energy excitations are discussed with emphasis on some of the most relevant issues, such as the Fermi surface and remnant Fermi surface, the superconducting gap, the pseudogap and $d$-wave-like dispersion, evidence of electronic inhomogeneity and nanoscale phase separation, the emergence of coherent quasiparticles through the superconducting transition, and many-body effects in the one-particle spectral function due to the interaction of the charge with magnetic and/or lattice degrees of freedom. Given the dynamic nature of the field, we chose to focus mainly on reviewing the experimental data, as on the experimental side a general consensus has been reached, whereas interpretations and related theoretical models can vary significantly. The first part of the paper introduces photoemission spectroscopy in the context of strongly interacting systems, along with an update on the state-of-the-art instrumentation. The second part provides an overview of the scientific issues relevant to the investigation of the low-energy electronic structure by ARPES. The rest of the paper is devoted to the experimental results from the cuprates, and the discussion is organized along conceptual lines: normal-state electronic structure, interlayer interaction, superconducting gap, coherent superconducting peak, pseudogap, electron self-energy, and collective modes. Within each topic, ARPES data from the various copper oxides are presented.

https://arxiv.org/pdf/cond-mat/0208504.pdf

Angle-resolved photoemission studies of the cuprate superconductors

We consider a gas of fermions interacting via an attractive potential. We study the ground state of that system and calculate the critical temperature for the onset of superconductivity as a function of the coupling strength. We compare the behavior of continuum and lattice models and show that the evolution from weak to strong coupling superconductivity is smooth.

Bose condensation in an attractive fermion gas: From weak to strong coupling superconductivity

The universal anomalies in the normal state of Cu-O high-temperature superconductors follow from a single hypothesis: There exist charge- and spin-density excitations with the absorptive part of the polarizability at low frequencies \ensuremath{\omega} proportional to \ensuremath{\omega}/T, where T is the temperature, and constant otherwise. The behavior in such a situation may be characterized as that of a marginal Fermi liquid. The consequences of this hypothesis are worked out for a variety of physical properties including superconductivity.

https://link.aps.org/pdf/10.1103/PhysRevLett.63.1996

Phenomenology of the normal state of Cu-O high-temperature superconductors.

We analyze theoretically the optical properties of ideal semiconductor crystallites so small that they show quantum confinement in all three dimensions [quantum dots (QD's)]. In the limit of a QD much smaller than the bulk exciton size, the linear spectrum will be a series of lines, and we consider the phonon broadening of these lines. The lowest interband transition will saturate like a two-level system, without exchange and Coulomb screening. Depending on the broadening, the absorption and the changes in absorption and refractive index resulting from saturation can become very large, and the local-field effects can become so strong as to give optical bistability without external feedback. The small QD limit is more readily achieved with narrow-band-gap semiconductors.

Theory of the linear and nonlinear optical properties of semiconductor microcrystallites

In this article we review the experimental and theoretical investigations of the linear and nonlinear optical properties of semiconductor quantum well structures, including the effects of electrostatic fields, extrinsic carriers and real or virtual photocarriers.

S. Schmitt-Rink

Papers

Bose condensation in an attractive fermion gas: From weak to strong coupling superconductivity

Phenomenology of the normal state of Cu-O high-temperature superconductors.

Theory of the linear and nonlinear optical properties of semiconductor microcrystallites

Linear and nonlinear optical properties of semiconductor quantum wells

Theory of the linear and nonlinear optical properties of semiconductor microcrystallites