▪ Abstract Solution phase syntheses and size-selective separation methods to prepare semiconductor and metal nanocrystals, tunable in size from ∼1 to 20 nm and monodisperse to ≤5%, are presented. Preparation of monodisperse samples enables systematic characterization of the structural, electronic, and optical properties of materials as they evolve from molecular to bulk in the nanometer size range. Sample uniformity makes it possible to manipulate nanocrystals into close-packed, glassy, and ordered nanocrystal assemblies (superlattices, colloidal crystals, supercrystals). Rigorous structural characterization is critical to understanding the electronic and optical properties of both nanocrystals and their assemblies. At inter-particle separations 5–100 A, dipole-dipole interactions lead to energy transfer between neighboring nanocrystals, and electronic tunneling between proximal nanocrystals gives rise to dark and photoconductivity. At separations <5 A, exchange interactions cause otherwise insulating ass...

Synthesis and Characterization of Monodisperse Nanocrystals and Close-Packed Nanocrystal Assemblies

Random-matrix theories in quantum physics : common concepts

How localized electrons interact with delocalized electrons is a central question to many problems in sold-state physics1,2,3. The simplest manifestation of this situation is the Kondo effect, which occurs when an impurity atom with an unpaired electron is placed in a metal2. At low temperatures a spin singlet state is formed between the unpaired localized electron and delocalized electrons at the Fermi energy. Theories predict4,5,6,7 that a Kondo singlet should form in a single-electron transistor (SET), which contains a confined ‘droplet’ of electrons coupled by quantum-mechanical tunnelling to the delocalized electrons in the transistor's leads. If this is so, a SET could provide a means of investigating aspects of the Kondo effect under controlled circumstances that are not accessible in conventional systems: the number of electrons can be changed from odd to even, the difference in energy between the localized state and the Fermi level can be tuned, the coupling to the leads can be adjusted, voltage differences can be applied to reveal non-equilibrium Kondo phenomena7, and a single localized state can be studied rather than a statistical distribution. But for SETs fabricated previously, the binding energy of the spin singlet has been too small to observe Kondo phenomena. Ralph and Buhrman8 have observed the Kondo singlet at a single accidental impurity in a metal point contact, but with only two electrodes and without control over the structure they were not able to observe all of the features predicted. Here we report measurements on SETs smaller than those made previously, which exhibit all of the predicted aspects of the Kondo effect in such a system.

Kondo effect in a single-electron transistor

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.

Random Matrix Theories in Quantum Physics: Common Concepts

This article reviews recent theoretical and experimental advances in the fundamental understanding and active control of quantum fluids of light in nonlinear optical systems. In the presence of effective photon-photon interactions induced by the optical nonlinearity of the medium, a many-photon system can behave collectively as a quantum fluid with a number of novel features stemming from its intrinsically nonequilibrium nature. A rich variety of recently observed photon hydrodynamical effects is presented, from the superfluid flow around a defect at low speeds, to the appearance of a Mach-Cherenkov cone in a supersonic flow, to the hydrodynamic formation of topological excitations such as quantized vortices and dark solitons at the surface of large impenetrable obstacles. While the review is mostly focused on a specific class of semiconductor systems that have been extensively studied in recent years (planar semiconductor microcavities in the strong light-matter coupling regime having cavity polaritons as elementary excitations), the very concept of quantum fluids of light applies to a broad spectrum of systems, ranging from bulk nonlinear crystals, to atomic clouds embedded in optical fibers and cavities, to photonic crystal cavities, to superconducting quantum circuits based on Josephson junctions. The conclusive part of the article is devoted to a review of the future perspectives in the direction of strongly correlated photon gases and of artificial gauge fields for photons. In particular, several mechanisms to obtain efficient photon blockade are presented, together with their application to the generation of novel quantum phases.

Quantum fluids of light

Unusual structure and large electric-field--induced oscillations have been observed in the current-voltage curves of small-area tunnel junctions arranged in a low-capacitance (\ensuremath{\lesssim}1 fF) multiple-junction configuration. This behavior arises from the tunneling of individual electrons charging and discharging the capacitance. The observations are in accord with what would be expected from a simple model of the charging energies and voltage fluctuations of e/C associated with such effects.

Observation of single-electron charging effects in small tunnel junctions.

We have measured the low-temperature magnetization response of ${10}^{7}$ isolated mesoscopic copper rings to a slowly varying magnetic flux. At sufficiently low temperature, the total magnetization response oscillates as a function of the enclosed magnetic flux on the scale of half of a flux quantum. The amplitude of the oscillatory moment is \ensuremath{\approxeq}1.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{Am}}^{2}$ and decreases exponentially with increasing temperature on the scale of the correlation energy ${\mathit{E}}_{\mathit{c}}$=hD/(2L${)}^{2}$\ensuremath{\approxeq}80 mK. This is evidence for a flux-periodic persistent current in each ring of average value 3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$e${\ensuremath{\nu}}_{\mathit{F}}$/L.

Magnetization of mesoscopic copper rings: Evidence for persistent currents.

The high-resolution Bitter pattern technique has been used to reveal the magnetic structure of single-crystal samples of high-${T}_{c}$ superconductor Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$ at 42 K Typical patterns consist of hexagonally correlated, singly quantized vortices of flux $\frac{\mathrm{hc}}{2e}$ That is, the structures are comparable to those that would be observed in conventional type-II superconductors under similar conditions

Observation of Hexagonally Correlated Flux Quanta In YBa2Cu3O7

Resistance measurements were made on high-resistivity thin-film metal strips at temperatures as low as 10 mK. Unexpected logarithmic variations of the resistance with temperature and applied electric field were observed for strips with sheet resistance below ${R}_{\ensuremath{\square}}\ensuremath{\sim}10$ k\ensuremath{\Omega}/\ensuremath{\square} and widths \ensuremath{\gtrsim} 1 \ensuremath{\mu}m. Exponential increases in resistance were observed for similar films when the film width was decreased to about 0.1 \ensuremath{\mu}m or when ${R}_{\ensuremath{\square}}$ was increased to \ensuremath{\sim} 10 k\ensuremath{\Omega}/\ensuremath{\square}.

Nonmetallic Conduction in Thin Metal Films at Low Temperatures

We have used complementary sets of normal and superconducting probes to study the nonequilibrium region near phase-slip centers in narrow superconducting strips. An exponentially decaying branch imbalance potential, ${\ensuremath{\mu}}_{Q}$, is observed and the decay length, the quasiparticle diffusion length, is measured directly and compared to the phase-slip resistance.

G. J. Dolan

Papers

Observation of single-electron charging effects in small tunnel junctions.

Magnetization of mesoscopic copper rings: Evidence for persistent currents.

Observation of Hexagonally Correlated Flux Quanta In YBa2Cu3O7

Nonmetallic Conduction in Thin Metal Films at Low Temperatures

Voltage Measurements within the Nonequilibrium Region near Phase-Slip Centers