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In this Mini Review, we summarize major corrections to the dark-bright exciton theory [ Efros et al. Phys. Rev B 1996 , 54 , 4843 - 4856 ], which should be used for quantitative description of the band edge exciton in II-VI and III-V compound quantum-dot nanocrystals (NCs). The theory previously did not take into account the long-range exchange interaction, resulting in the under-estimation of the splitting between the upper bright and lower dark or quasi-dark exciton, as reported by several experimental groups. Another type of correction originates from the closeness in energy of the ground, 1S 3/2 , and the first excited, 1P 3/2 , hole levels in a spherical NC, resulting in significant energetic overlap of the levels from the 1S 3/2 1S e and 1P 3/2 1S e exciton manifolds connected with the ground 1S e electron level. The thermal occupation of the optically forbidden 1P 3/2 1S e exciton levels changes the radiative decay time of the NCs at both helium and room temperatures. We demonstrate the role of both effects in CdSe NCs and compare our predictions with available experimental data.

Success in the projects aimed at providing an advanced understanding of the brain is directly predicated on making critical advances in nanotechnology. This Perspective addresses the unique interface of neuroscience and nanomaterials by considering the foundational problem of sensing neuron membrane voltage and offers a potential solution that may be facilitated by a prototypical nanomaterial. Despite substantial improvements, the visualization of instantaneous voltage changes within individual neurons, whether in cell culture or in vivo, at both the single-cell and network level at high speed remains complex and problematic. The unique properties of semiconductor quantum dots (QDs) have made them powerful fluorophores for bioimaging. What is not widely appreciated, however, is that QD photoluminescence is exquisitely sensitive to proximal electric fields. This property should be suitable for sensing voltage changes that occur in the active neuronal membrane. Here, we examine the potential role of QDs in addressing the important challenge of real-time optical voltage imaging.

Vibrations are important cues for tactile perception across species. Whisker-based sensation in mice is a powerful model system for investigating mechanisms of tactile perception. However, the role vibration plays in whisker-based sensation remains unsettled, in part due to difficulties in modeling the vibration of whiskers. Here, we develop an analytical approach to calculate the vibrations of whiskers striking objects. We use this approach to quantify vibration forces during active whisker touch at a range of locations along the whisker. The frequency and amplitude of vibrations evoked by contact are strongly dependent on the position of contact along the whisker. The magnitude of vibrational shear force and bending moment is comparable to quasi-static forces. The fundamental vibration frequencies are in a detectable range for mechanoreceptor properties and below the maximum spike rates of primary sensory afferents. These results suggest two dynamic cues exist that rodents can use for object localization: vibration frequency and comparison of vibrational to quasi-static force magnitude. These complement the use of quasi-static force angle as a distance cue, particularly for touches close to the follicle, where whiskers are stiff and force angles hardly change during touch. Our approach also provides a general solution to calculation of whisker vibrations in other sensing tasks.

Nanostructured semiconductors emit light from electronic states known as excitons. For organic materials, Hund's rules state that the lowest-energy exciton is a poorly emitting triplet state. For inorganic semiconductors, similar rules predict an analogue of this triplet state known as the 'dark exciton'. Because dark excitons release photons slowly, hindering emission from inorganic nanostructures, materials that disobey these rules have been sought. However, despite considerable experimental and theoretical efforts, no inorganic semiconductors have been identified in which the lowest exciton is bright. Here we show that the lowest exciton in caesium lead halide perovskites (CsPbX 3 , with X = Cl, Br or I) involves a highly emissive triplet state. We first use an effective-mass model and group theory to demonstrate the possibility of such a state existing, which can occur when the strong spin-orbit coupling in the conduction band of a perovskite is combined with the Rashba effect. We then apply our model to CsPbX 3 nanocrystals, and measure size- and composition-dependent fluorescence at the single-nanocrystal level. The bright triplet character of the lowest exciton explains the anomalous photon-emission rates of these materials, which emit about 20 and 1,000 times faster than any other semiconductor nanocrystal at room and cryogenic temperatures, respectively. The existence of this bright triplet exciton is further confirmed by analysis of the fine structure in low-temperature fluorescence spectra. For semiconductor nanocrystals, which are already used in lighting, lasers and displays, these excitons could lead to materials with brighter emission. More generally, our results provide criteria for identifying other semiconductors that exhibit bright excitons, with potential implications for optoelectronic devices.

Non-magnetic colloidal nanostructures can demonstrate magnetic properties typical for diluted magnetic semiconductors because the spins of dangling bonds at their surface can act as the localized spins of magnetic ions. Here we report the observation of dangling-bond magnetic polarons (DBMPs) in 2.8-nm diameter CdSe colloidal nanocrystals (NCs). The DBMP binding energy of 7 meV is measured from the spectral shift of the emission lines under selective laser excitation. The polaron formation at low temperatures occurs by optical orientation of the dangling-bond spins (DBSs) that result from dangling-bond-assisted radiative recombination of spin-forbidden dark excitons. Modelling of the temperature dependence of the DBMP-binding energy and emission intensity shows that the DBMP is composed of a dark exciton and about 60 DBSs. The exchange integral of one DBS with the electron confined in the NC is ∼0.12 meV.

We report the development of a quantum dot (QD)-peptide-fullerene (C 60 ) electron transfer (ET)-based nanobioconjugate for the visualization of membrane potential in living cells. The bioconjugate is composed of (1) a central QD electron donor, (2) a membrane-inserting peptidyl linker, and (3) a C 60 electron acceptor. The photoexcited QD donor engages in ET with the C 60 acceptor, resulting in quenching of QD photoluminescence (PL) that tracks positively with the number of C 60 moieties arrayed around the QD. The nature of the QD-capping ligand also modulates the quenching efficiency; a neutral ligand coating facilitates greater QD quenching than a negatively charged carboxylated ligand. Steady-state photophysical characterization confirms an ET-driven process between the donor-acceptor pair. When introduced to cells, the amphiphilic QD-peptide-C 60 bioconjugate labels the plasma membrane by insertion of the peptide-C 60 portion into the hydrophobic bilayer, while the hydrophilic QD sits on the exofacial side of the membrane. Depolarization of cellular membrane potential augments the ET process, which is manifested as further quenching of QD PL. We demonstrate in HeLa cells, PC12 cells, and primary cortical neurons significant QD PL quenching (ΔF/F 0 of 2-20% depending on the QD-C 60 separation distance) in response to membrane depolarization with KCl. Further, we show the ability to use the QD-peptide-C 60 probe in combination with conventional voltage-sensitive dyes (VSDs) for simultaneous two-channel imaging of membrane potential. In in vivo imaging of cortical electrical stimulation, the optical response of the optimal QD-peptide-C 60 configuration exhibits temporal responsivity to electrical stimulation similar to that of VSDs. Notably, however, the QD-peptide-C 60 construct displays 20- to 40-fold greater ΔF/F 0 than VSDs. The tractable nature of the QD-peptide-C 60 system offers the advantages of ease of assembly, large ΔF/F 0 , enhanced photostability, and high throughput without the need for complicated organic synthesis or genetic engineering, respectively, that is required of traditional VSDs and fluorescent protein constructs.

Semiconductor nanocrystals offer an enormous diversity of potential device applications, based on their size-tunable photoluminescence, high optical stability and 'bottom-up' chemical approaches to self-assembly. However, the promise of such applications can be seriously limited by photoluminescence intermittency in nanocrystal emission, that is, 'blinking', arising from the escape of either one or both of the photoexcited carriers to the nanocrystal surface. In the first scenario, the remaining nanocrystal charge quenches photoluminescence via non-radiative Auger recombination, whereas for the other, the exciton is thought to be intercepted before thermalization and does not contribute to the photoluminescence. This Review summarizes the current understanding of the mechanisms responsible for nanocrystal blinking kinetics as well as core-shell engineering efforts to control such phenomena. In particular, 'softening' of the core-shell confinement potential strongly suppresses non-radiative Auger processes in charged nanocrystals, with successful non-blinking implementations demonstrated in CdSe-CdS core-thick-shell nanocrystals and their modifications.

The intrinsic properties of quantum dots (QDs) and the growing ability to interface them controllably with living cells has far-reaching potential applications in probing cellular processes such as membrane action potential. We demonstrate that an electric field typical of those found in neuronal membranes results in suppression of the QD photoluminescence (PL) and, for the first time, that QD PL is able to track the action potential profile of a firing neuron with millisecond time resolution. This effect is shown to be connected with electric-field-driven QD ionization and consequent QD PL quenching, in contradiction with conventional wisdom that suppression of the QD PL is attributable to the quantum confined Stark effect.

We predict theoretically that nonmagnetic CdSe nanocrystals may possess macroscopic magnetic moments due to the formation of dangling-bond magnetic polarons (DBMPs). A DBMP is created in optically pumped nanocrystals by dynamic polarization of dangling bond spins (DBSs) at the nanocrystal surface during radiative recombination of the ground state "dark" exciton assisted by a spin-flip of the DBS. The formation of DBMPs suppresses the radiative recombination of the dark exciton and leads to a temperature-dependent contribution to the Stokes shift of the photoluminescence. This model consistently explains the experimentally observed low-temperature photoluminescence features of nonmagnetic CdSe nanocrystals as manifestations of their spin-related magnetic properties.

We calculate the rate of nonradiative Auger recombination in negatively charged CdSe nanocrystals (NCs). The rate is nonmonotonic, strongly oscillating with NC size, and sensitive to the NC surface. The oscillations result in nonexponential decay of carriers in NC ensembles. Using a standard single-exponential approximation of the decay dynamics, we determine the apparent size dependence of the Auger rate in an ensemble and derive CdSe surface parameters consistent with the experimental dependence on size.

The electronic structure of single InSb quantum dots (QDs) with diameters between 3 and 7 nm was investigated using atomic force microscopy (AFM) and scanning tunneling spectroscopy (STS). In this size regime, InSb QDs show strong quantum confinement effects which lead to discrete energy levels on both valence and conduction band states. Decrease of the QD size increases the measured band gap and the spacing between energy levels. Multiplets of equally spaced resonance peaks are observed in the tunneling spectra. There, multiplets originate from degeneracy lifting induced by QD charging. The tunneling spectra of InSb QDs are qualitatively different from those observed in the STS of other III-V materials, for example, InAs QDs, with similar band gap energy. Theoretical calculations suggest the electron tunneling occurs through the states connected with L-valley of InSb QDs rather than through states of the Γ-valley. This observation calls for better understanding of the role of indirect valleys in strongly quantum-confined III-V nanomaterials.

We report the synthesis and characterization of Pb-chalcogenide fused quantum-dot (QD) dimer structures. The resulting QD dimers range in length from 6 to 16 nm and are produced by oriented attachment of single QD monomers with diameters of 3.1-7.8 nm. QD monomers with diameters exceeding about 5 nm appear to have the greatest affinity for QD dimer formation and, therefore, gave the greatest yields of fused structures. We find a new absorption feature in the first exciton QD dimer spectra and assign this to a splitting of the 8-fold degenerate 1S-level. The dimer splitting increases from 50 to 140 meV with decrease of the QD-monomer size, and we present a mechanism that accounts for this splitting. We also demonstrate the possibility of fusing two QDs with different sizes into a heterostructure.

Solar energy production, one of the world's most important unsolved problems, has the potential to be a source of clean, renewable energy if scientists can find a way of generating cheap and efficient solar cells. Generation of multiple excitons from single photons is one way to increase the efficiency of solar energy collection, but the process suffers from low efficiency in bulk materials. An increase of multiexciton generation efficiency in nanocrystals was proposed by Nozik in 2002 and demonstrated by Schaller and Klimov in 2004 in PbSe nanocrystals. Since then, scientists have observed efficient multiexciton generation in nanostructures made of many semiconductors using various measurement techniques. Although the experimental evidence of efficient carrier multiplication is overwhelming, there is no complete theory of this phenomenon. Researchers cannot develop such a theory without a self-consistent description of the Coulomb interaction and a knowledge of mechanisms of electron and hole thermalization in nanostructures. The full theoretical description requires the strength of the Coulomb interaction between exciton and multiexciton states and the thermalization rates, which both vary with the dimensionality of the confining potential. As a result, the efficiency of multiexciton generation depends strongly on the material and the shape of the nanostructure. In this Account, we discuss the theoretical aspects of efficient carrier multiplication in nanostructures. The Coulomb interaction couples single excitons with multiexciton states. Phenomenological many-electron calculations of the evolution of single-photon excitations have shown that efficient multiexciton generation can exist only if the rate of the Coulomb mixing between photo-created exciton and biexciton states is significantly faster than the rate of exciton relaxation. Therefore, to increase multiexciton generation efficiency, we need to either increase the exciton-biexciton mixing rate or suppress the exciton relaxation rate. Following this simple recipe, we show that multiexciton generation efficiency should be higher in semiconductor nanorods and nanoplatelets, which have stronger exciton-biexciton coupling due to the enhancement of the Coulomb interaction through the surrounding medium.

Rodents explore the world by palpating objects with their whiskers. Whiskers interact with objects, causing stresses in whisker follicles and spikes in sensory neurons, which are interpreted by the brain to produce tactile perception. The mechanics of the whisker thus couple self-movement and the structure of the world to sensation. Whiskers are elastic thin rods; hence, they tend to vibrate. Whisker vibrations could be a key ingredient of rodent somatosensation. However, the specific conditions under which vibrations contribute appreciably to the stresses in the follicle remain unclear. We present an analytical solution for the deformation of individual whiskers in response to a time-varying force. We tracked the deformation of mouse whiskers during a pole localization task to extract the whisker Young's modulus and damping coefficient. We further extracted the time course and amplitude of steady-state forces during whisker-object contact. We use our model to calculate the relative contribution of steady-state and vibrational forces to stresses in the follicle in a variety of active sensation tasks and during the passive whisker stimuli typically used for sensory physiology. Vibrational stresses are relatively more prominent compared with steady-state forces for short contacts and for contacts close to the whisker tip. Vibrational stresses are large for texture discrimination, and under some conditions, object localization tasks. Vibrational stresses are negligible for typical ramp-and-hold stimuli. Our calculation provides a general framework, applicable to most experimental situations.

A theory of photo- and dark-band conductivities in semiconductor supercrystals consisting of nanocrystals is developed by assuming scattering by structural defects in the supercrystals. A new proposed mechanism of photoexcitation, which is triggered by an efficient Auger ionization of charged nanocrystals, provides explanation for the measured photocurrent being 2-3 orders of magnitude larger than the dark current. For dark conductivity, the metal-insulator transitions and temperature dependence of mobility in the metal phase are considered.

The ability of luminescent semiconductor quantum dots (QDs) to engage in diverse energy transfer processes with organic dyes, light-harvesting proteins, metal complexes, and redox-active labels continues to stimulate interest in developing them for biosensing and light-harvesting applications. Within biosensing configurations, changes in the rate of energy transfer between the QD and the proximal donor, or acceptor, based upon some external (biological) event form the principle basis for signal transduction. However, designing QD sensors to function optimally is predicated on a full understanding of all relevant energy transfer mechanisms. In this report, we examine energy transfer between a range of CdSe-ZnS core-shell QDs and a redox-active osmium(II) polypyridyl complex. To facilitate this, the Os complex was synthesized as a reactive isothiocyanate and used to label a hexahistidine-terminated peptide. The Os-labeled peptide was ratiometrically self-assembled to the QDs via metal affinity coordination, bringing the Os complex into close proximity of the nanocrystal surface. QDs displaying different emission maxima were assembled with increasing ratios of Os-peptide complex and subjected to detailed steady-state, ultrafast transient absorption, and luminescence lifetime decay analyses. Although the possibility exists for charge transfer quenching interactions, we find that the QD donors engage in relatively efficient Förster resonance energy transfer with the Os complex acceptor despite relatively low overall spectral overlap. These results are in contrast to other similar QD donor-redox-active acceptor systems with similar separation distances, but displaying far higher spectral overlap, where charge transfer processes were reported to be the dominant QD quenching mechanism.

We have shown theoretically that efficient multiple-exciton generation (MEG) by a single photon can be observed in small nanocrystals. Our quantum simulations that include hundreds of thousands of exciton and multiexciton states demonstrate that the complex time-dependent dynamics of these states in a closed electronic system yields a saturated MEG effect on a picosecond time scale. Including phonon relaxation confirms that efficient MEG requires the exciton-biexciton coupling time to be faster than exciton relaxation time.

The regular Einstein relation, connecting the coefficient of ambipolar diffusion and the Dember field with mobilities, is generalized for the case of an interacting electron-hole plasma. The calculations are presented for a nondegenerate plasma injected by light into semiconductors of silicon and germanium type. The Debye-Huckel correlation and the Wigner-Seitz exchange terms are considered. Corrections to the mobilities of carriers due to the difference between average and acting electric fields within the electron-hole plasma are taken into account. The deviation of the generalized relation from the regular Einstein relation is pronounced at low temperatures and can explain the anomaly of the coefficient of ambipolar diffusion, recently discovered experimentally.

We explore how the size and shape of the microscopic confinement potential affects the nonradiative Auger decay rate of confined carriers. Calculations conducted in the two-band, effective mass Kane model unambiguously show that smoothing out the confinement potential could reduce the rate by more than 3 orders of magnitude relative to the rate in structures with abruptly terminating boundaries. As the confinement potential width is increased, the calculated rate decreases overall, exhibiting very deep minima at regular widths. Such minima suggest that nanocrystals of "magic sizes" can exist for which nonradiative Auger processes are strongly suppressed.

The photoluminescence from a variety of individual molecules and nanometre-sized crystallites is defined by large intensity fluctuations, known as 'blinking', whereby their photoluminescence turns 'on' and 'off' intermittently, even under continuous photoexcitation. For semiconductor nanocrystals, it was originally proposed that these 'off' periods corresponded to a nanocrystal with an extra charge. A charged nanocrystal could have its photoluminescence temporarily quenched owing to the high efficiency of non-radiative (for example, Auger) recombination processes between the extra charge and a subsequently excited electron-hole pair; photoluminescence would resume only after the nanocrystal becomes neutralized again. Despite over a decade of research, completely non-blinking nanocrystals have not been synthesized and an understanding of the blinking phenomenon remains elusive. Here we report ternary core/shell CdZnSe/ZnSe semiconductor nanocrystals that individually exhibit continuous, non-blinking photoluminescence. Unexpectedly, these nanocrystals strongly photoluminesce despite being charged, as indicated by a multi-peaked photoluminescence spectral shape and short lifetime. To model the unusual photoluminescence properties of the CdZnSe/ZnSe nanocrystals, we softened the abrupt confinement potential of a typical core/shell nanocrystal, suggesting that the structure is a radially graded alloy of CdZnSe into ZnSe. As photoluminescence blinking severely limits the usefulness of nanocrystals in applications requiring a continuous output of single photons, these non-blinking nanocrystals may enable substantial advances in fields ranging from single-molecule biological labelling to low-threshold lasers.

Magnetic doping of semiconductor nanostructures is actively pursued for applications in magnetic memory and spin-based electronics. Central to these efforts is a drive to control the interaction strength between carriers (electrons and holes) and the embedded magnetic atoms. In this respect, colloidal nanocrystal heterostructures provide great flexibility through growth-controlled 'engineering' of electron and hole wavefunctions in individual nanocrystals. Here, we demonstrate a widely tunable magnetic sp-d exchange interaction between electron-hole excitations (excitons) and paramagnetic manganese ions using 'inverted' core-shell nanocrystals composed of Mn(2+)-doped ZnSe cores overcoated with undoped shells of narrower-gap CdSe. Magnetic circular dichroism studies reveal giant Zeeman spin splittings of the band-edge exciton that, surprisingly, are tunable in both magnitude and sign. Effective exciton g-factors are controllably tuned from -200 to +30 solely by increasing the CdSe shell thickness, demonstrating that strong quantum confinement and wavefunction engineering in heterostructured nanocrystal materials can be used to manipulate carrier-Mn(2+) wavefunction overlap and the sp-d exchange parameters themselves.

The paper describes droplet-to-bubble transition in block copolymer stabilized perfluoropentane nanoemulsions. Three physical factors that trigger droplet-to-bubble transition in liquid emulsions and gels were evaluated, namely heat, ultrasound, and injections through fine-gauge needles. Among those listed, ultrasound irradiation was found the most efficient factor. Possible mechanisms of bubble generation and growth discussed in the paper include liquid-to-gas transition inside the individual bubble; bubble coalescence; and diffusion of dissolved air and/or perfluoropentane from small bubbles into larger bubbles (i.e., Oswald ripening). The last two factors result in irreversibility of the droplet-to-bubble transition. In gel matrices, ultrasound-induced droplet-to-bubble transition was substantially inhibited but was catalyzed by large (hundred micron) pre-existing bubbles irradiated by low frequency (hundred kilohertz) ultrasound. The dependence of the droplet-to-bubble transition on initial bubble size is theoretically treated and the role of increase of surface area in promoting bubble coalescence is discussed. Therapeutic implications of observed effects are discussed.

The critical role that dopants play in semiconductor devices has stimulated research on the properties and the potential applications of semiconductor nanocrystals, or colloidal quantum dots, doped with intentional impurities. We review advances in the chemical synthesis of doped nanocrystals, in the theoretical understanding of the fundamental mechanisms that control doping, and in the creation of highly conducting nanocrystalline films. Because impurities can be used to alter the properties of nanoscale materials in desirable and controllable ways, doped nanocrystals can address key problems in applications from solar cells to bioimaging.

We examine the impact of growth kinetics on the incorporation of Mn dopants into ZnSe nanocrystals. We synthesize such particles, also known as colloidal quantum dots, and use optical spectroscopy to extract information about the average number of Mn impurities per nanocrystal as the reaction proceeds. We find that this number increases with particle growth until the Zn and/or Se precursors are depleted in the reaction solution. If the reaction is continued further, then ripening of the colloid begins and the average number of Mn per nanocrystal decreases, even as the particles slowly increase in size. We show that this effect, which is detrimental for enhanced doping, can be avoided if the reactant concentration is maintained by addition of more reactants. We consider several explanations and conclude that intraparticle ripening, in which material is redistributed on the same nanocrystal due to evolution of the particle shape, is the most consistent with experimental observations.

Doping--the intentional introduction of impurities into a material--is fundamental to controlling the properties of bulk semiconductors. This has stimulated similar efforts to dope semiconductor nanocrystals. Despite some successes, many of these efforts have failed, for reasons that remain unclear. For example, Mn can be incorporated into nanocrystals of CdS and ZnSe (refs 7-9), but not into CdSe (ref. 12)--despite comparable bulk solubilities of near 50 per cent. These difficulties, which have hindered development of new nanocrystalline materials, are often attributed to 'self-purification', an allegedly intrinsic mechanism whereby impurities are expelled. Here we show instead that the underlying mechanism that controls doping is the initial adsorption of impurities on the nanocrystal surface during growth. We find that adsorption--and therefore doping efficiency--is determined by three main factors: surface morphology, nanocrystal shape, and surfactants in the growth solution. Calculated Mn adsorption energies and equilibrium shapes for several nanocrystals lead to specific doping predictions. These are confirmed by measuring how the Mn concentration in ZnSe varies with nanocrystal size and shape. Finally, we use our predictions to incorporate Mn into previously undopable CdSe nanocrystals. This success establishes that earlier difficulties with doping are not intrinsic, and suggests that a variety of doped nanocrystals--for applications from solar cells to spintronics--can be anticipated.

We report ultra-efficient multiple exciton generation (MEG) for single photon absorption in colloidal PbSe and PbS quantum dots (QDs). We employ transient absorption spectroscopy and present measurement data acquired for both intraband as well as interband probe energies. Quantum yields of 300% indicate the creation, on average, of three excitons per absorbed photon for PbSe QDs at photon energies that are four times the QD energy gap. Results indicate that the threshold photon energy for MEG in QDs is twice the lowest exciton absorption energy. We find that the biexciton effect, which shifts the transition energy for absorption of a second photon, influences the early time transient absorption data and may contribute to a modulation observed when probing near the lowest interband transition. We present experimental and theoretical values of the size-dependent interband transition energies for PbSe QDs. We present experimental and theoretical values of the size-dependent interband transition energies for PbSe QDs, and we also introduce a new model for MEG based on the coherent superposition of multiple excitonic states.

A new lens that is a modification of the Veselago lens is proposed. It consists of a slab of the left-handed material embedded into a regular material. The materials for the new lens should have the same refractive index, unlike that of the Veselago lens in which the materials should in addition have the same impedance. Therefore the new lens should be easier to manufacture. As the Veselago lens, the new lens might be useful for the three dimensional imaging. In contrast to the Veselago lens the new lens has multiple foci, and it may image an object that is located at any large distance from the slab.

An analytical theory of low frequency electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. The evidence for such waves has been obtained recently by experiments and computations. The cutoff frequency of these waves, omega(0), is studied. An analytical expression for the permittivity epsilon is obtained and shown to be negative below omega(0). If the crystal is embedded into a medium with a negative mu, there are no propagating modes at any frequency. Thus, such a compound system is not a left-handed material (LHM). The recent experimental results on the LHM are discussed.

Computer modeling of the variable-range-hopping (VRH) conductivity in two-dimensional systems has been done by a kinetic Monte Carlo method, which includes some new elements. Study of the temperature dependence of the conductivity, testing of the different scaling relations, and study of the size effect show the detailed validity of the Efros-Shklovskii theory of the VRH in the system of interacting electrons. It has also been shown that simultaneous transitions of many electrons are not important. The reasons for disagreement with previous computational works are thoroughly analyzed.

We report on a new class of magnetoresistance oscillations observed in a high-mobility two-dimensional electron gas (2DEG) in GaAs-Al(x)Ga(1--x)As heterostructures. Appearing in a weak magnetic field ( B < 0.3 T) and only in a narrow temperature range ( 2 K < T < 9 K), these oscillations are periodic in 1/B with a frequency proportional to the electron Fermi wave vector, k(F). We interpret the effect as a magnetophonon resonance of the 2DEG with leaky interface-acoustic phonon modes carrying a wave vector q = 2k(F). Calculations show a few branches of such modes existing on the GaAs-Al(x)Ga(1--)xAs interface, and their velocities are in quantitative agreement with the observation.

An uncommon electron spin resonance technique is used to show that a universal distribution of residual carriers exists in tetrahedrally coordinated amorphous semiconductors following optical excitation at low temperatures. This universal behavior at long decay times results because statistical fluctuations in the electron and hole densities cannot occur and therefore do not affect the kinetics. This behavior is confirmed for carrier densities between 10(16) and 10(17) cm (-3) and decay times as long as 10(4) s.