Showing 1–50 of 64 results for author: Efros, A L

Extinction Coefficients of CdSe, CdS, and CdTe Nanoplatelets in Solution: A Practical Tool for Concentration Determination

Authors: Michael H. Stewart, Michael W. Swift, Farwa Awan, Liam Burke, Christopher M. Green, Barbara A. Marcheschi, Igor L. Medintz, Todd D. Krauss, Alexander L. Efros

Abstract: Semiconductor nanoplatelets possess exceptional optical properties that make them promising candidates for next-generation optoelectronic applications. However, unlike quantum dots where absorption spectroscopy alone can determine both size and concentration, nanoplatelets present a significant characterization challenge: the absorption peak position reveals only thickness, providing no informatio… ▽ More Semiconductor nanoplatelets possess exceptional optical properties that make them promising candidates for next-generation optoelectronic applications. However, unlike quantum dots where absorption spectroscopy alone can determine both size and concentration, nanoplatelets present a significant characterization challenge: the absorption peak position reveals only thickness, providing no information about lateral dimensions or concentration. This limitation forces researchers to rely on time-consuming and costly elemental analysis techniques for complete sample characterization. Here, we present an experimentally verified theoretical framework that predicts the frequency-dependent absorption coefficient of randomly oriented CdSe, CdS, and CdTe nanoplatelets, enabling concentration determination from absorption measurements and lateral size estimates. Our model shows that the integrated absorption coefficient depends universally on nanoplatelet surface area and thickness, yielding a practical tool to extract concentrations without laborious elemental analysis. This approach bridges the characterization gap between quantum dots and nanoplatelets, offering a streamlined method for rapid sample analysis that could accelerate nanoplatelet research and applications. △ Less

Submitted 21 October, 2025; originally announced October 2025.

Comments: 13 pages, 3 figures. Supporting Information: 12 pages, 3 figures

Non-perturbative macroscopic theory of interfaces with discontinuous dielectric constant

Authors: Y. M. Beltukov, A. V. Rodina, A. Alekseev, Al. L. Efros

Abstract: Discontinuity of dielectric constants at the interface is a common feature of all nanostructures and semiconductor heterostructures. Near such interfaces, a charged particle creates a singular self-interaction potential which may be attributed to interaction with fictitious mirror charges. The singularity of this interaction at the interface presents an obstruction to a perturbative approach. In s… ▽ More Discontinuity of dielectric constants at the interface is a common feature of all nanostructures and semiconductor heterostructures. Near such interfaces, a charged particle creates a singular self-interaction potential which may be attributed to interaction with fictitious mirror charges. The singularity of this interaction at the interface presents an obstruction to a perturbative approach. In several limiting cases, this problem can be avoided by zeroing out the carrier wave function at the interface. In this paper, we have developed a non-perturbative theory which gives a self-consistent description of carrier propagation through an interface with a dielectric discontinuity. It is based on conservation of the current density propagating through the interface, and it is formulated in terms of general boundary conditions (GBC) for the wave function at the interface with a single phenomenological parameter W. For these GBC, we find exact solutions of the Schrödinger equation near the interface and the carrier energy spectrum including resonances. Using these results, we describe the photo effect at the semiconductor/vacuum interface and the energy spectrum of quantum wells (QWs) at the interface with the vacuum or a high-k dielectric. For a surface of liquid helium, we estimate the parameter W, and match the resulting electron spectrum with the existing experimental data and theoretical analysis. △ Less

Submitted 9 October, 2025; v1 submitted 21 July, 2025; originally announced July 2025.

Landé g-factors and spin dynamics of charge carriers in CuCl nanocrystals in a glass matrix

Authors: Dennis Kudlacik, Evgeny A. Zhukov, Dmitri R. Yakovlev, Gang Qiang, Marina A. Semina, Aleksandr A. Golovatenko, Anna V. Rodina, Alexander L. Efros, Alexey I. Ekimov, Manfred Bayer

Abstract: The spin properties of charge carriers confined in CuCl semiconductor nanocrystals (NCs) of different sizes (radius from 1.8 nm up to 28 nm) crystallized in a glass matrix are studied experimentally and theoretically. By means of photoluminescence, spin-flip Raman scattering, time-resolved Faraday ellipticity, and time-resolved differential transmission performed at temperatures in the range of… ▽ More The spin properties of charge carriers confined in CuCl semiconductor nanocrystals (NCs) of different sizes (radius from 1.8 nm up to 28 nm) crystallized in a glass matrix are studied experimentally and theoretically. By means of photoluminescence, spin-flip Raman scattering, time-resolved Faraday ellipticity, and time-resolved differential transmission performed at temperatures in the range of $1.6 - 120$ K at magnetic fields up to 8 T, comprehensive information on the Landé $g$-factors as well as the population and spin dynamics is received. The spin signals are contributed by confined electrons with a $g$-factor close to 2, which shows a weak increase with decreasing NC size, i.e. increasing electron confinement energy. We revisit the theory of exciton confinement as a whole in spherical NCs within the six-band valence band model in order to describe the size dependence of the $Z_3$ and $Z_{1,2}$ exciton energies in CuCl NCs. We demonstrate theoretically that the stronger increase of the $Z_{1,2}$ energy transitions with decreasing radius can be explained by the strong absorption from the excited exciton state caused by strong heavy hole-light hole mixing in the exciton. The parameters of the six-band Hamiltonian describing both the exciton and hole kinetic energies are estimated from the comparison of the calculated and experimental size dependences of the exciton transitions. A theoretical model of the size-dependent Landé $g$-factors for electron and hole confined in spherical NCs of semiconductors with negative spin-orbit splitting of the valence band is developed. △ Less

Submitted 3 December, 2024; originally announced December 2024.

Comments: 33 pages Main file and 9 pages SI

Surface Exciton Polariton

Authors: Jason Hao, Jeffrey Owrutsky, Daniel Ratchford, Blake Simpkins, Alexander L. Efros

Abstract: In this paper, we have developed a theory describing surface exciton polariton (SEPs) that accounts for the spatial dispersion of the dielectric constant connected with exciton momentum. Due to strong coupling between light and bulk excitons in the frequency separation, $\hbarω_{LT}$, between the longitudinal and transverse exciton, the SEP is formed and behaves at partially light and partially ma… ▽ More In this paper, we have developed a theory describing surface exciton polariton (SEPs) that accounts for the spatial dispersion of the dielectric constant connected with exciton momentum. Due to strong coupling between light and bulk excitons in the frequency separation, $\hbarω_{LT}$, between the longitudinal and transverse exciton, the SEP is formed and behaves at partially light and partially matter. The dispersion of the SEP was found through a combined solution of Maxwell's and Thomas-Hopfield's equations. The analytical theory describes SEPs at any bulk exciton/vacuum interface and provides its complete dispersion if one knows $\hbarω_{LT}$, the exciton effective mass, $M$, and the high frequency dielectric constant, $κ_\infty$. The presented theory is in excellent agreement with the only numerical modeling of this problem, which was conducted for SEPs at a ZnO/vacuum interface. Calculations show the spatial dispersion of the dielectric constant leads to rather small broadening of the photon-like quasi-particle and suggests using SEPs for long-range coherence transfer. △ Less

Submitted 30 October, 2024; originally announced November 2024.

Double-Rashba materials for nanocrystals with bright ground-state excitons

Authors: Michael W. Swift, Peter C. Sercel, Alexander L. Efros, John L. Lyons, David J. Norris

Abstract: While nanoscale semiconductor crystallites provide versatile fluorescent materials for light-emitting devices, such nanocrystals suffer from the "dark exciton"$\unicode{x2014}$an optically inactive electronic state into which the nanocrystal relaxes before emitting. Recently, a theoretical mechanism was discovered that can potentially defeat the dark exciton. The Rashba effect can invert the order… ▽ More While nanoscale semiconductor crystallites provide versatile fluorescent materials for light-emitting devices, such nanocrystals suffer from the "dark exciton"$\unicode{x2014}$an optically inactive electronic state into which the nanocrystal relaxes before emitting. Recently, a theoretical mechanism was discovered that can potentially defeat the dark exciton. The Rashba effect can invert the order of the lowest-lying levels, creating a bright excitonic ground state. To identify materials that exhibit this behavior, here we perform an extensive high-throughput computational search of two large open-source materials databases. Based on a detailed understanding of the Rashba mechanism, we define proxy criteria and screen over 500,000 solids, generating 173 potential "bright-exciton" materials. We then refine this list with higher-level first-principles calculations to obtain 28 candidates. To confirm the potential of these compounds, we select five and develop detailed effective-mass models to determine the nature of their lowest-energy excitonic state. We find that four of the five solids (BiTeCl, BiTeI, Ga$_2$Te$_3$, and KIO$_3$) can yield bright ground-state excitons. Our approach thus reveals promising materials for future experimental investigation of bright-exciton nanocrystals. △ Less

Submitted 30 October, 2023; originally announced October 2023.

Comments: 19 pages, 4 figures

Journal ref: ACS Nano 18, 30, 19561-19567 (2024)

Dark and Bright Excitons in Halide Perovskite Nanoplatelets

Authors: Moritz Gramlich, Michael W. Swift, Carola Lampe, Markus Döblinger, John L. Lyons, Alexander L. Efros, Peter C. Sercel, Alexander S. Urban

Abstract: Semiconductor nanoplatelets (NPLs), with their large exciton binding energy, narrow photoluminescence (PL), and absence of dielectric screening for photons emitted normal to the NPL surface, could be expected to become the fastest luminophores amongst all colloidal nanostructures. However, super-fast emission is suppressed by a dark (optically passive) exciton ground state, substantially split fro… ▽ More Semiconductor nanoplatelets (NPLs), with their large exciton binding energy, narrow photoluminescence (PL), and absence of dielectric screening for photons emitted normal to the NPL surface, could be expected to become the fastest luminophores amongst all colloidal nanostructures. However, super-fast emission is suppressed by a dark (optically passive) exciton ground state, substantially split from a higher-lying bright (optically active) state. Here, the exciton fine structure in 2-8 monolayer (ML) thick Cs_{n-1}Pb_nBr_{3n+1} NPLs is revealed by merging temperature-resolved PL spectra and time-resolved PL decay with an effective mass modeling taking quantum confinement and dielectric confinement anisotropy into account. This approach exposes a thickness-dependent bright-dark exciton splitting reaching 32.3meV for the 2ML NPLs. The model also reveals a 5-16 meV splitting of the bright exciton states with transition dipoles polarized parallel and perpendicular to the NPL surfaces, the order of which is reversed for the thinnest NPLs, as confirmed by TR-PL measurements. Accordingly, the individual bright states must be taken into account, while the dark exciton state strongly affects the optical properties of the thinnest NPLs even at room temperature. Significantly, the derived model can be generalized for any isotropically or anisotropically confined nanostructure. △ Less

Submitted 1 October, 2021; originally announced October 2021.

Circular dichroism in non-chiral metal halide perovskites

Authors: Peter C. Sercel, Zeev Valy Vardeny, Alexander L. Efros

Abstract: We demonstrate theoretically that non-chiral perovskite layers can exhibit circular dichroism (CD) in the absence of a magnetic field and without chiral activation by chiral molecules. The effect is shown to be due to splitting of helical excitonic states which can form in structures of orthorhombic or lower symmetry that exhibit Rashba spin effects. The selective coupling of these helical exciton… ▽ More We demonstrate theoretically that non-chiral perovskite layers can exhibit circular dichroism (CD) in the absence of a magnetic field and without chiral activation by chiral molecules. The effect is shown to be due to splitting of helical excitonic states which can form in structures of orthorhombic or lower symmetry that exhibit Rashba spin effects. The selective coupling of these helical exciton states to helical light is shown to give rise to circular dichroism. Polarization dependent absorption is shown to occur due to the combined effect of Rashba splitting, in-plane symmetry breaking, and the effect of the exciton momentum on its fine structure, which takes the form of Zeeman splitting in an effective magnetic field. We calculate significant CD with an anisotropy factor of up to 30% in orthorhombic perovskite layers under off-normal top illumination conditions, raising the possibility of its observation in non-chiral perovskite structures. △ Less

Submitted 13 July, 2020; v1 submitted 30 June, 2020; originally announced July 2020.

Comments: 26 pages, 5 figures, 1 table. Jul5 revision, clarified description after Eq. 11, added ref. Jul 13 revision, typo corrections; added refs

Journal ref: Nanoscale, 2020, 12, 18067

Bright triplet excitons in lead halide perovskites

Authors: Michael A. Becker, Roman Vaxenburg, Georgian Nedelcu, Peter C. Sercel, Andrew Shabaev, Michael J. Mehl, John G. Michopoulos, Samuel G. Lambrakos, Noam Bernstein, John L. Lyons, Thilo Stöferle, Rainer F. Mahrt, Maksym V. Kovalenko, David J. Norris, Gabriele Rainò, Alexander L. Efros

Abstract: Nanostructured semiconductors emit light from electronic states known as excitons[1]. According to Hund's rules[2], the lowest energy exciton in organic materials should be a poorly emitting triplet state. Analogously, the lowest exciton level in all known inorganic semiconductors is believed to be optically inactive. These 'dark' excitons (into which the system can relax) hinder light-emitting de… ▽ More Nanostructured semiconductors emit light from electronic states known as excitons[1]. According to Hund's rules[2], the lowest energy exciton in organic materials should be a poorly emitting triplet state. Analogously, the lowest exciton level in all known inorganic semiconductors is believed to be optically inactive. These 'dark' excitons (into which the system can relax) hinder light-emitting devices based on semiconductor nanostructures. While strategies to diminish their influence have been developed[3-5], no materials have been identified in which the lowest exciton is bright. Here we show that the lowest exciton in quasi-cubic lead halide perovskites is optically active. We first use the effective-mass model and group theory to explore this possibility, which can occur when the strong spin-orbit coupling in the perovskite conduction band is combined with the Rashba effect [6-10]. We then apply our model to CsPbX3 (X=Cl,Br,I) nanocrystals[11], for which we measure size- and composition-dependent fluorescence at the single-nanocrystal level. The bright character of the lowest exciton immediately explains the anomalous photon-emission rates of these materials, which emit 20 and 1,000 times faster[12] than any other semiconductor nanocrystal at room[13-16] and cryogenic[17] temperatures, respectively. The bright exciton is further confirmed by detailed analysis of the fine structure in low-temperature fluorescence spectra. For semiconductor nanocrystals[18], which are already used in lighting[19,20], lasers[21,22], and displays[23], these optically active excitons can lead to materials with brighter emission and enhanced absorption. More generally, our results provide criteria for identifying other semiconductors exhibiting bright excitons with potentially broad implications for optoelectronic devices. △ Less

Submitted 10 July, 2017; originally announced July 2017.

Comments: 14 pages and 3 figures in the main text, Methods and extended data 16 pages which include 11 figures, and supporting information 28 pages

Journal ref: Nature 553, 189 (2018)

Tight-binding calculations of image charge effects in colloidal nanoscale platelets of CdSe

Authors: R. Benchamekh, N. A. Gippius, J. Even, M. O. Nestoklon, J. -M. Jancu, S. Ithurria, B. Dubertret, Al. L. Efros, P. Voisin

Abstract: CdSe nanoplatelets show perfectly quantized thicknesses of few monolayers. They present a situation of extreme, yet well defined quantum confinement. Due to large dielectric contrast between the semiconductor and its ligand environment, interaction between carriers and their dielectric images strongly renormalize bare single particle states. We discuss the electronic properties of this original sy… ▽ More CdSe nanoplatelets show perfectly quantized thicknesses of few monolayers. They present a situation of extreme, yet well defined quantum confinement. Due to large dielectric contrast between the semiconductor and its ligand environment, interaction between carriers and their dielectric images strongly renormalize bare single particle states. We discuss the electronic properties of this original system in an advanced tight-binding model, and show that Coulomb interactions, including self-energy corrections and enhanced electron-hole interaction, lead to exciton binding energies up to several hundred meVs. △ Less

Submitted 21 November, 2013; originally announced November 2013.

Photoluminescence in array of doped semiconductor nanocrystals

Authors: K. V. Reich, Tianran Chen, Al. L. Efros, B. I. Shklovskii

Abstract: We study the dependence of the quantum yield of photoluminescence of a dense, periodic array of semiconductor nanocrystals (NCs) on the level of doping and NC size. Electrons introduced to NCs via doping quench photoluminescence by the Auger process, so that practically only NCs without electrons contribute to the photoluminescence. Computer simulation and analytical theory are used to find a frac… ▽ More We study the dependence of the quantum yield of photoluminescence of a dense, periodic array of semiconductor nanocrystals (NCs) on the level of doping and NC size. Electrons introduced to NCs via doping quench photoluminescence by the Auger process, so that practically only NCs without electrons contribute to the photoluminescence. Computer simulation and analytical theory are used to find a fraction of such empty NCs as a function of the average number of donors per NC and NC size. For an array of small spherical NCs, the quantization gap between 1S and 1P levels leads to transfer of electrons from NCs with large number of donors to those without donors. As a result, empty NCs become extinct, and photoluminescence is quenched abruptly at an average number of donors per NC close to 1.8. The relative intensity of photoluminescence is shown to correlate with the type of hopping conductivity of an array of NCs. △ Less

Submitted 3 January, 2014; v1 submitted 2 October, 2013; originally announced October 2013.

Journal ref: Phys. Rev. B 88, 245311 (2013)

Fine structure of the band edge excitons and trions in CdSe/CdS core/shell nanocrystals

Authors: A. Shabaev, A. V. Rodina, Al. L. Efros

Abstract: We present a theoretical description of excitons and positively and negatively charged trions in "giant" CdSe/CdS core-shell nanocrystals (NCs). The developed theory provides the parameters describing the fine structure of excitons in CdSe/CdS core/thick shell NCs as a function of the CdSe/CdS conduction band offset and the CdSe core radius. We have also developed a general theory describing the f… ▽ More We present a theoretical description of excitons and positively and negatively charged trions in "giant" CdSe/CdS core-shell nanocrystals (NCs). The developed theory provides the parameters describing the fine structure of excitons in CdSe/CdS core/thick shell NCs as a function of the CdSe/CdS conduction band offset and the CdSe core radius. We have also developed a general theory describing the fine structure of positively charged trions created in semiconductor NCs with a degenerate valence band. The calculations take into account the complex structure of the CdSe valence band and inter-particle Coulomb and exchange interaction. Presented in this paper are the CdSe core size and CdSe/CdS conduction band offset dependences (i) of the positively charged trion fine structure, (ii) of the binding energy of the negatively charged trion, and (iii) of the radiative decay time for excitons and trions. The results of theoretical calculations are in qualitative agreement with available experimental data. △ Less

Submitted 5 November, 2012; originally announced November 2012.

Comments: Accepted for publication in Phys. Rev. B

Coulomb gap in the one-particle density of states in three-dimensional systems with localized electrons

Authors: A. L. Efros, Brian Skinner, B. I. Shklovskii

Abstract: The one-particle density of states (1P-DOS) in a system with localized electron states vanishes at the Fermi level due to the Coulomb interaction between electrons. Derivation of the Coulomb gap uses stability criteria of the ground state. The simplest criterion is based on the excitonic interaction of an electron and a hole and leads to a quadratic 1P-DOS in the three-dimensional (3D) case. In 3D… ▽ More The one-particle density of states (1P-DOS) in a system with localized electron states vanishes at the Fermi level due to the Coulomb interaction between electrons. Derivation of the Coulomb gap uses stability criteria of the ground state. The simplest criterion is based on the excitonic interaction of an electron and a hole and leads to a quadratic 1P-DOS in the three-dimensional (3D) case. In 3D, higher stability criteria, including two or more electrons, were predicted to exponentially deplete the 1P-DOS at energies close enough to the Fermi level. In this paper we show that there is a range of intermediate energies where this depletion is strongly compensated by the excitonic interaction between single-particle excitations, so that the crossover from quadratic to exponential behavior of the 1P-DOS is retarded. This is one of the reasons why such exponential depletion was never seen in computer simulations. △ Less

Submitted 20 May, 2011; v1 submitted 9 May, 2011; originally announced May 2011.

Comments: 6 pages, 1 figure

Journal ref: Phys. Rev. B 84, 064204 (2011)

High volumetric capacitance near insulator-metal percolation transition

Authors: A. L. Efros

Abstract: A new type of a capacitor with a very high volumetric capacitance is proposed. It is based upon the known phenomenon of a sharp increase of the dielectric constant of the metal-insulator composite in the vicinity of the percolation threshold, but still on the insulator side. The optimization suggests that the metallic particles should be of nanoscale and that the distance between planar electrodes… ▽ More A new type of a capacitor with a very high volumetric capacitance is proposed. It is based upon the known phenomenon of a sharp increase of the dielectric constant of the metal-insulator composite in the vicinity of the percolation threshold, but still on the insulator side. The optimization suggests that the metallic particles should be of nanoscale and that the distance between planar electrodes should be somewhat larger than the correlation length of the percolation theory and 10 to 20 times larger than the size of the particles while the area of the electrodes might be unlimited. The random electric field in the capacitors is found to be larger than the average field corresponding to the potential difference of electrodes. This random field is potentially responsible for dielectric breakdown. The estimated breakdown voltage of the new capacitor shows that the stored energy density might be significantly larger than that of electrolytic capacitors while the volumetric capacitances might be comparable. The charging and discharging times should be significantly smaller than corresponding times of batteries and even electrolytic capacitors. △ Less

Submitted 7 July, 2011; v1 submitted 20 March, 2011; originally announced March 2011.

Comments: 10 pages 1 EPS figure

Electron spin synchronization induced by optical nuclear magnetic resonance feedback

Authors: M. M. Glazov, I. A. Yugova, Al. L. Efros

Abstract: We predict a new physical mechanism explaining the electron spin precession frequency focusing effect observed recently in singly charged quantum dots exposed to a periodic train of resonant circularly polarized short optical pulses [A. Greilich et al, Science 317, 1896 (2007), Ref. 1]. We show that electron spin precession in an external magnetic field and a field of nuclei creates a Knight field… ▽ More We predict a new physical mechanism explaining the electron spin precession frequency focusing effect observed recently in singly charged quantum dots exposed to a periodic train of resonant circularly polarized short optical pulses [A. Greilich et al, Science 317, 1896 (2007), Ref. 1]. We show that electron spin precession in an external magnetic field and a field of nuclei creates a Knight field oscillating at the frequency of nuclear spin resonance. This field drives the projection of the nuclear spin onto magnetic field to the value that makes the electron spin precession frequency a multiple of the train cyclic repetition frequency, which is the condition at which the Knight field vanishes. △ Less

Submitted 14 January, 2012; v1 submitted 16 March, 2011; originally announced March 2011.

Comments: 4+ pages, 3 figures

Journal ref: Phys. Rev. B 85, 041303(R) (2012)

Electronic states and optical properties of PbSe nanorods and nanowires

Authors: A. C. Bartnik, Al. L. Efros, W. -K. Koh, C. B. Murray, F. W. Wise

Abstract: A theory of the electronic structure and excitonic absorption spectra of PbS and PbSe nanowires and nanorods in the framework of a four-band effective mass model is presented. Calculations conducted for PbSe show that dielectric contrast dramatically strengthens the exciton binding in narrow nanowires and nanorods. However, the self-interaction energies of the electron and hole nearly cancel the C… ▽ More A theory of the electronic structure and excitonic absorption spectra of PbS and PbSe nanowires and nanorods in the framework of a four-band effective mass model is presented. Calculations conducted for PbSe show that dielectric contrast dramatically strengthens the exciton binding in narrow nanowires and nanorods. However, the self-interaction energies of the electron and hole nearly cancel the Coulomb binding, and as a result the optical absorption spectra are practically unaffected by the strong dielectric contrast between PbSe and the surrounding medium. Measurements of the size-dependent absorption spectra of colloidal PbSe nanorods are also presented. Using room-temperature energy-band parameters extracted from the optical spectra of spherical PbSe nanocrystals, the theory provides good quantitative agreement with the measured spectra. △ Less

Submitted 28 October, 2010; originally announced October 2010.

Comments: 35 pages, 12 figures

Quantum simulation of multiple-exciton generation in a nanocrystal by a single photon

Authors: Wayne M. Witzel, Andrew Shabaev, C. Stephen Hellberg, Verne L. Jacobs, Alexander L. Efros

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

Submitted 22 September, 2010; v1 submitted 21 May, 2010; originally announced May 2010.

Journal ref: Phys. Rev. Lett. 105, 137401 (2010)

Anomalous low temperature ambipolar diffusion and Einstein relation

Authors: A. L. Efros

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

Submitted 14 December, 2009; originally announced December 2009.

Comments: 4 pages, 2 eps figures

Pump-Probe Faraday Rotation and Ellipticity in an Ensemble of Singly Charged Quantum Dots

Authors: I. A. Yugova, M. M. Glazov, E. L. Ivchenko, Al. L. Efros

Abstract: A description of spin Faraday rotation, Kerr rotation and ellipticity signals for single- and multi-layer ensembles of singly charged quantum dots (QDs) is developed. The microscopic theory considers both the single pump-pulse excitation and the effect of a train of such pulses, which in the case of long resident-electron spin coherence time leads to a stationary distribution of the electron spi… ▽ More A description of spin Faraday rotation, Kerr rotation and ellipticity signals for single- and multi-layer ensembles of singly charged quantum dots (QDs) is developed. The microscopic theory considers both the single pump-pulse excitation and the effect of a train of such pulses, which in the case of long resident-electron spin coherence time leads to a stationary distribution of the electron spin polarization. The calculations performed for single-color and two-color pump-probe setups show that the three experimental techniques: Faraday rotation, Kerr rotation and ellipticity measurements provide complementary information about an inhomogeneous ensemble of QDs. The microscopic theory developed for a three-dimensional ensemble of QDs is shown to agree with the phenomenological description of these effects. The typical time-dependent traces of pump-probe Faraday rotation, Kerr rotation and ellipticity signals are calculated for various experimental conditions. △ Less

Submitted 19 June, 2009; v1 submitted 8 May, 2009; originally announced May 2009.

Comments: 19 pages, 12 figures

Journal ref: Physical Review B 80, 104436 (2009)

Collective single mode precession of electron spins in a quantum dot ensemble

Authors: A. Greilich, S. Spatzek, I. A. Yugova, I. A. Akimov, D. R. Yakovlev, Al. L. Efros, D. Reuter, A. D. Wieck, M. Bayer

Abstract: We show that the spins of all electrons, each confined in a quantum dot of an (In,Ga)As/GaAs dot ensemble, can be driven into a single mode of precession about a magnetic field. This regime is achieved by allowing only a single mode within the electron spin precession spectrum of the ensemble to be synchronized with a train of periodic optical excitation pulses. Under this condition a nuclei ind… ▽ More We show that the spins of all electrons, each confined in a quantum dot of an (In,Ga)As/GaAs dot ensemble, can be driven into a single mode of precession about a magnetic field. This regime is achieved by allowing only a single mode within the electron spin precession spectrum of the ensemble to be synchronized with a train of periodic optical excitation pulses. Under this condition a nuclei induced frequency focusing leads to a shift of all spin precession frequencies into the synchronized mode. The macroscopic magnetic moment of the electron spins that is created in this regime precesses without dephasing. △ Less

Submitted 11 November, 2008; originally announced November 2008.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. B 79, 201305(R) (2009)

Tunable magnetic exchange interactions in manganese-doped inverted core/shell ZnSe/CdSe nanocrystals

Authors: David A. Bussian, Scott A. Crooker, Ming Yin, Marcin Brynda, Alexander L. Efros, Victor I. Klimov

Abstract: 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 via growth-controlled `engineering' of e… ▽ More 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 via growth-controlled `engineering' of electron and hole wavefunctions within 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-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 utilized to manipulate carrier-Mn wavefunction overlap and the sp-d exchange parameters themselves. △ Less

Submitted 6 November, 2008; originally announced November 2008.

Comments: To appear in Nature Materials; 18 pages, 4 figures + Supp. Info

Journal ref: Nature Materials v8, pp35-40 (2009)

Anomalous circular polarization of magneto-photoluminescence from individual CdSe nanocrystals

Authors: H. Htoon, S. A. Crooker, M. Furis, S. Jeong, Al. L. Efros, V. I. Klimov

Abstract: We study the low-temperature magneto-photoluminescence (PL) from individual CdSe nanocrystals. Nanocrystals having a small "bright" exciton fine structure splitting ($<$0.5 meV) exhibit a conventional left- and right-circularly polarized Zeeman PL doublet in applied magnetic fields. In contrast, nanocrystals with large fine structure splitting ($>$1 meV) show an anomalous magneto-PL polarization… ▽ More We study the low-temperature magneto-photoluminescence (PL) from individual CdSe nanocrystals. Nanocrystals having a small "bright" exciton fine structure splitting ($<$0.5 meV) exhibit a conventional left- and right-circularly polarized Zeeman PL doublet in applied magnetic fields. In contrast, nanocrystals with large fine structure splitting ($>$1 meV) show an anomalous magneto-PL polarization, wherein the lower-energy peak becomes circularly polarized with increasing field, while the higher-energy peak remains linearly polarized. This unusual behavior arises from strong mixing between the absorbing and emitting bright exciton levels due to strong anisotropic exchange interactions. △ Less

Submitted 5 September, 2008; originally announced September 2008.

Comments: 15 pages, 3 figures; submitted

Journal ref: Physical Review Letters 102, 017402 (2009)

Negative density of states: screening, Einstein relation, and negative diffusion

Authors: A. L. Efros

Abstract: In strongly interacting electron systems with low density and at low temperature the thermodynamic density of states is negative. It creates difficulties with understanding of the Einstein relation between conductivity and diffusion coefficient. Using the expression for electrochemical potential that takes into account the long range part of the Coulomb interaction it is shown that at negative d… ▽ More In strongly interacting electron systems with low density and at low temperature the thermodynamic density of states is negative. It creates difficulties with understanding of the Einstein relation between conductivity and diffusion coefficient. Using the expression for electrochemical potential that takes into account the long range part of the Coulomb interaction it is shown that at negative density of states Einstein relation gives a negative sign of the diffusion coefficient D, but under this condition there is no thermodynamic limitation on the sign of D. It happens because the unipolar relaxation of inhomogeneous electron density is not described by the diffusion equation. The relaxation goes much faster due to electric forces caused by electron density and by neutralizing background. Diffusion coefficient is irrelevant in this case and it is not necessarily positive because process of diffusion does not contribute to the positive production of entropy. In the case of bipolar diffusion negative D results in a global absolute instability that leads to formation of neutral excitons. Graphene is considered as an example of a system, where the density relaxation is expected to be due to electric force rather than diffusion. It may also have a negative density of states. △ Less

Submitted 27 August, 2008; v1 submitted 30 July, 2008; originally announced July 2008.

Comments: 12 pages, no figures, references added, some points clarified

Comment on "Self-Purification in Semiconductor Nanocrystals"

Authors: M. -H. Du, S. C. Erwin, Al. L. Efros, D. J. Norris

Abstract: In a recent Letter [PRL 96, 226802 (2006)], Dalpian and Chelikowsky claimed that formation energies of Mn impurities in CdSe nanocrystals increase as the size of the nanocrystal decreases, and argued that this size dependence leads to "self-purification" of small nanocrystals. They presented density-functional-theory (DFT) calculations showing a strong size dependence for Mn impurity formation e… ▽ More In a recent Letter [PRL 96, 226802 (2006)], Dalpian and Chelikowsky claimed that formation energies of Mn impurities in CdSe nanocrystals increase as the size of the nanocrystal decreases, and argued that this size dependence leads to "self-purification" of small nanocrystals. They presented density-functional-theory (DFT) calculations showing a strong size dependence for Mn impurity formation energies, and proposed a general explanation. In this Comment we show that several different DFT codes, pseudopotentials, and exchange-correlation functionals give a markedly different result: We find no such size dependence. More generally, we argue that formation energies are not relevant to substitutional doping in most colloidally grown nanocrystals. △ Less

Submitted 2 May, 2008; originally announced May 2008.

Comments: 1 page, 1 figure

Journal ref: Phys. Rev. Lett. 100, 179702 (2008)

The problem of a perfect lens made of a slab with negative refraction

Authors: A. L. Efros

Abstract: The problem of the principal existence of the perfect lens and superlensing is discussed. We have demonstrated that in the case of the virtual focus the idea of perfect lens based upon amplification of evanescent waves as proposed by Pendry is perfectly right unlike the case of the real foci. We think that some experimental results claiming superlensing can be explained in terms of the proposed… ▽ More The problem of the principal existence of the perfect lens and superlensing is discussed. We have demonstrated that in the case of the virtual focus the idea of perfect lens based upon amplification of evanescent waves as proposed by Pendry is perfectly right unlike the case of the real foci. We think that some experimental results claiming superlensing can be explained in terms of the proposed theory for the case when the virtual focus is inside the lens but very close to the rear face of it. △ Less

Submitted 8 September, 2006; originally announced September 2006.

Comments: 7 pages, 2 fugures, pdf format, FTM 2006 Workshop

Report number: FTM 2006/06

Theory of Electric Dipole Spin Resonance in a Parabolic Quantum Well

Authors: Al. L. Efros, E. I. Rashba

Abstract: A theory of Electric Dipole Spin Resonance (EDSR), that is caused by various mechanisms of spin-orbit coupling, is developed as applied to free electrons in a parabolic quantum well. Choosing a parabolic shape of the well has allowed us to find explicit expressions for the EDSR intensity and its dependence on the magnetic field direction in terms of the basic parameters of the Hamiltonian. By us… ▽ More A theory of Electric Dipole Spin Resonance (EDSR), that is caused by various mechanisms of spin-orbit coupling, is developed as applied to free electrons in a parabolic quantum well. Choosing a parabolic shape of the well has allowed us to find explicit expressions for the EDSR intensity and its dependence on the magnetic field direction in terms of the basic parameters of the Hamiltonian. By using these expressions, we have investigated and compared the effect of specific mechanisms of spin orbit (SO) coupling and different polarizations of ac electric field on the intensity of EDSR. Angular dependences of the EDSR intensity are indicative of the relative contributions of the competing mechanisms of SO coupling. Our results show that electrical manipulating electron spins in quantum wells is generally highly efficient, especially by an in-plane ac electric field. △ Less

Submitted 10 February, 2006; originally announced February 2006.

Comments: 45 pages 6 figure

Image of Veselago lens based upon two-dimensional photonic crystal with triangular lattice

Authors: C. Y. Li, J. M. Holt, A. L. Efros

Abstract: The construction of the multi-focal Veselago lens predicted earlier is proposed on the basis of a uniaxial photonic crystal consisting of cylindrical air holes in silicon that make a triangular lattice in a plane perpendicular to the axis of the crystal. The object and image are in air. The period of the crystal should be $0.44μ{\rm m}$ to work at the wavelength $1.5μ{\rm m}$. The lens does not… ▽ More The construction of the multi-focal Veselago lens predicted earlier is proposed on the basis of a uniaxial photonic crystal consisting of cylindrical air holes in silicon that make a triangular lattice in a plane perpendicular to the axis of the crystal. The object and image are in air. The period of the crystal should be $0.44μ{\rm m}$ to work at the wavelength $1.5μ{\rm m}$. The lens does not provide superlensing but the half-width of the image is $0.5λ$. The lens is shown to have wave guiding properties depending on the substrate material. △ Less

Submitted 18 August, 2005; originally announced August 2005.

Comments: 15 pages, 10 figures

Far-field image of Veselago lens

Authors: C. Y. Li, J. M. Holt, A. L. Efros

Abstract: It is shown that perfect imaging of a point source both in near- and far-field regions contradicts electrodynamics although ``superlensing'' is impossible only in the far-field region. These general statements are illustrated by detailed study of evanescent wave propagation in a photonic crystal that is known to be a left-handed medium. An analytical expression for the intensity distribution nea… ▽ More It is shown that perfect imaging of a point source both in near- and far-field regions contradicts electrodynamics although ``superlensing'' is impossible only in the far-field region. These general statements are illustrated by detailed study of evanescent wave propagation in a photonic crystal that is known to be a left-handed medium. An analytical expression for the intensity distribution near the far-field focus is obtained. This distribution contains some novel features and establishes a new ``diffraction limit'' for flat lenses. It is generalized for multiple sources located at different points. The distribution is in very good agreement with computer simulation. △ Less

Submitted 4 July, 2005; originally announced July 2005.

Comments: 19 pages, 12 figures

Evanescent waves in photonic crystals and image of Veselago lens

Authors: A. L. Efros, C. Y. Li, A. L. Pokrovsky

Abstract: It is shown that negative electric permittivity and magnetic permeability recently discovered in a photonic crystal in the vicinity of the Gamma-point are properties of propagating modes only. The evanescent modes rather decay than increase in the bulk of the crystal though they may be amplified by surface waves. If surface support such waves, the evanescent waves may improve the image of a thin… ▽ More It is shown that negative electric permittivity and magnetic permeability recently discovered in a photonic crystal in the vicinity of the Gamma-point are properties of propagating modes only. The evanescent modes rather decay than increase in the bulk of the crystal though they may be amplified by surface waves. If surface support such waves, the evanescent waves may improve the image of a thin Veselago lens. It is shown that a ``perfect lens'' contradicts to the wave optics and a criterion of ``superlensing'' is formulated. △ Less

Submitted 19 March, 2005; originally announced March 2005.

Comments: 4 pages, 3figures

Optical pumping of electronic and nuclear spin in single charge-tunable quantum dots

Authors: A. S. Bracker, E. A. Stinaff, D. Gammon, M. E. Ware, J. G. Tischler, A. Shabaev, Al. L. Efros, D. Park, D. Gershoni, V. L. Korenev, I. A. Merkulov

Abstract: We present a comprehensive examination of optical pumping of spins in individual GaAs quantum dots as we change the charge from positive to neutral to negative using a Schottky diode. We observe that photoluminescence polarization memory has the same sign as the net charge of the dot. Optical pumping of ground state electron spins enhances this effect, as demonstrated through the first measureme… ▽ More We present a comprehensive examination of optical pumping of spins in individual GaAs quantum dots as we change the charge from positive to neutral to negative using a Schottky diode. We observe that photoluminescence polarization memory has the same sign as the net charge of the dot. Optical pumping of ground state electron spins enhances this effect, as demonstrated through the first measurements of the Hanle effect on an individual quantum dot. With the Overhauser effect in a high longitudinal magnetic field, we demonstrate efficient optical pumping of the quantum dot's nuclear spins for all three charge states. △ Less

Submitted 20 August, 2004; originally announced August 2004.

Maximum thermal conductivity of aligned single wall carbon nanotubes

Authors: A. L. Efros

Abstract: I estimate maximum thermal conductivity $κ$ of a perfectly aligned bundle of single wall carbon nanotubes. Each row of aligned nanotubes has a discrete structure. It consists of segments of nanotubes with length $L$. The spacing between the segments block the phonon path through the row. Only the scattering due to the finite length of the segments is taken into account. The result is that the 'e… ▽ More I estimate maximum thermal conductivity $κ$ of a perfectly aligned bundle of single wall carbon nanotubes. Each row of aligned nanotubes has a discrete structure. It consists of segments of nanotubes with length $L$. The spacing between the segments block the phonon path through the row. Only the scattering due to the finite length of the segments is taken into account. The result is that the 'effective'' mean free path is of the order of $L/7$. For 1 micron tubes (10,10) we get maximum value of $κ\approx 300$W/m K at room temperature. This result is in a reasonable agreement with the experiment by Hone {\it et al.} assuming that in their samples $L\approx 1μ{\rm m}$ △ Less

Submitted 20 May, 2004; originally announced May 2004.

Comments: 10 pages, 3 figures

1D Exciton Spectroscopy of Semiconductor Nanorods

Authors: A. Shabaev, Al. L. Efros

Abstract: We have theoretically shown that optical properties of semiconductor nanorods are controlled by 1D excitons. The theory, which takes into account anisotropy of spacial and dielectric confinement, describes size dependence of interband optical transitions, exciton binding energies. We have demonstrated that the fine structure of the ground exciton state explains the linear polarization of photolu… ▽ More We have theoretically shown that optical properties of semiconductor nanorods are controlled by 1D excitons. The theory, which takes into account anisotropy of spacial and dielectric confinement, describes size dependence of interband optical transitions, exciton binding energies. We have demonstrated that the fine structure of the ground exciton state explains the linear polarization of photoluminescence. Our results are in good agreement with the measurements in CdSe nanorods. △ Less

Submitted 31 March, 2004; originally announced March 2004.

Efficient electron spin manipulation in a quantum well by an in-plane electric field

Authors: E. I. Rashba, Al. L. Efros

Abstract: Electron spins in a semiconductor quantum well couple to an electric field {\it via} spin-orbit interaction. We show that the standard spin-orbit coupling mechanisms can provide extraordinary efficient electron spin manipulation by an in-plane ac electric field. Electron spins in a semiconductor quantum well couple to an electric field {\it via} spin-orbit interaction. We show that the standard spin-orbit coupling mechanisms can provide extraordinary efficient electron spin manipulation by an in-plane ac electric field. △ Less

Submitted 8 October, 2003; originally announced October 2003.

Dielectric photonic crystal as medium with negative electric permittivity and magnetic permeability

Authors: A. L. Efros, A. L. Pokrovsky

Abstract: We show that a two-dimensional photonic crystal (PC) made from a non-magnetic dielectric is a left-handed material in the sense defined by Veselago. Namely, it has negative values of both the electric permittivity $ε$ and the magnetic permeability $μ$ in some frequency range. This follows from a recently proven general theorem. The negative values of $ε$ and $μ$ are found by a numerical simulati… ▽ More We show that a two-dimensional photonic crystal (PC) made from a non-magnetic dielectric is a left-handed material in the sense defined by Veselago. Namely, it has negative values of both the electric permittivity $ε$ and the magnetic permeability $μ$ in some frequency range. This follows from a recently proven general theorem. The negative values of $ε$ and $μ$ are found by a numerical simulation. Using these values we demonstrate the Veselago lens, a unique optical device predicted by Veselago. An approximate analytical theory is proposed to calculate the values of $ε$ and $μ$ from the PC band structure. It gives the results that are close to those obtained by the numerical simulation. The theory explains how a non-zero magnetization arises in a non-magnetic PC. △ Less

Submitted 29 August, 2003; originally announced August 2003.

Comments: 11 pages 4 figures

Long time relaxation of interacting electrons in the regime of hopping conduction

Authors: D. N. Tsigankov, E. Pazy, B. D. Laikhtman, A. L. Efros

Abstract: Using numerical simulations we studied the long time relaxation of the hopping conductivity. Even though no modern computation is able to simulate the behavior of a large size system over minutes or hours so as to observe the relaxation, still we have been able to show that the long time relaxation and aging effect observed in experiments can be explained in terms of slow transitions between dif… ▽ More Using numerical simulations we studied the long time relaxation of the hopping conductivity. Even though no modern computation is able to simulate the behavior of a large size system over minutes or hours so as to observe the relaxation, still we have been able to show that the long time relaxation and aging effect observed in experiments can be explained in terms of slow transitions between different pseudoground states. This was achieved by showing that different pseudoground states may have different conductivities and that the dispersion of conductivities is in agreement with the experimental data. We considered two different two-dimensional models with electron-electron interaction: the lattice model and the random site model, corresponding to ``strong'' and ``weak'' effective disorder. For the lattice model, effectively strong disorder, we have shown that the universality of the Coulomb gap, which is responsible for the universal Efros-Shklovskii law for the conductivity, suppresses the long time relaxation of conductivity since the universality strongly decreases the dispersion of conductivities of the pseudoground states. △ Less

Submitted 22 July, 2003; originally announced July 2003.

Comments: 25 pages, 8 figures, 1 table

Optical Read-Out and Initialization of an Electron Spin in a Single Quantum Dot

Authors: A. Shabaev, Al. L. Efros, D. Gammon, I. A. Merkulov

Abstract: We describe theoretically the resonant optical excitation of a trion with circularly polarized light and discuss how this trion permits the read-out of a single electron spin through a recycling transition. Optical pumping through combination of circularly polarized optical $π$--pulses with permanent or $π$-- pulsed transverse magnetic fields suggests feasible protocols for spin initialization. We describe theoretically the resonant optical excitation of a trion with circularly polarized light and discuss how this trion permits the read-out of a single electron spin through a recycling transition. Optical pumping through combination of circularly polarized optical $π$--pulses with permanent or $π$-- pulsed transverse magnetic fields suggests feasible protocols for spin initialization. △ Less

Submitted 15 July, 2003; originally announced July 2003.

Journal ref: Phys. Rev. B v. 68, 201305(R) (2003).

Orbital mechanisms of electron spin manipulation by an electric field

Authors: E. I. Rashba, Al. L. Efros

Abstract: A theory of spin manipulation of quasi-two-dimensional (2D) electrons by a time-dependent gate voltage applied to a quantum well is developed. The Dresselhaus and Rashba spin-orbit coupling mechanisms are shown to be rather efficient for this purpose. The spin response to a perpendicular-to-plane electric field is due to a deviation from the strict 2D limit and is controlled by the ratios of the… ▽ More A theory of spin manipulation of quasi-two-dimensional (2D) electrons by a time-dependent gate voltage applied to a quantum well is developed. The Dresselhaus and Rashba spin-orbit coupling mechanisms are shown to be rather efficient for this purpose. The spin response to a perpendicular-to-plane electric field is due to a deviation from the strict 2D limit and is controlled by the ratios of the spin, cyclotron and confinement frequencies. The dependence of this response on the magnetic field direction is indicative of the strenghts of the competing spin-orbit coupling mechanisms. △ Less

Submitted 6 June, 2003; originally announced June 2003.

Journal ref: Phys. Rev. Lett. v. 91, 126405 (2003)

New type of lenses based upon left-handed materials

Authors: A. L. Pokrovsky, A. L. Efros

Abstract: New type of lenses which are a slab of a left-handed material embedded into a regular material is proposed. These two materials should have equal refractive indices. Lenses with a focal length larger than the width of the slab can be constructed. These lenses should be easier to make than the well known Veselago lens, because the materials of the Veselago lens should obey an additional matching… ▽ More New type of lenses which are a slab of a left-handed material embedded into a regular material is proposed. These two materials should have equal refractive indices. Lenses with a focal length larger than the width of the slab can be constructed. These lenses should be easier to make than the well known Veselago lens, because the materials of the Veselago lens should obey an additional matching condition. Lenses of new type have multiple foci and might be useful for the 3D imaging. △ Less

Submitted 12 December, 2002; originally announced December 2002.

Effect of the Surface on the Electron Quantum Size Levels and Electron g-Factor in Spherical Semiconductor Nanocrystals

Authors: A. V. Rodina, Al. L. Efros, A. Yu. Alekseev

Abstract: The structure of the electron quantum size levels in spherical nanocrystals is studied in the framework of an eight--band effective mass model at zero and weak magnetic fields. The effect of the nanocrystal surface is modeled through the boundary condition imposed on the envelope wave function at the surface. We show that the spin--orbit splitting of the valence band leads to the surface--induce… ▽ More The structure of the electron quantum size levels in spherical nanocrystals is studied in the framework of an eight--band effective mass model at zero and weak magnetic fields. The effect of the nanocrystal surface is modeled through the boundary condition imposed on the envelope wave function at the surface. We show that the spin--orbit splitting of the valence band leads to the surface--induced spin--orbit splitting of the excited conduction band states and to the additional surface--induced magnetic moment for electrons in bare nanocrystals. This additional magnetic moment manifests itself in a nonzero surface contribution to the linear Zeeman splitting of all quantum size energy levels including the ground 1S electron state. The fitting of the size dependence of the ground state electron g factor in CdSe nanocrystals has allowed us to determine the appropriate surface parameter of the boundary conditions. The structure of the excited electron states is considered in the limits of weak and strong magnetic fields. △ Less

Submitted 23 October, 2002; originally announced October 2002.

Comments: 11 pages, 4 figures, submitted to Phys. Rev. B

Journal ref: Phys. Rev. B, 67, 155312 (2003)

Sign of refractive index and group velocity in left-handed media

Authors: A. L. Pokrovsky, A. L. Efros

Abstract: We argue that the widely spread opinion that the left-handed media (LHM) are characterized by a negative refractive index $n_-$ is misleading. Since n does not enter into Maxwell's equations and boundary conditions, any medium may be described by both positive n and negative $n_-=-n$. Two thermodynamic inequalities are presented, that make a difference between the LHM and the regular media (RM… ▽ More We argue that the widely spread opinion that the left-handed media (LHM) are characterized by a negative refractive index $n_-$ is misleading. Since n does not enter into Maxwell's equations and boundary conditions, any medium may be described by both positive n and negative $n_-=-n$. Two thermodynamic inequalities are presented, that make a difference between the LHM and the regular media (RM). The first one reads that the group velocity is positive in the RM and negative in the LHM. The second one is that the product ${\rm Re}(n) {\rm Im}(n)$ is positive in the RM and negative in the LHM. Both inequalities are invariant with respect to the change $n \to n_-$. However, to use $n_-$ one should change some traditional electrodynamics definitions. △ Less

Submitted 19 September, 2002; v1 submitted 18 September, 2002; originally announced September 2002.

Comments: 10 pages 2 figures

Propagation of waves in metallic photonic crystals at low frequencies and some theoretical aspects of left-handed materials

Authors: A. L. Pokrovsky, A. L. Efros

Abstract: An analytical theory of low frequency electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. The evidence of the existence of such waves has been found recently via experiments and computations. We have obtained an exact dispersion equation for omega (k) and studied the cutoff frequency omega_0 = omega(0) as a function of parameters of the photo… ▽ More An analytical theory of low frequency electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. The evidence of the existence of such waves has been found recently via experiments and computations. We have obtained an exact dispersion equation for omega (k) and studied the cutoff frequency omega_0 = omega(0) as a function of parameters of the photonic crystal. An analytical expression for the permittivity epsilon is calculated. It is shown, that if the crystal is embedded into a medium with negative mu, it has 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. △ Less

Submitted 22 July, 2002; originally announced July 2002.

Comments: 8 pages, 3 figures

Diffraction theory and focusing of light by left-handed materials

Authors: A. L. Pokrovsky, A. L. Efros

Abstract: A diffraction theory in a system consisting of left-handed and right-handed materials is proposed. The theory is based upon the Huygens's principle and the Kirchhoff's integral and it is valid if the wavelength is smaller than any relevant length of the system. The theory is applied to the calculation of the smearing of the foci of the Veselago lens due to the finite wavelength. We show that the… ▽ More A diffraction theory in a system consisting of left-handed and right-handed materials is proposed. The theory is based upon the Huygens's principle and the Kirchhoff's integral and it is valid if the wavelength is smaller than any relevant length of the system. The theory is applied to the calculation of the smearing of the foci of the Veselago lens due to the finite wavelength. We show that the Veselago lens is a unique optical instrument for the 3D imaging, but it is not a ``superlens'' as it has been claimed recently. △ Less

Submitted 22 July, 2002; originally announced July 2002.

Comments: 7 pages, 2 figures

Manipulation of the Spin Memory of Electrons in n-GaAs

Authors: R. I. Dzhioev, V. L. Korenev, I. A. Merkulov, B. P. Zakharchenya, D. Gammon, Al. L. Efros, D. S. Katzer

Abstract: We report on the optical manipulation of the electron spin relaxation time in a GaAs based heterostructure. Experimental and theoretical study shows that the average electron spin relaxes through hyperfine interaction with the lattice nuclei, and that the rate can be controlled by the electron-electron interactions. This time has been changed from 300 ns down to 5 ns by variation of the laser fr… ▽ More We report on the optical manipulation of the electron spin relaxation time in a GaAs based heterostructure. Experimental and theoretical study shows that the average electron spin relaxes through hyperfine interaction with the lattice nuclei, and that the rate can be controlled by the electron-electron interactions. This time has been changed from 300 ns down to 5 ns by variation of the laser frequency. This modification originates in the optically induced depletion of n-GaAs layer. △ Less

Submitted 16 May, 2002; originally announced May 2002.

Journal ref: Physical Review Letters v.88, p.256801 (2002)

Spin dynamics in semiconductor nanocrystals

Authors: J. A. Gupta, D. D. Awschalom, Al. L. Efros, A. V. Rodina

Abstract: Time-resolved Faraday rotation is used to study both transverse and longitudinal spin relaxation in chemically-synthesized CdSe nanocrystals (NCs) 22-80 Angstroms in diameter. The precession of optically-injected spins in a transverse magnetic field occurs at distinct frequencies whose assignment to electron and exciton spins is developed through systematic studies of the size-dependence and the… ▽ More Time-resolved Faraday rotation is used to study both transverse and longitudinal spin relaxation in chemically-synthesized CdSe nanocrystals (NCs) 22-80 Angstroms in diameter. The precession of optically-injected spins in a transverse magnetic field occurs at distinct frequencies whose assignment to electron and exciton spins is developed through systematic studies of the size-dependence and theoretical calculations. It is shown that the transverse spin lifetime is limited by inhomogeneous dephasing to a degree that cannot be accounted for by the NC size distribution alone. Longitudinal spin relaxation in these NCs occurs on several distinct timescales ranging from 100 ps-10 microseconds and exhibits markedly different dependencies on temperature and field in comparison to transverse spin relaxation. △ Less

Submitted 10 April, 2002; originally announced April 2002.

Comments: 25 pages, 11 figures, table

Electron spin relaxation by nuclei in semiconductor quantum dots

Authors: I. A. Merkulov, Al. L. Efros, M. Rosen

Abstract: We have studied theoretically the electron spin relaxation in semiconductor quantum dots via interaction with nuclear spins. The relaxation is shown to be determined by three processes: (i) -- the precession of the electron spin in the hyperfine field of the frozen fluctuation of the nuclear spins; (ii) -- the precession of the nuclear spins in the hyperfine field of the electron; and (iii) -- t… ▽ More We have studied theoretically the electron spin relaxation in semiconductor quantum dots via interaction with nuclear spins. The relaxation is shown to be determined by three processes: (i) -- the precession of the electron spin in the hyperfine field of the frozen fluctuation of the nuclear spins; (ii) -- the precession of the nuclear spins in the hyperfine field of the electron; and (iii) -- the precession of the nuclear spin in the dipole field of its nuclear neighbors. In external magnetic fields the relaxation of electron spins directed along the magnetic field is suppressed. Electron spins directed transverse to the magnetic field relax completely in a time on the order of the precession period of its spin in the field of the frozen fluctuation of the nuclear spins. Comparison with experiment shows that the hyperfine interaction with nuclei may be the dominant mechanism of electron spin relaxation in quantum dots. △ Less

Submitted 15 February, 2002; originally announced February 2002.

Journal ref: Physical Review B, volume 65, 205309 (2002)

Diffraction in left-handed materials and theory of Veselago lens

Authors: A. L. Pokrovsky, A. L. Efros

Abstract: A theory of diffraction in the system consisting of the left-handed and the right-handed materials is proposed. The theory is based upon the Huygens's principle and the Kirchhoff's integral and it is valid if the wavelength is smaller than any relevant length of the system. The theory is applied to the calculation of the smearing of the foci of the Veselago lens due to the finite wavelength. We… ▽ More A theory of diffraction in the system consisting of the left-handed and the right-handed materials is proposed. The theory is based upon the Huygens's principle and the Kirchhoff's integral and it is valid if the wavelength is smaller than any relevant length of the system. The theory is applied to the calculation of the smearing of the foci of the Veselago lens due to the finite wavelength. We show that the Veselago lens is a unique optical instrument for the 3D imaging, but it is not a ``superlens'' as it has been claimed recently. △ Less

Submitted 10 May, 2002; v1 submitted 5 February, 2002; originally announced February 2002.

Comments: 5 pages, 2 figures

Electrodynamics of metallic photonic crystals and problem of left-handed materials

Authors: A. L. Pokrovsky, A. L. Efros

Abstract: An exact analytical theory of the electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. It is shown that there are waves with a very low cutoff frequency $ω_0$ and that the permittivity $ε$ is negative below $ω_0$. We show that if the crystal is embedded into a medium with negative $μ$, it has no propagating modes at any frequency. Thus, such a… ▽ More An exact analytical theory of the electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. It is shown that there are waves with a very low cutoff frequency $ω_0$ and that the permittivity $ε$ is negative below $ω_0$. We show that if the crystal is embedded into a medium with negative $μ$, it has 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. △ Less

Submitted 23 May, 2002; v1 submitted 26 December, 2001; originally announced December 2001.

Comments: 5 pages, 1 figure

General boundary conditions for the envelope function in multiband k.p model

Authors: A. V. Rodina, A. Yu. Alekseev, Al. L. Efros, M. Rosen, B. K. Meyer

Abstract: We have derived general boundary conditions (BC) for the multiband envelope functions (which do not contain spurious solutions) in semiconductor heterostructures with abrupt heterointerfaces. These BC require the conservation of the probability flux density normal to the interface and guarantee that the multiband Hamiltonian be self--adjoint. The BC are energy independent and are characteristic… ▽ More We have derived general boundary conditions (BC) for the multiband envelope functions (which do not contain spurious solutions) in semiconductor heterostructures with abrupt heterointerfaces. These BC require the conservation of the probability flux density normal to the interface and guarantee that the multiband Hamiltonian be self--adjoint. The BC are energy independent and are characteristic properties of the interface. Calculations have been performed of the effect of the general BC on the electron energy levels in a potential well with infinite potential barriers using a coupled two band model. The connection with other approaches to determining BC for the envelope function and to the spurious solution problem in the multiband k.p model are discussed. △ Less

Submitted 19 December, 2001; originally announced December 2001.

Comments: 15 pages, 2 figures; to be published in Phys. Rev. B 65, March 15 issue 2002

Variable-range-hopping in two-dimensional system

Authors: D. N. Tsigankov, A. L. Efros

Abstract: Computer modeling of the VRH conductivity in the two-dimensional system has been done by 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 that the Efros-Shklovskii mechanism of the VRH is valid in the slightest details. It has been also shown that si… ▽ More Computer modeling of the VRH conductivity in the two-dimensional system has been done by 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 that the Efros-Shklovskii mechanism of the VRH is valid in the slightest details. It has been also shown that simultaneous transitions of many electrons are not important. The reasons of disagreement with previous works are thoroughly analyzed. △ Less

Submitted 5 June, 2001; originally announced June 2001.

Comments: 4 pages, 2 figures

Nonlocal electrodynamics of two-dimensional wire mesh photonic crystals

Authors: A. L. Pokrovsky, A. L. Efros

Abstract: We calculate analytically the spectra of plasma waves and electromagnetic waves (EMW) in metallic photonic crystal consisting of the parallel thin infinite metallic cylinders embedded in the dielectric media. The axes of metallic cylinders form a regular square lattice in a plane perpendicular to them. The metal inside the cylinders is assumed to be in the high frequency regime $ωτ>> 1$, where… ▽ More We calculate analytically the spectra of plasma waves and electromagnetic waves (EMW) in metallic photonic crystal consisting of the parallel thin infinite metallic cylinders embedded in the dielectric media. The axes of metallic cylinders form a regular square lattice in a plane perpendicular to them. The metal inside the cylinders is assumed to be in the high frequency regime $ωτ>> 1$, where $τ$ is the relaxation time. The proposed analytical theory is based upon small parameters $f << 1$, where $f$ is the volume fraction of the metal, and $kR << 1$, where $k$ is the wave vector and $R$ is the radius of the cylinder. It is shown that there are five different branches of the EMW that cover all frequency range under consideration except one very small omnidirectional gap in the vicinity of the frequency of the surface plasmon. However, at some directions of propagation and polarizations the gap may be much larger. The reflection and refraction of the EMW is also considered. The general theory of refraction is proposed which is complicated by the spatial dispersion of the dielectric constant, and one particular geometry of the incident EMW is considered. △ Less

Submitted 31 May, 2001; originally announced May 2001.

Comments: 14 pages, 8 figures

Thermodynamics and transport properties of interacting systems with localized electrons

Authors: A. L. Efros

Abstract: The review of the modern results in the theoretical and experimental study of the localized interacting electrons is given. After theoretical prediction of the Coulomb gap and the new temperature law in the variable range hopping conduction many efforts have been made to discover it experimentally. The most important of them are attempts to demonstrate experimentally that the long range Coulomb… ▽ More The review of the modern results in the theoretical and experimental study of the localized interacting electrons is given. After theoretical prediction of the Coulomb gap and the new temperature law in the variable range hopping conduction many efforts have been made to discover it experimentally. The most important of them are attempts to demonstrate experimentally that the long range Coulomb interaction is not screened in this system and that it is the origin of the gap. The next stage begins when the recent experiments have discovered glassy properties of the interacting system with localized electrons. This review is concentrated on the origin of the glassy properties of this system and it connects the glassy properties with another interesting phenomenon - insulator-metal transition. △ Less

Submitted 6 November, 2000; originally announced November 2000.

Comments: 16 pages, 4 figures, Proceedings of an Interspecialist Workshop: Phase Transitions and Self-Organization in Electronic and Molecular Networks. July 2000, Cambridge UK. To be published by Kluwer