arXiv subjects

M. E. Raikh

Publications and source records attributed to M. E. Raikh.

At least 109 records · Page 6Linked to original sources

arXiv2004

Incomplete Photonic Bandgap as Inferred from the Speckle Pattern of Scattered Light Waves

Motivated by recent experiments on intensity correlations of the waves transmitted through disordered media, we demonstrate that the speckle pattern from disordered photonic crystal with incomplete band-gap represents a sensitive tool for determination the stop-band width. We establish the quantitative relation between this width and the {\em angualar anisotropy} of the intensity correlation function.

cond-mat.mes-hall↗

arXiv2003

Many-body luminescence from highly excited quantum-confined structures

We review recent results on many-body effects in the luminescence from semiconductor nanostructures. Many-body luminescence from highly excited quantum-confined structures is conceptually important topic since a new parameter, a level spacing, plays a crucial role. This spacing is not merely a discretization of the bulk luminescence spectrum, as it could seem. The interplay of finite spacing with interactions (even weak) results in a highly nontrivial sequence of emission lines, their heights revealing the many-body correlations in the system. Here the complex structure of the emission spectrum, resulting from the shakeup processes in many-particle (but finite) system, is demonstrated for a confined electron-hole system of a particular geometry, in which the interacting carriers are confined to a ring. For this geometry, the Luttinger liquid theory allows one to exactly calculate the intensities of all many-body spectral lines. The positions of the lines are governed by the relation of the level spacings for electrons and holes. While close to the emission threshold the interactions cause only weak shakeup satellites of the single-particle lines, away from the threshold the discrete luminescence spectrum is completely dominated by the many-body transitions. We describe the Luttinger liquid approach for calculations of optical spectra in finite one-dimensional systems. The calculations are preceded by a detailed review of experimental and theoretical work on many-body luminescence from various infinite systems. We also review the current status of the experimental and theoretical research on quantum nanorings.

cond-mat.mes-hall↗

arXiv2003

Anomalously Localized States in the Anderson Model

In a diffusive conductor the eigenstates are spread over the entire sample. However, with certain probability, an anomalously localized state (ALS) can occur, i.e. the wave function assumes anomalously large values in some region of space. Existing analytical theories of ALS are based on models described by a continuous (Gaussian) random potential. In the present paper we study ALS in a lattice (Anderson) model. We demonstrate that close to the center of the band, E=0, a new type of ALS exist and calculate analytically their likelihood. These ALS are lattice-specific and have no analog in the continuum. Our findings are relevant to numerical simulations, which are necessarily performed on a lattice. We demonstrate that inconsistencies with "continuous" results reported in the previous numerical work on ALS can be explained within our analytical theory. Finally, we point out that, in order to compare the numerics with the "continuous" ALS theories, simulations must be carried out not too far from the band edges, within the band, where the continuous description applies. Simulations performed for $E$ close to the band center reveal lattice-specific ALS that do not exist in continuous models.

cond-mat.dis-nn↗

arXiv2003

Localization Length in Anderson Insulator with Kondo Impurities

The localization length, $ξ$, in a 2--dimensional Anderson insulator depends on the electron spin scattering rate by magnetic impurities, $τ_s^{-1}$. For antiferromagnetic sign of the exchange, %constant, the time $τ_s$ is {\em itself a function of $ξ$}, due to the Kondo correlations. We demonstrate that the unitary regime of localization is impossible when the concentration of magnetic impurities, $n_{\tiny M}$, is smaller than a critical value, $n_c$. For $n_{\tiny M}>n_c$, the dependence of $ξ$ on the dimensionless conductance, $g$, is {\em reentrant}, crossing over to unitary, and back to orthogonal behavior upon increasing $g$. Sensitivity of Kondo correlations to a weak {\em parallel} magnetic field results in a giant parallel magnetoresistance.

cond-mat.mes-hall↗

arXiv2003

Interplay of Short-Range Interactions and Quantum Interference Near the Integer Quantum Hall Transition

Short-range electron-electron interactions are incorporated into the network model of the integer quantum Hall effect. In the presence of interactions, the electrons, propagating along one link, experience exchange scattering off the Friedel oscillations of the density matrix of electrons on the neighboring links. As a result, the energy dependence of the transmission, ${\cal T}(ε)$, of the node, connecting the two links, develops an anomaly at the Fermi level, $ε=ε_F$. We show that this interaction-induced anomaly in ${\cal T}(ε)$ translates into the anomalous behavior of the Hall conductivity, $σ_{xy}(ν)$, where $ν$ is the filling factor (we assume that the electrons are {\em spinless}). At low temperatures, $T \to 0$, the evolution of the quantized $σ_{xy}$ with decreasing $ν$ proceeds as $1\to 2 \to 0$, in apparent violation of the semicircle relation. The anomaly in ${\cal T}(ε)$ also affects the temperature dependence of the peak in the diagonal conductivity, $σ_{xx}(ν, T)$. In particular, unlike the case of noninteracting electrons,the maximum value of $σ_{xx}$ stays at $σ_{xx} = 0.5$ within a wide temperature interval.

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arXiv2003

A classical model for the negative dc conductivity of ac-driven 2D electrons near the cyclotron resonance

A classical model for {\em dc} transport of two dimensional electrons in a perpendicular magnetic field and under strong irradiation is considered. We demonstrate that, near the cyclotron resonance condition, and for {\em linear} polarization of the {\em ac} field, a strong change of the diagonal component, $σ_d$, of the {\em dc} conductivity occurs in the presence of a {\em weak} nonparabolicity of the electron spectrum. Small change in the electron effective mass due to irradiation can lead to negative $σ_d$, while the Hall component of the {\em dc} conductivity remains practically unchanged. Within the model considered, the sign of $σ_d$ depends on the relative orientation of the {\em dc} and {\em ac} fields, the sign of the detuning of the {\em ac} frequency from the cyclotron resonance, and the sign of nonparabolic term in the energy spectrum.

cond-mat.dis-nn↗

arXiv2002

Coherent Random Lasing and "Almost Localized" Photon Modes

A pulse of light, injected into a weakly disordered dielectric medium, typically, will leave its initial location in a short time, by diffusion. However, due to some rare configurations of disorder, there is a possibility of formation of high quality resonators which can trap light for a long time. We present a rather detailed, quantitative study of such random resonators and of the "almost localized" states that they can support. After presenting a brief review of the earlier work on the subject, we concentrate on a detailed computation of the "prefactor": knowledge of the latter is crucial for varifying the viability of the random rasonators and their areal density. Both short range disorder (white noise) and correlated disorder are studied, and the important effect of the correlation radius, $R_c$, on the probability of formation of resonators with a given quality factor $Q$ is discussed. The random resonators are "self-formed", in the sense that no sharp features (like Mie scatterers or other "resonant entities") are introduced: our model is a featureless dielectric medium with fluctuating dielectric constant. We point out the relevance of the random resonators to the recently discovered phenomenon of coherent "random" lasing and review the existing work on that subject. We emphasize, however, that the random resonators exist already in the {\em passive} medium: gain is only needed to "make them visible".

cond-mat.dis-nn↗

arXiv2002

Strongly Localized State of a Photon at the Intersection of the Phase Slips in 2D Photonic Crystal with Low Contrast of Dielectric Constant

Two-dimensional photonic crystal with a rectangular symmetry and low contrast (< 1) of the dielectric constant is considered. We demonstrate that, despite the {\em absence} of a bandgap, strong localization of a photon can be achieved for certain ``magic'' geometries of a unit cell by introducing two $π/2$ phase slips along the major axes. Long-living photon mode is bound to the intersection of the phase slips. We calculate analytically the lifetime of this mode for the simplest geometry -- a square lattice of cylinders of a radius, $r$. We find the magic radius, $r_c$, of a cylinder to be 43.10 percent of the lattice constant. For this value of $r$, the quality factor of the bound mode exceeds $10^6$. Small ($\sim 1%$) deviation of $r$ from $r_c$ results in a drastic damping of the bound mode.

cond-mat↗

arXiv2002

Coulomb Drag for Strongly Localized Electrons: Pumping Mechanism

The mutual influence of two layers with strongly loclized electrons is exercised through the random Coulomb shifts of site energies in one layer caused by electron hops in the other layer. We trace how these shifts give rise to a voltage drop in the passive layer, when a current is passed through the active layer. We find that the microscopic origin of drag lies in the time correlations of the occupation numbers of the sites involved in a hop. These correlations are neglected within the conventional Miller-Abrahams scheme for calculating the hopping resistance.

cond-mat.mes-hall↗

arXiv2002

Directional Emission from a Microdisk Resonator with a Linear Defect

Microdisk resonator with a linear defect at some distance away from the circumference is studied theoretically. We demonstrate that the presence of the defect leads to ({\em i}) enhancement of the output efficiency, and ({\em ii}) directionality of the outgoing light. The dependence of the radiative losses and of the far-field distribution on the position and orientation of the defect are calculated. The angular dependence of the far field is given by a lorentzian with a width that has a sharp minimum for a certain optimal orientation of the defect line. For this orientation the whispering-gallery mode of a circular resonator is scattered by the extended defect in the direction normal to the disk boundary.

cond-mat↗

arXiv2002

Zero-Field Satellites of a Zero-Bias Anomaly

Spin-orbit (SO) splitting, $\pm ω_{SO}$, of the electron Fermi surface in two-dimensional systems manifests itself in the interaction-induced corrections to the tunneling density of states, $ν(ε)$. Namely, in the case of a smooth disorder, it gives rise to the satellites of a zero-bias anomaly at energies $ε=\pm 2ω_{SO}$. Zeeman splitting, $\pm ω_{Z}$, in a weak parallel magnetic field causes a narrow {\em plateau} of a width $δε=2ω_{Z}$ at the top of each sharp satellite peak. As $ω_{Z}$ exceeds $ω_{SO}$, the SO satellites cross over to the conventional narrow maxima at $ε= \pm 2ω_{Z}$ with SO-induced plateaus $δε=2ω_{SO}$ at the tops.

cond-mat.mes-hall↗

arXiv2001

Integer quantum Hall transition in the presence of a long-range-correlated quenched disorder

We theoretically study the effect of long-ranged inhomogeneities on the critical properties of the integer quantum Hall transition. For this purpose we employ the real-space renormalization-group (RG) approach to the network model of the transition. We start by testing the accuracy of the RG approach in the absence of inhomogeneities, and infer the correlation length exponent nu=2.39 from a broad conductance distribution. We then incorporate macroscopic inhomogeneities into the RG procedure. Inhomogeneities are modeled by a smooth random potential with a correlator which falls off with distance as a power law, r^{-alpha}. Similar to the classical percolation, we observe an enhancement of nu with decreasing alpha. Although the attainable system sizes are large, they do not allow one to unambiguously identify a cusp in the nu(alpha) dependence at alpha_c=2/nu, as might be expected from the extended Harris criterion. We argue that the fundamental obstacle for the numerical detection of a cusp in the quantum percolation is the implicit randomness in the Aharonov-Bohm phases of the wave functions. This randomness emulates the presence of a short-range disorder alongside the smooth potential.

cond-mat.mes-hall↗

arXiv2001

Random Resonators and Prelocalized Modes in Disordered Dielectric Films

Areal density of disorder-induced resonators with a high quality factor, $Q\gg 1$, in a film with fluctuating refraction index is calculated theoretically. We demonstrate that for a given $kl>1$, where $k$ is the light wave vector, and $l$ is the transport mean free path, when {\em on average} the light propagation is diffusive, the likelihood for finding a random resonator increases dramatically with increasing the correlation radius of the disorder. Parameters of {\em most probable} resonators as functions of $Q$ and $kl$ are found.

cond-mat.dis-nn↗

arXiv2001

Crossover Between Universality Classes in the Statistics of Rare Events in Disordered Conductors

The crossover from orthogonal to the unitary universality classes in the distribution of the anomalously localized states (ALS) in two-dimensional disordered conductors is traced as a function of magnetic field. We demonstrate that the microscopic origin of the crossover is the change in the symmetry of the underlying disorder configurations, that are responsible for ALS. These disorder configurations are of weak magnitude (compared to the Fermi energy) and of small size (compared to the mean free path). We find their shape explicitly by means of the direct optimal fluctuation method.

cond-mat.dis-nn↗

arXiv2001

Luminescence from highly excited nanorings: Luttinger liquid description

We study theoretically the luminescence from quantum dots of a ring geometry. For high excitation intensities, photoexcited electrons and holes form Fermi seas. Close to the emission threshold, the single-particle spectral lines aquire weak many-body satellites. However, away from the threshold, the discrete luminescence spectrum is completely dominated by many-body transitions. We employ the Luttinger liquid approach to exactly calculate the intensities of all many-body spectral lines. We find that the transition from single-particle to many-body structure of the emission spectrum is governed by a single parameter and that the distribution of peaks away from the threshold is universal.

cond-mat↗

arXiv2001

Random Lasing from Weakly Scattering Media: Universality in the Emission Spectra from Pi-Conjugated Polymer Films

When films of Pi-conjugated polymers are optically excited above a certain threshold intensity, then the emission spectrum acquires a multimode finely structured shape, which depends on the position of the excitation spot. We demonstrate that the power Fourier transform (PFT) of the emission spectrum exhibits a certain peak-like structure, which also depends on the excitation spot. Our intriguing observation is that averaging the individual PFTs does not lead to a structureless curve, but rather yields a series of distinct transform peaks. This suggests universality, namely that the underlying random resonators that are responsible for the laser emission from the pi-conjugated polymer film are almost identical. We argue that the reason for such an universality is the large size of a typical resonator, which we determined from the PFT, as compared to the emission wavelength, lambda. This fact is, in turn, a consequence of the large light mean free path, l* approximately 10 lambda in the polymer film. This contrasts previous observations of random lasing in powders, where l* approx. lambda. We develop a simple theory that explains the presence of peaks in the average PFT and predicts their shape. The results of the theory agree quantitatively with the data.

cond-mat.mes-hall↗

arXiv2001

Evidence for Braggoriton Excitations in Opal Photonic Crystals Infiltrated with Highly Polarizable Dyes

We studied angle-dependent reflectivity spectra of opal photonic crystals infiltrated with cyanine dyes, which are highly polarizable media with very large Rabi frequency. We show that when resonance conditions between the exciton-polariton of the infiltrated dye and Bragg frequencies exist, then the Bragg stop band decomposes into two reflectivity bands with a semi-transparent spectral range in between that is due to light propagation inside the gap caused by the existence of braggoriton excitations. These novel excitations result from the interplay interaction between the Bragg gap with spatial modulation origin and the polariton gap due to the excitons, and may lead to optical communication traffic inside the gap of photonic crystals via channel waveguiding.

cond-mat.mes-hall↗

arXiv2000

Coherent Umklapp Scattering of Light from Disordered Photonic Crystals

A theoretical study of the coherent light scattering from disordered photonic crystal is presented. In addition to the conventional enhancement of the reflected light intensity into the backscattering direction, the so called coherent backscattering (CBS), the periodic modulation of the dielectric function in photonic crystals gives rise to a qualitatively new effect: enhancement of the reflected light intensity in directions different from the backscattering direction. These additional coherent scattering processes, dubbed here {\em umklapp scattering} (CUS), result in peaks, which are most pronounced when the incident light beam enters the sample at an angle close to the the Bragg angle. Assuming that the dielectric function modulation is weak, we study the shape of the CUS peaks for different relative lengths of the modulation-induced Bragg attenuation compared to disorder-induced mean free path. We show that when the Bragg length increases, then the CBS peak assumes its conventional shape, whereas the CUS peak rapidly diminishes in amplitude. We also study the suppression of the CUS peak upon the departure of the incident beam from Bragg resonance: we found that the diminishing of the CUS intensity is accompanied by substantial broadening. In addition, the peak becomes asymmetric.

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