arXiv subjects

M. E. Raikh

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

At least 127 records · Page 7Linked to original sources

arXiv2000

Spin dynamics in nonlinear optical spectroscopy of Fermi sea systems

We discuss the role of many-body spin correlations in nonlinear optical response of a Fermi sea system with a deep impurity level. Due to the Hubbard repulsion between electrons at the impurity, the optical transitions between the impurity level and the Fermi sea states lead to an optically-induced Kondo effect. In particular, the third-order nonlinear optical susceptibility logarithmiclly diverges at the absorption threshold. The shape of the pump-probe spectrum is governed by the light-induced Kondo temperature, which can be tuned by varying the intensity and frequency of the pump optical field. In the Kondo limit, corresponding to off-resonant pump excitation, the nonlinear absorption spectrum exhibits a narrow peak below the linear absorption onset.

cond-mat↗

arXiv2000

Anomalous Coherent Backscattering of Light from Opal Photonic Crystals

We studied coherent backscattering (CBS) of light from opal photonic crystals in air at different incident inclination angles, wavelengths and along various [hkl] directions inside the opals. Similar to previously obtained CBS cones from various random media, we found that when Bragg condition with the incident light beam is not met then the CBS cones from opals show a triangular line shape in excellent agreement with light diffusion theory. At Bragg condition, however, we observed a dramatic broadening of the opal CBS cones that depends on the incident angle and [hkl] direction. This broadening is explained as due to the light intensity decay in course of propagation along the Bragg direction {\em before the first} and {\em after the last} scattering events. We modified the CBS theory to incorporate the attenuation that results from the photonic band structure of the medium. Using the modified theory we extract from our CBS data the light mean free path and Bragg attenuation length at different [hkl]. Our study shows that CBS measurements are a unique experimental technique to explore photonic crystals with disorder, when other spectroscopical methods become ambiguous due to disorder-induced broadening.

cond-mat.dis-nn↗

arXiv2000

The Aharonov-Bohm effect for an exciton

We study theoretically the exciton absorption on a ring shreded by a magnetic flux. For the case when the attraction between electron and hole is short-ranged we get an exact solution of the problem. We demonstrate that, despite the electrical neutrality of the exciton, both the spectral position of the exciton peak in the absorption, and the corresponding oscillator strength oscillate with magnetic flux with a period $Φ_0$---the universal flux quantum. The origin of the effect is the finite probability for electron and hole, created by a photon at the same point, to tunnel in the opposite directions and meet each other on the opposite side of the ring.

cond-mat.str-el↗

arXiv2000

Braggoriton--Excitation in Photonic Crystal Infiltrated with Polarizable Medium

Light propagation in a photonic crystal infiltrated with polarizable molecules is considered. We demonstrate that the interplay between the spatial dispersion caused by Bragg diffraction and polaritonic frequency dispersion gives rise to novel propagating excitations, or braggoritons, with intragap frequencies. We derive the braggoriton dispersion relation and show that it is governed by two parameters, namely, the strength of light-matter interaction and detuning between the Bragg frequency and that of the infiltrated molecules. We also study defect-induced states when the photonic band gap is divided into two subgaps by the braggoritonic branches and find that each defect creates two intragap localized states inside each subgap.

cond-mat↗

arXiv2000

Spin correlations in nonlinear optical response: Light-induced Kondo effect

We study the role of spin correlations in nonlinear absorption due to optical transitions from a deep impurity level to states above a Fermi sea. We demonstrate that the Hubbard repulsion between two electrons occupying the impurity state leads to a logarithmic divergence of the third-order nonlinear optical susceptibility at the absorption threshold. This divergence is a manifestation of the Kondo physics in the nonlinear optical response of Fermi sea systems. Remarkably, the light-induced Kondo temperature, which governs the shape of the Kondo-absorption spectrum, can be tuned by varying the intensity and frequency of the pump optical field. We also show that, for off-resonant pump excitation, the pump-probe spectrum exhibits a narrow peak below the linear absorption onset.

cond-mat↗

arXiv2000

Mesoscopic Cooperative Emission From a Disordered System

We study theoretically the cooperative light emission from a system of $N\gg 1$ classical oscillators confined within a volume with spatial scale, $L$, much smaller than the radiation wavelength, $λ_0=2πc/ω_0$. We assume that the oscillators frequencies are randomly distributed around a central frequency, $ω_0$, with some characteristic width, $Ω\llω_0$. In the absence of disorder, that is $Ω=0$, the cooperative emission spectrum is composed of a narrow subradiant peak superimposed on a wide superradiant band. When $Ω\neq 0$, we demonstrate that if $N$ is large enough, the subradiant peak is not simply broadened by the disorder but rather splits into a system of random narrow peaks. We estimate the spectral width of these peaks as a function of $N, L, Ω$, and $λ_0$. We also estimate the amplitude of this mesoscopic structure in the emission spectrum.

cond-mat↗

arXiv2000

Emission Spectrum of a Dipole in a Semi-infinite Periodic Dielectric Structure: Effect of the Boundary

The emission spectrum of a dipole embedded in a semi-infinite photonic crystal is calculated. For simplicity we study the case in which the dielectric function is sinusoidally modulated only along the direction perpendicular to the boundary surface plane. In addition to oscillations of the emission rate with the distance of the dipole from the interface we also observed that the shape of the emission spectrum srongly depends on the $\em initial$ $\em phase$ of the dielectric modulation. When the direction of light propagation inside the periodic structure is not normal to the boundary surface plane we observed aditional singularities in the emission spectrum, which arise due to different angle-dependence of the Bragg stop-band for $TE$ and $TM$ polarizations.

cond-mat↗

arXiv2000

Shallow Coulomb Gap and Weak Level-Level Correlations in a Deeply Insulating Electron System with Interactions

We consider a system of two-dimensional electrons strongly localized by disorder. Interactions create a gap in the average tunneling density of states $ν(E)$ at energies, E, close to the Fermi level. We derive a system of self-consistent equations for the correlators of local densities of occupied and empty states. When either the interactions are screened by the gate or the temperature, T, is high enough, so that the Coulomb gap is shallow, the perturbative solution of the system yields analytical expressions for the interaction-induced correction $δν(E)$ and the level-level correlator. We show that even with short-range interactions, $δν(E)$ exhibits a singular energy dependence at T=0. We also demonstrate that at high T this energy dependence is a universal function of the the ratio $E/T$. Regarding the level correlations, we trace how the correlator falls off as a function of spatial and energy separation between the levels. We also trace how the correlations vanish with increasing T. Our most noticeable observation is that for two close energies the correlator changes sign from positive (attraction) at small distances to negative (repulsion) at large distances.

cond-mat.mes-hall↗

arXiv1999

Does spin-orbit coupling play a role in metal-nonmetal transition in two-dimensional systems?

We propose an experiment, which would allow to pinpoint the role of spin-orbit coupling in the metal-nonmetal transition observed in a number of two-dimensional systems at low densities. Namely, we demonstrate that in a parallel magnetic field the interplay between the spin-orbit coupling and the Zeeman splitting leads to a characteristic anisotropy of resistivity with respect to the direction of the in-plane magnetic field. Though our analytic calculation is done in the deeply insulating regime, the anisotropy is expected to persist far beyond that regime.

cond-mat.mes-hall↗

arXiv1998

Chiral electromagnetic waves at the boundary of optical isomers: Quantum Cotton-Mouton effect

We demonstrate that the boundary of two optical isomers with opposite directions of the gyration vectors (both parallel to boundary) can support propagation of electromagnetic wave in the direction perpendicular to the gyration axes (Cotton-Mouton geometry). The components of electromagnetic field in this wave decay exponentially into both media. The characteristic decay length is of the order of the Faraday rotation length for the propagation along the gyration axis. The remarkable property of the boundary wave is its chirality. Namely, the wave can propagate only in one direction determined by the relative sign of non-diagonal components of the dielectric tensor in contacting media. We find the dispersion law of the boundary wave for the cases of abrupt and smooth boundaries. We also study the effect of asymmetry between the contacting media on the boundary wave and generalize the result to the case of two parallel boundaries. Finally we consider the arrangement when the boundaries form a random network. We argue that at a point, when this network percolates, the corresponding boundary waves undergo quantum delocalization transition, similar to the quantum Hall transition.

cond-mat.mes-hall↗

arXiv1998

Interaction-Induced Enhancement of Spin-Orbit Coupling in Two-Dimensional Electronic System

We study theoretically the renormalization of the spin-orbit coupling constant of two-dimensional electrons by electron-electron interactions. We demonstrate that, similarly to the $g$ factor, the renormalization corresponds to the enhancement, although the magnitude of the enhancement is weaker than that for the $g$ factor. For high electron concentrations (small interaction parameter $r_s$) the enhancement factor is evaluated analytically within the static random phase approximation. For large $r_s\sim 10$ we use an approximate expression for effective electron-electron interaction, which takes into account the local field factor, and calculate the enhancement numerically. We also study the interplay between the interaction-enhanced Zeeman splitting and interaction-enhanced spin-orbit coupling.

cond-mat.mes-hall↗

arXiv1998

Small-$q$ Anomaly in the Dielectric Function and High-Temperature Oscillations of Screening Potential in 2D Electron Gas with Spin-Orbit Coupling

We study the static dielectric function $ε(q)$ of 2D electron system with spin-orbit coupling in the frame of the random phase approximation. We demonstrate that, in addition to the well-known $2k_F$-Kohn anomaly, spin-orbit coupling gives rise to the novel anomaly in the dielectric function at small $q=q_0\ll k_F$, where $q_0$ is the distance between two Fermi surfaces. As a result of this anomaly a large-distance behavior of the potential from a point charge exhibits (in addition to the conventional Friedel oscillations) novel oscillations with a period $2π/q_0$. The remarkable feature of these oscillations is that they are not smeared out by the temperature. We show that the small-$q$ anomaly also modifies the indirect exchange interaction of localized magnetic moments (RKKY interaction). In the presense of spin-orbit coupling this interaction acquires a high-temperature component.

cond-mat.mes-hall↗

arXiv1997

Disorder-Induced Broadening of the Density of States for 2D Electrons with Strong Spin-Orbit Coupling

We study theoretically the disorder-induced smearing of the density of states in a two-dimensional electron system taking into account a spin-orbit term in the Hamiltonian of a free electron. We show that the characteristic energy scale for the smearing increases with increasing the spin-orbit coupling. We also demonstrate that in the limit of a strong spin-orbit coupling the diagrams with self-intersections give a parametrically small contribution to the self-energy. As a result, the coherent potential approximation becomes asymptotically exact in this limit. The tail of the density of states has the energy scale which is much smaller than the magnitude of the smearing. We find the shape of the tail using the instanton approach.

cond-mat.mes-hall↗

arXiv1997

Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach

We consider the network model of the integer quantum Hall effect transition. By generalizing the real--space renormalization group procedure for the classical percolation to the case of quantum percolation, we derive a closed renormalization group (RG) equation for the universal distribution of conductance of the quantum Hall sample at the transition. We find an approximate solution of the RG equation and use it to calculate the critical exponent of the localization length and the central moments of the conductance distribution. The results obtained are compared with the results of recent numerical simulations.

cond-mat.mes-hall↗

arXiv1996

``Splitting'' of Delocalized States in a Double--Layer System in a Strong Magnetic Field

A double--layer system in a strong perpendicular magnetic field is considered. We assume a random potential in each layer to be smooth. We also assume that there is no correlation between random potentials in different layers. Under these conditions the equipotential lines from different layers, corresponding to the same energy, may cross each other. We show that, if the tunnel coupling between the layers exceeds some characteristic value (which is much smaller than the width of the Landau level), then the probability for an electron to switch equipotential (and, thus, the layer) at the intersection is close to one. As a result, the structure of each delocalized state in a double--layer system becomes completely different from that for an isolated layer. The state is composed of alternating pieces of equipotentials from different planes. These combined equipotentials form a percolation network. We demonstrate that the regions, where equipotentials from different planes touch each other, play the role of saddle points for such a network. The energy separation between two delocalized states is of the order of the width of the Landau level, and the critical exponent of the localization length is $7/3$--the same as for an isolated layer.

cond-mat↗

arXiv1996

Exact shape of the lowest Landau level in a double--layer system and a superlattice with uncorrelated disorder

We extend Wegner's exact solution for the 2D density of states at the lowest Landau level with a short--range disorder to the cases of a double--layer system and a superlattice. For the double--layer system, an analytical expression for the density of states, illustrating the interplay between the tunnel splitting of Landau levels and the disorder--induced broadening, is obtained. For the superlattice, we derive an integral equation, the eigenvalue of which determines the exact density of states. By solving this equation numerically, we trace the disappearance of the miniband with increasing disorder.

cond-mat↗

arXiv1996

Randomly inhomogeneous Luttinger liquid: Fluctuations of the tunnel conductance

The Luttinger liquid in which the concentration of electrons varies randomly with coordinate is considered. We study the fluctuations of the tunnel conductance, caused by the randomness in the concentration. If the concentration changes slowly on the scale of the Fermi wavelength, its prime role reduces to the scattering of the plasmon waves, propagating along the system. As a result of such a scattering, plasmons get localized. We show that the localization length, $l_ω$, of a plasmon with frequency $ω$ is inverse proportional to the square of the interaction strength and changes with frequency as $l_ω\propto ω^{-2}$. If the relative variation of the concentration is small, the randomness--induced correction to the tunnel conductance, $δG(V)$, where $V$ is the applied bias, can be expressed through the spectral characteristics of the localized plasmons. The magnitude of the correction, $(\overline{ δG^2})^{1/2}/ G$, increases with $V$ as $\sqrt V$. The typical period of the fluctuations in $δG(V)$ is of the order of $V$. At a fixed $V$, the correlator of $δG$ at different points of the liquid falls off with distance as a power law and oscillates with the period which is one half of the wavelength of a plasmon with frequency $ω= eV/\hbar$.

cond-mat↗

arXiv1996

Tunneling into a periodically modulated Luttinger liquid

We study the tunneling into the edge of the Luttinger liquid with periodically modulated concentration of electrons. It is shown that the modulation,by causing a gap in the spectrum of plasmons, leads to an additional anomaly in the density of states at frequency corresponding to the center of the gap. The shape of the anomaly depends strongly on the {\em phase} of the modulation. The sensitivity to the phase is related to the plasmon mode, localized at the edge, its frequency lying within the gap (analog of the Tamm state for an electron in an interrupted periodic potential).

cond-mat↗