Searcharxiv⌕ Search

arXiv subjects

V. M. Apalkov

Publications and source records attributed to V. M. Apalkov.

At least 19 recordsLinked to original sources
arXiv2013

Incompressible States of Dirac Fermions in Graphene with Anisotropic Interactions

We report on the properties of incompressible states of Dirac fermions in graphene in the presence of anisotropic interactions and a quantizing magnetic field. We introduce the necessary formalism to incorporate the anisotropy in the system. The incopmpressible state in graphene is found to survive the anisotropy upto a critical value of the anisotropy parameter. The anisotropy also introduces two branches in the collective excitations of the corresponding Laughlin state. It strongly influences the short-range behavior of the pair-correlation functions in the incompressible ground state.

cond-mat.mes-hall↗
arXiv2005

Spin transitions in an incompressible liquid Coulomb coupled to a quantum dot

We report on our investigation of the low-lying energy spectra and charge density of a two-dimensional quantum Hall liquid at $ν=\frac25$ that is Coulomb coupled to a quantum dot. The dot contains a hole and two/three electrons. We found that any external perturbation (caused by the close proximity of the quantum dot) locally changes the spin polarization of the incompressible liquid. The effect depends crucially on the separation distance of the quantum dot from the electron plane. Electron density distribution in the quantum Hall layer indicates creation of a quasihole that is localized by the close proximity of the quantum dot. Manifestation of this effect in the photoluminescence spectroscopy is also discussed.

cond-mat.mes-hall↗
arXiv2004

Electron Dynamics in a DNA Molecule

We report on our theoretical investigations of the electronic states in a DNA molecule. We have used a two-leg charge ladder model where electron-electron interactions and the electron spin have been taken into account. The energy spectra for G-C and A-T base pairs obtained by numerically diagonalizing the Hamiltonian reveal a gap structure and the interaction is found to enhance the energy gaps. We also present the charge distribution in the ground state and low-lying excited states for the A-T and G-C base pairs.

cond-mat.dis-nn↗
arXiv2004

Transmission distribution, P(\ln T), of 1D disordered chain: low-T tail

We demonstrate that the tail of transmission distribution through 1D disordered Anderson chain is a strong function of the correlation radius of the random potential, $a$, even when this radius is much shorter than the de Broglie wavelength, $k_F^{-1}$. The reason is that the correlation radius defines the phase volume of the trapping configurations of the random potential, which are responsible for the low-$T$ tail. To see this, we perform the averaging over the low-$T$ disorder configurations by first introducing a finite lattice spacing $\sim a$, and then demonstrating that the prefactor in the corresponding functional integral is exponentially small and depends on $a$ even as $a \to 0$. Moreover, we demonstrate that this restriction of the phase volume leads to the dramatic change in the shape of the tail of ${\cal P}(\ln T)$ from universal Gaussian in $\ln T $ to a simple exponential (in $\ln T $) with exponent depending on $a$. Severity of the phase-volume restriction affects the shape of the low-$T$ disorder configurations transforming them from almost periodic (Bragg mirrors) to periodically-sign-alternating (loose mirrors).

cond-mat.dis-nn↗
arXiv2004

Effective Drag Between Strongly Inhomogeneous Layers: Exact Results and Applications

We generalize Dykhne's calculation of the effective resistance of a 2D two-component medium to the case of frictional drag between the two parallel two-component layers. The resulting exact expression for the effective transresistance, $ρ^D_{eff}$, is analyzed in the limits when the resistances and transresistances of the constituting components are strongly different - situation generic for the vicinity of the {\em classical} (percolative) metal-insulator transition (MIT). On the basis of this analysis we conclude that the evolution of $ρ^D_{eff}$ across the MIT is determined by the type of correlation between the components, constituting the 2D layers. Depending on this correlation, in the case of two electron layers, $ρ^D_{eff}$ changes either monotonically or exhibits a sharp maximum. For electron-hole layers $ρ^D_{eff}$ is negative and $|ρ^D_{eff}|$ exhibits a sharp minimum at the MIT.

cond-mat.dis-nn↗
arXiv2004

Universal Fluctuations of the Random Lasing Threshold in a Sample of a Finite Area

We consider the random lasing from a weakly scattering medium and demonstrate that the distribution of the threshold gain over the ensemble of statistically independent finite-size samples is universal. Universality stems from the facts that: (i) lasing threshold in a given sample is determined by the highest-quality mode of all the random resonators present in the sample, and (ii) the areal {\em density} of the random resonators decays sharply with the quality factor of the mode that they trap. We find analytically the shape of the universal distribution function of the lasing threshold. The shape of this function is governed by a single dimensionless parameter, $β$. This parameter increases as a power law with $\ln S$, where $S$ is the sample area (length, volume), and decreases as a power law with disorder strength. The powers depend on the microscopic mechanism of the light trapping. As a result, the distribution of the thresholds narrows with $S$ and broadens with the disorder strength.

cond-mat.dis-nn↗
arXiv2004

Spin-orbit-induced correlations of the local density of states in two-dimensional electron gas

We study the local density of states (LDOS) of two-dimensional electrons in the presence of spin-orbit (SO) coupling. Although SO coupling has no effect on the average density of states, it manifests itself in the correlations of the LDOS. Namely, the correlation function acquires two satellites centered at energy difference equal to the SO splitting, $2ω_{SO}$, of the electron Fermi surface. For a smooth disorder the satellites are well separated from the main peak. Weak Zeeman splitting $ω_{Z} \ll ω_{SO}$ in a parallel magnetic field causes an anomaly in the shape of the satellites. We consider the effect of SO-induced satellites in the LDOS correlations on the shape of the correlation function of resonant-tunneling conductances at different source-drain biases, which can be measured experimentally. This shape is strongly sensitive to the relation between $ω_{SO}$ and $ω_{Z}$.

cond-mat.dis-nn↗
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

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

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.

cond-mat.mes-hall↗
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

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

Two-phonon scattering of magnetorotons in fractional quantum Hall liquids

We study the phonon-assisted process of dissociation of a magnetoroton, in a fractional quantum Hall liquid, into an unbound pair of quasiparticles. Whilst the dissociation is forbidden to first order in the electron-phonon interaction, it can occur as a two-phonon process. Depending on the value of final separation between the quasiparticles, the dissociation is either a single event involving absorption of one phonon and emission of another phonon of similar energy, or a two-phonon diffusion of a quasiexciton in momentum space. The dependence of the magnetoroton dissociation time on the filling factor of the incompressible liquid is found.

cond-mat.mes-hall↗
arXiv2001

Phonon-assisted luminescence of magnetoexcitons in semiconductor quantum wells

We consider a line-shape of magnetoexciton photoluminescence from quantum wells when the disorder is sufficiently small. In this case the phonon-assisted optical transitions become important for the line formation. We study both inter-band and intra-band excitons. For inter-band excitons the width of a single peak emission line is calculated as a function of temperature and quantum well width. For intra-band excitons the double peak of the emission line is predicted when the electron filling factor is odd and greater or equal to three. In the latter case the lowest magnetoexciton dispersion curve has a minimum at non-zero momentum. Then the higher-energy peak results from the direct optical emission of zero-momentum excitons. The origin of the lower-energy peak is the phonon-assisted transitions from the non-zero momentum exciton states. With increasing temperature, the higher-energy peak becomes more pronounced and the lower-energy peak vanishes.

cond-mat.mes-hall↗
arXiv2001

Electron-phonon interaction in a two-subband quasi-2D system in a quantizing magnetic field

We predict a double-resonant feature in the magnetic field dependence of the phonon-mediated mobility of a two-subband quasi-two-dimensional electron system. These resonances take place when two Landau levels corresponding to different size-quantized subbands are close to each other but do not coincide. We also discuss the effect of non-equilibrium phonons. Rabi-like oscillations of electron population and emission of the phonons at new frequencies are predicted.

cond-mat.mes-hall↗