Exciton polaritons and their one-dimensional localization in disordered quantum-well structures

A theory of the Anderson localization of light in randomly arranged ultrathin layers (quantum wells) uniform in lateral dimensions and possessing intrinsic optical resonances is put forward. To solve the multiple-scattering problem, a model of layers with a δ-function resonance dielectric polarization is proposed. The model is an electromagnetic counterpart of the electronic model of zero-radius potentials. Interlayer disorder is included under the assumption of a low average concentration of identical layers in order to calculate analytically the one-and two-photon characteristics of electromagnetic-radiation transport, in particular, the average energy density and the Anderson localization length of light. The analysis is carried out for a structure with randomly distributed quantum wells in which quasi-two-dimensional excitons of different quantum wells are in resonance while their wave functions do not overlap. It is shown that the average electromagnetic field propagates through this disordered structure in the form of polaritons but are produced in exciton reemission between quantum wells. The localization length of light in the polariton spectral region decreases substantially, because the scattering (reflection) of light by individual quantum wells grows near the excitonic resonance.     

Statistics of disordered chains

The statistical weights of the stationary states in various ensembles of isotopically disordered harmonic chains are compared. It is proven that the ensemble defined by boundary conditions at both ends of the chain is constructed with correct statistical weights as follows: One matches at sitei the stationary states of the ensemble defined by the boundary condition at one end and frequencyω with those of the ensemble defined by the boundary condition at the other end andω. Finally one integrates overω and sums over all sitesi. This confirms and substantiates the conjecture on the exponential localization of the eigenstates in one dimension. The matching procedure yields an equation for the density of states.     

Nonlinear charge transport mechanism in periodic and disordered DNA

We study a model for polaron-like charge transport mechanism along DNA molecules with emphasis on the impact of parametrical and structural disorder. Our model Hamiltonian takes into account the coupling of the charge carrier to two different kinds of modes representing fluctuating twist motions of the base pairs and H-bond distortions within the double helix structure of λ-DNA. Localized stationary states are constructed with the help of a nonlinear map approach for a periodic double helix and in the presence of intrinsic static parametrical and/or structural disorder reflecting the impact of ambient solvent coordinates. It is demonstrated that charge transport is mediated by moving polarons and breather compounds carrying not only the charge but also causing local temporal deformations of the helix structure through the traveling torsion and bond breather components illustrating the interplay of structure and function in biomolecules.     

Magnetooptical absorption in binary disordered alloys

The coherent potential approximation is used to compute the antisymmetric part (which depends linearly on the spin-orbital interaction) of the optical conductivity tensor of a disordered ferromagnetic alloy. The scattering of magnetized conduction electrons on the impurity potential of the alloy and on thermal vibrations of the lattice is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 95–99, September, 1976.In conclusion we would like to express our deep gratitude to E. I. Kondorskii for posing the problem and for a number of valuable comments during discussions of the results.     

Thermal conductivity of nonlinear waves in disordered chains

We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity κ(T). We find indications for an asymptotic low-temperature κ ∼ T ⁴ and intermediate temperature κ ∼ T ² laws. These findings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (Laptyeva et al, Europhys. Lett. 91, 30001 (2010)).     

Delocalization in disordered chains with random symmetrical impurities

We study in this paper, with the context of a tight-binding on-side model, the electronic properties of one-dimensional random lattices with correlated impurities. We show that, when symmetrical impurities are inserted in a host chain of site energy and a constant hopping interaction V, diffusion will occur even when is random. We provide analytic expressions for the transmittance and confirm the theoretical results by a great deal of numerical calculations. When = V, we find that the mean-square displacement (MSD) follows the law m ² ∝t ^β with β = 2.0 for = constant and β = 1.0 for = = random, respectively. Received 15 January 2001 and Received in final form 30 April 2001     

Exciton-polariton state in nanocrystalline SiC films

We studied the features of optical absorption in the films of nanocrystalline SiC (nc-SiC) obtained on the sapphire substrates by the method of direct ion deposition. The optical absorption spectra of the films with a thickness less than ~500 nm contain a maximum which position and intensity depend on the structure and thickness of the nc-SiC films. The most intense peak at 2.36 eV is observed in the nc-SiC film with predominant 3C-SiC polytype structure and a thickness of 392 nm. Proposed is a resonance absorption model based on excitation of exciton polaritons in a microcavity. In the latter, under the conditions of resonance, there occurs strong interaction between photon modes of light with λ_ph=521 nm and exciton of the 3С polytype with an excitation energy of 2.36 eV that results in the formation of polariton. A mismatch of the frequencies of photon modes of the cavity and exciton explains the dependence of the maximum of the optical absorption on the film thickness.     

Adsorption of polymer chains by disordered traps

We study the adsorption cross-over of ideal polymer chains in an environment of disordered traps. Starting from the assumption of an optimal cluster size of traps (optimal fluctuation method) we derive a general scaling form of the free energy function for arbitrary spatial dimensions. For small concentrations of traps we find a cross-over from localized (adsorbed) behavior to delocalized behavior depending on the chain's length and on the depth of the traps; this is connected with the non-monotonic behavior of the chain's extension. In terms of the free energy of the chain this cross-over resembles a first order transition scenario, the chain gets localized at many traps at once. Received 18 November 1998     

Spectral properties and scaling relations in off diagonally disordered chains

We obtain the localization lengthL as a function of the energyE and the disorder widthW for an off-diagonally disordered chain. This is done performing numerical simulations involving the continued fraction representations of the transfer matrix. The scaling relationL=W ^s is obtained with values of the exponents in agreement with calculations of other authors. We also obtain the relationL|E| ^v forE0, and use it in the Herbert-Spencer-Thouless formula forL to describe the singularity of the density of states nearE=0. We show that the slightest diagonal disorder obliterates this singularity. A practical method is presented to calculate the Green function by exploiting its continued fraction expansion.     

Scaling and universality in the optics of disordered exciton chains

The joint probability distribution of exciton energies and transition dipole moments determines a variety of optical observables in disordered exciton systems. We demonstrate numerically that this distribution obeys a one-parameter scaling, originating from the fact that both the energy and the dipole moment are determined by the number of coherently bound molecules. A universal underlying distribution is found, which is identical for uncorrelated Gaussian disorder in the molecular transition energies or in the intermolecular transfer interactions. The universality breaks down for disorder in the transfer interactions resulting from variations in the molecular positions. We suggest the possibility to probe the joint distribution by means of single-molecule spectroscopy.     

Exciton-polariton interference in thick crystals

A limiting transition between two solutions to the problem of total absorption in the region of exciton resonance in the presence of spatial dispersion (i.e., the solution considering a wave with lower absorption and the solution taking into account the exciton-polariton interference) is found. The crystal thicknesses at which the additional wave can be neglected are estimated. The dispersion relations for the bulk characteristics of dispersion and absorption are considered within the approximation obtained.     

Insulating phases and superfluid-insulator transition of disordered boson chains

Using a strong disorder real-space renormalization group, we study the phase diagram of a fully disordered chain of interacting bosons. Since this approach does not suffer from runaway flows, it allows a direct study of the insulating phases, not accessible in a weak disorder perturbative treatment. We find that the universal properties of the insulating phase are determined by the details and symmetries of the on-site chemical-potential disorder. Three insulating phases are possible: (i) an incompressible Mott glass with a finite superfluid susceptibility, (ii) a random-singlet glass with diverging compressibility and superfluid susceptibility, (iii) a Bose glass with a finite compressibility but diverging superfluid susceptibility. In addition to characterizing the insulating phases, we show that the superfluid-insulator transition is always described by Kosterlitz-Thouless-like flows.     

New class of level statistics in correlated disordered chains

We study the properties of the level statistics of 1D disordered systems with long-range spatial correlations. We find a threshold value in the degree of correlations below which in the limit of large system size the level statistics follows a Poisson distribution (as expected for 1D uncorrelated-disordered systems), and above which the level statistics is described by a new class of distribution functions. At the threshold, we find that with increasing system size, the standard deviation of the function describing the level statistics converges to the standard deviation of the Poissonian distribution as a power law. Above the threshold we find that the level statistics is characterized by different functional forms for different degrees of correlations.     

Light localization signatures in backscattering from periodic disordered media

The backscattering line shape is analytically predicted for thick disordered medium films where, remarkably, the medium configuration is periodic along the direction perpendicular to the incident light. A blunt triangular peak is found to emerge on the sharp top. The phenomenon roots in the coexistence of quasi-1D localization and 2D extended states.     

Light localization signatures in backscattering from periodic disordered media

The backscattering line shape is analytically predicted for thick disordered medium films where, remarkably, the medium configuration is periodic along the direction perpendicular to the incident light. A blunt triangular peak is found to emerge on the sharp top. The phenomenon roots in the coexistence of quasi-1D localization and 2D extended states. The text was submitted by the author in English.     

Multiphonon absorption of light in quantum-well systems in uniform electric and magnetic fields

The effect of a transverse electric field on the multiphonon absorption of light in quantum-well systems in a uniform magnetic field aligned parallel to the spatial quantization axis is investigated. It is shown that, when the interaction of an electron with long-wavelength vibrations is taken into account, the half-width of the absorption line does not depend on the electric-field vector E. As the electric field strength increases, the maximum of the light absorption shifts toward the long-wavelength range and decreases. The effect of the electric field on the shape of the zero-phonon line and first vibrational satellites is analyzed with due regard for the interaction of charge carriers with optical phonons. It is demonstrated in particular that the half-width of the zero-phonon line substantially depends on the electric-field vector E and can reach several millielectron-volts at the electric field strength E = 2 × 10⁴ V/cm.     

Ferromagnetism and Kondo insulator behavior in the disordered periodic Anderson model

The effect of binary alloy disorder on the ferromagnetic phases of f-electron materials is studied within the periodic Anderson model. We find that disorder in the conduction band can drastically enhance the Curie temperature T{c} due to an increase of the local f moment. The effect may be explained qualitatively and even quantitatively by a simple theoretical ansatz. The emergence of an alloy Kondo insulator at noninteger filling is also pointed out.