Acousto-exciton interaction in a gas of 2D indirect dipolar excitons in the presence of disorder

A theory for the linear and quadratic responses of a 2D gas of indirect dipolar excitons to an external surface acoustic wave perturbation in the presence of a static random potential is considered. The theory is constructed both for high temperatures, definitely greater than the exciton gas condensation temperature, and at zero temperature by taking into account the Bose–Einstein condensation effects. The particle Green functions, the density–density correlation function, and the quadratic response function are calculated by the “cross” diagram technique. The results obtained are used to calculate the absorption of Rayleigh surface waves and the acoustic exciton gas drag by a Rayleigh wave. The damping of Bogoliubov excitations in an exciton condensate due to theirs scattering by a random potential has also been determined.     

Complex random matrix models with possible applications to spin-impurity scattering in quantum Hall fluids

We study the one-point and two-point Green functions in a complex random matrix model to sub-leading orders in the large-N limit. We take this complex matrix model as a model for the two-state scattering problem, as applied to spin-dependent scattering of impurities in quantum Hall fluids. The density of state shows a singularity at the band center due to reflection symmetry. We also compute the one-point Green function for a generalized situation by putting random matrices on a lattice of arbitrary dimensions.     

Transport and cyclotron resonance theory for GaAs-AlGaAs heterostructures

A theory for static and dynamic transport of a two-dimensional electron gas in GaAs-AlGaAs heterostructures at temperature zero is presented. Charged impurities, separated from the electron gas by a spacer layer, are considered as the dominant scattering mechanism. Finite extension of the wave function of the two-dimensional electron gas is taken into account. Multiple scattering effects are included and are shown to lead to a metal insulator transition at low electron densities. Due to plasmon dynamics the scattering is strongly frequency dependent, and this dissipative process determines the width of the cyclotron resonance. The corresponding reactive effect determines the shift of the cyclotron resonance. It is shown that a correlation between line width maximum and zero frequency shift of the cyclotron mode exists, in agreement with experimental results.     

Bulk plasma waves in a randomly inhomogeneous conductor

The modification of the spectrum and damping of bulk plasma waves due to three-dimensional random inhomogeneities of the density of a degenerate electron gas in a conductor have been investigated using the averaged Green??s function method. The dependences of the frequency and damping of the averaged plasma waves, as well as the position ?? _m and width ???? of the peak of the imaginary part of the Fourier trans-form of the averaged Green??s function, on the wave vector k have been determined in the self-consistent approximation, which makes it possible to take into account multiple scattering of plasma waves by inhomogeneities. It has been found that, in the long-wavelength region of the spectrum, the decrease revealed in the frequency of the plasma waves is caused by the inhomogeneities, which agrees qualitatively with the behavior of the position of the peak ?? _m . In the range of large values of the correlation length of inhomogeneities and small values of k, the damping of the plasma waves tends to zero, whereas the width of the peak ???? remains finite, which is due to the nonuniform broadening. A comparison with the data of numerical calculations has been performed.     

Fully quantum treatment of the Landau-Pomeranchik-Migdal effect in QED and QCD

A rigorous quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD is given for the first time. The rate of photon (gluon) radiation by an electron (quark) in a medium is expressed in terms of the Green’s function of a two-dimensional Schrödinger equation with an imaginary potential. In QED this potential is proportional to the dipole cross section for scattering of an e ⁺ e ^? pair off an atom, while in QCD it is proportional to the cross section of interaction of the color singlet quark-antiquark-gluon system with a color center.     

Rigorous mean-field model for coherent-potential approximation: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner'sn-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites, but free. Freeness of random variables is an analog of the concept of independence for noncommuting random operators. A possible realization is the ensemble of randomly rotated matrices at different lattice sites. The one- and two-particle Green functions of the proposed Hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is novanishing everywhere inside the band. The long-range behavior and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multisite) model is a rigorous mean-field model for the (single-site) CPA. We show how the Lloyd model is included in our model and treat various kinds of noises.     

Diffusion of charged particles in strong large-scale random and regular magnetic fields

The nonlinear collision integral for the Green’s function averaged over a random magnetic field is transformed using an iteration procedure taking account of the strong random scattering of particles on the correlation length of the random magnetic field. Under this transformation the regular magnetic field is assumed to be uniform at distances of the order of the correlation length. The single-particle Green’s functions of the scattered particles in the presence of a regular magnetic field are investigated. The transport coefficients are calculated taking account of the broadening of the cyclotron and Cherenkov resonances as a result of strong random scattering. The mean-free path lengths parallel and perpendicular to the regular magnetic field are found for a power-law spectrum of the random field. The analytical results obtained are compared with the experimental data on the transport ranges of solar and galactic cosmic rays in the interplanetary magnetic field. As a result, the conditions for the propagation of cosmic rays in the interplanetary space and a more accurate idea of the structure of the interplanetary magnetic field are determined.     

Optical conductivity in a 2D model of the pseudogap state

A 2D model of the pseudogap state is considered on the basis of the scenario of strong electron scattering by short-range-order fluctuations of the “dielectric” (antiferromagnetic or charge density wave) type. A system of recurrence relations is constructed for a one-particle Green’s function and the vertex part, describing the interaction of electrons with an external field. This system takes into account all Feynman diagrams for electron scattering at short-range-order fluctuations. The results of detailed calculations of optical conductivity are given for various geometries (topologies) of the Fermi surface, demonstrating both the effects of pseudogap formation in the electron spectrum and the localization effects. The obtained results are in qualitative agreement with experimental data for underdoped HTSC cuprates.     

Anderson localization in strongly coupled disordered electron–phonon systems

Based on the statistical dynamic mean-field theory, we investigate, in a generic model for a strongly coupled disordered electron–phonon system, the competition between polaron formation and Anderson localization. The statistical dynamic mean-field approximation maps the lattice problem to an ensemble of self-consistently embedded impurity problems. It is a probabilistic approach, focusing on the distribution instead of the average values for observables of interest. We solve the self-consistent equations of the theory with a Monte Carlo sampling technique, representing distributions for random variables by random samples, and discuss various ways to determine mobility edges from the random sample for the local Green function. Specifically, we give, as a function of the ‘polaron parameters’, such as adiabaticity and electron–phonon coupling constants, a detailed discussion of the localization properties of a single polaron, using a bare electron as a reference system.     

Statistical mechanics of “atoms” in hot,partially ionized matter: The theory of the one electron green function

We have considered the problem of calculating the one electron Green function for hot, partially ionized condensed matter as a means of computing the statistical thermodynamics and transport properties of the system. Abandoning the Wigner-Seitz sphere and using instead the correlation sphere defined by the ion-ion correlation length of the system we define a reference model for calculating the Hartree-Fock (H-F) states of the system. No ion microfields are needed. The reference model naturally gives rise to a static ion-micropotential. This, plus the electron H-F Hamiltonian is diagonalized to give the solutions of the reference model. Next, we consider the corrections to the energy levels arising from the dynamically screened charge density fluctuations of the system with its bound and free electrons, ions, and also taking into account the effect of the non-uniform distributions prevailing within the correlation sphere. By identifying response function like components in the mass operator and replacing them by their hydrodynamic approximations the screened 2nd order mass operator is obtained in a very tractable form. This 2nd order mass operator could be converted to an all-order form using a non-linear ion-electron pseudopotential V_ie. The construction of V_ie and the effective non-linear ion-ion potential V_i?i needed for calculating the ion-ion structure factor are considered. The effect of the inhomogeneities is brought in through these structure factors S(q, Q) which enter naturally into the theory. The final expressions provide, for example, an explicit formula for the correlation effects arising from ion dynamics and contributing to the position and width of the electronic levels of an “atom” immersed in a plasma.     

On calculation of electronic states in disordered alloys

A new representation of the Green function for a disordered multicomponent substitution alloy is proposed, using which it is easy to separate one-, two-, etc. contributions to this Green function in corresponding equations. Due to this representation we succeed in obtaining common expressions for the configurationally averaged electron Green function with allowance for the electron scattering on clusters formed by an arbitrary number of atoms. The approach used is equally appropriate to described alloys both in the weak binding model, and in the tight binding one.     

On the acoustic wave attenuation in a turbulent medium

The equation for the mean acoustic field has been obtained for a random turbulent medium using the Green function approach. The correlation function was described by the Karman distribution with the index n=2 approximately≃11/6. Applying Bourret's approximation, the exact expression for the mass operator has been calculated analytically. The frequency dependence of the scattering coefficient of the mean field has been derived. Conditions of Cherenkov radiation are discussed.     

The influence of the surface roughness on dielectric function of two-dimensional electron gas: a Lindhard model approach

Low field response function calculations have been performed on a two-dimensional electron gas with well-defined electron-surface roughness scattering. The Lindhard model was employed to compute the response function. In particular, detailed investigations were made on the system searching for an interplay between surface roughness with well-defined correlation function, (characterizes by asperity height and correlation length) spatial confinement and the dielectric function. We analyze to what extent the normal behavior and functionality of dielectric function of two-dimensional devices are modified by random scattering events caused by the contribution from the surface roughness. Results of the current work indicate that contribution of the surface roughness on scattering and absorption process could not be considered as an underestimating effect. We find, however, that functionality of the dielectric function seems to be quite independent of the particular roughness features.     

Interaction of long wavelength phonons with conduction electrons in impure metals

A formalism is developed to treat the interaction between electrons and the currents set up in a metal by the motion of the ions by many body techniques. As is known from the theories of ultrasonic absorption this interaction is important for the damping of transverse phonons. To write the interaction Hamiltonian in a convenient form we introduce a 4-component quantized electromagnetic field. This allows us to treat longitudinal and transverse phonons in a completely analogous fashion. Impurities, which act as scattering centers for electrons, are included in the theory. The Fourier transformv(p) of the impurity potential is taken to be an arbitrary function of momentump. A set of diagrams in the perturbation expansion of the phonon Green function is discussed that for constantv(p) yields well established expressions for the absorption coefficients of ultrasound.     

Magnetic and electric phase transitions in the Hubbard model

Within the Hubbard model, two boson Green’s functions that describe the propagation of collective excitations of the electronic system—magnons (states with a single electron spin flip) and doublons (states with two electrons at one site of the crystal lattice)—are calculated for a Coulomb interaction of arbitrary strength and for an arbitrary electron concentration by applying a decoupling procedure to the double-time X-operator Green’s functions. It is found that the magnon and doublon Green’s functions are similar in structure and there is a close analogy between them. Instability of the paramagnetic phase with respect to spin ordering is investigated using the magnon Green’s function, and instability of the metallic phase to charge ordering is analyzed with the help of the doublon Green’s function. Criteria for the paramagnet-ferromagnet and metal-insulator phase transitions are found.     

Spontaneous emission and elastic scattering of light from quantum-well excitons in a Fabry-Perot microcavity

A theory of spontaneous emission and elastic light scattering by quasi-two-dimensional excitons in a quantum well placed in a Fabry-Perot microcavity is developed. The problem is solved by means of electrodynamic Green’s functions with inclusion of fluctuations of the quantum-well width and cavity wall shape treated as a perturbation. General expressions are found in a zero approximation of perturbation theory (plane interfaces) for the radiative decay rates of quasi-two-dimensional excitons and for their energy shifts in the cavity. The boundary conditions for the electromagnetic field are taken into account through the coefficients of inward light reflection from the cavity walls. Resonance contributions to the scattering cross sections, which differ in the polarizations (p or s) of the incident and scattered waves, are derived in the lowest (Born) approximation in quantum-well width fluctuations. The spectral and angular dependences of elastic light scattering are studied numerically for Gaussian and exponential correlation functions. It is shown that the contribution from quantum-well width fluctuations to light scattering exceeds that due to single interfaces (surfaces) of a heterostructure by two orders of magnitude.     

Critical temperature of metallic hydrogen sulfide at 225-GPa pressure

The Eliashberg theory generalized for electron—phonon systems with a nonconstant density of electron states and with allowance made for the frequency behavior of the electron mass and chemical potential renormalizations is used to study T _c in the SH₃ phase of hydrogen sulfide under pressure. The phonon contribution to the anomalous electron Green’s function is considered. The pairing within the total width of the electron band and not only in a narrow layer near the Fermi surface is taken into account. The frequency and temperature dependences of the complex mass renormalization ReZ(ω), the density of states N(ε) renormalized by the electron—phonon interactions, and the electron—phonon spectral function obtained computationally are used to calculate the anomalous electron Green’s function. A generalized Eliashberg equation with a variable density of electron states has been solved. The frequency dependence of the real and imaginary parts of the order parameter in the SH₃ phase has been obtained. The value of T _c ≈ 177 K in the SH₃ phase of hydrogen sulfide at pressure P = 225 GPa has been determined by solving the system of Eliashberg equations.     

On the acoustic wave attenuation in a turbulent medium

Abstract

The equation for the mean acoustic field has been obtained for a random turbulent medium using the Green function approach. The correlation function was described by the Karman distribution with the index n=2 approximately?11/6. Applying Bourret's approximation, the exact expression for the mass operator has been calculated analytically. The frequency dependence of the scattering coefficient of the mean field has been derived. Conditions of Cherenkov radiation are discussed.     

Spatial correlation of an electron and hole in quasi-two-dimensional electronic system in a strong magnetic field and its relationship to the light-scattering tensor

The spatial correlation of light-generated electrons and holes in a quasi-two-dimensional electron gas in a strong magnetic field is investigated in an approximation linear in the intensity of the exciting light. The correlation is due to the interaction of the electrons and holes with longitudinal optical (LO) phonons. The theory permits calculating, on the basis of a special diagrammatic technique, two distribution functions of an electron-hole pair with respect to the distance between the electron and the hole after the emission of N phonons: first, the function determining the total number of pairs which have emitted N phonons and, second, the function related to the rank-4 light-scattering tensor in interband resonance Raman scattering of light. A special feature of the system is that the electron and hole energy levels are discrete. The calculation is performed for a square quantum well with infinitely high barriers. The distribution function and the total number of electron-hole pairs before the emission of phonons as well as the distribution function corresponding to two-phonon resonance Raman scattering are calculated. The theory predicts the appearance of several close-lying peaks in the excitation spectrum under resonance conditions. The number of peaks is related to the number of the Landau level participating in the optical transition. The distance between peaks is determined by the electron-phonon coupling constant. Far from resonance there is one peak, which is much weaker than the peaks obtained under resonance conditions. Zh. éksp. Teor. Fiz. 111, 2194–2214 (June 1997)