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A model for high Tc superconductivity in which polarons and bipolarons coexist is studied. The bipolarons are assumed to be in a bound or resonant state depending on the total charge carrier density and are allowed to decay into a pair of independent polarons. The critical temperature as a function of the total charge carrier density and of the ratio of the superconducting density to the superconducting charge carrier mass is calculated and compared with the experimental data. It is shown that the dependence on the total charge carrier density of the bipolaron resonant energy and of the bipolaron-polaron decay probability is important in order to obtain a satisfactory agreement with the experimental data.

A simple approach to the many-polaron problem for both weak and intermediate electron-phonon coupling and valid for densities much smaller than those typical of metals is presented. Within the model the total energy, the collective modes and the single-particle properties are studied and compared with the available theories. It is shown the occurrence of a charge density wave instability in the intermediate coupling regime., 26 pages, 12 figures. To appear on European Physical Journal B

We calculate the binding energy of a two-dimensional exciton for a set of states labelled by the quantum numberm associated to the angular momentum in the direction perpendicular to the surface. The Frohlich electron-phonon and hole-phonon interactions are taken into account. The statem=0 is more bound with respect to that obtained by the Wannier exciton theory with the screening given by the static dielectric constant and the reduced mass calculated by the electron and hole polaronic masses. The opposite effect is found for the statem=1,2,... Whenm becomes large, the hydrogenic series is recovered with the screening and reduced mass defined above. Our results are compared with the experimental data concerning exciton luminescence GaAs/Al x Ga1−x As, CuCl/CaF2 and CdTe/Cd1−x Zn x Te quantum wells.

The formation of spherical polaron clusters is studied within the Fr$\ddot{o}$hlich polaron theory. In a dilute polaron gas, using the non-local statistical approach and the polaron pair interaction obtained within the Pekar strong coupling theory, the homogeneous phase results to be unstable toward the appearance of polaron clusters. The physical conditions of formation for the clusters are determined calculating the critical values of electron-phonon interaction for which bound states in the collective polaron potential develop. Finally the sequence in the filling of the states is found and the stability of the clusters is assessed., Comment: 10 pages, 2 tables, 4 figures

The interplay of the electron-phonon interaction and of the double and super-exchange magnetic effects in the La 1-x Ca x MnO 3 perovskites with 0 < x < 0.5 is studied. It is shown that treating the electron-phonon interaction in a fully quantum manner in the intermediate electron-phonon coupling regime a charge density instability occurs near the metal-insulator transition, induced by either temperature or hole doping. Also the effects of the magnetic field and the oxygen isotope substitution on the phase diagram, the electron-phonon correlation function and the infrared absorption at x = 0.3 is studied. The lattice displacements show a strong correlation with the conductivity and the magnetic properties of the system. Finally the conductivity spectra are characterized by a marked sensitivity to the external parameters near the phase boundary.

The boson-fermion model is studied within the mean-field approximation including Pauli principle effects in the boson energy renormalization and Coulomb short-range repulsion among fermions and bosons. It is shown that there is a finite critical temperature at which Cooper pairing occurs accompanied by the divergence of the renormalized boson propagator at q = 0 and w = 0. The chemical potential, the entropy and the specific heat are also discussed. (C) 1998 Elsevier Science B.V. All rights reserved.

We investigate the effect of a phenomenological relaxation time on the magnetoplasma excitations of a 2D strip of electrons by using the scheme proposed in a previous paper. Particular attention is put on the lowest frequency mode which exhibits an "anomalous" dependence on the static magnetic field (perpendicular to the strip). We show that also the life time of the first mode has an anomalous dependence on the wavevector parallel to the strip and on the magnetic field.

The Green’s function method is used to study the problem of an impurity in a semi-infinite crystal. The connections between impurity and surface states are considered both from a general point of view and in specific models.

The electronic polaron model of the exciton is used to study the dielectric response of a medium to the excitation of a «core» level, by adopting the method of direct solution of the Eulerian functional variational equations. The dynamical response of the electronic polarization affects the electron-hole attraction and the exciton binding energy, in a way which depends on the basic parameters of the crystal (dielectric constant, effective masses, lattice parameter) through the core exciton radius and the polaron radius. When the former is much larger than the latter, static dielectric screening results. When the exciton radius is comparable to the polaron radius, the screening is reduced and the binding energy is increased. Core exciton binding energies are computed in a number of substances using the effective-mass approximation. Space dispersion of the dielectric function coupled to intervalley interaction may, however, contribute in some cases to reducing the excitonic radius and bringing about an instability to a deep state that would invalidate the effective-mass approximation.

The theory of the electronic states of crystals containing point defects in small concentration is reviewed and its application to the case of semiconductors is discussed. The basic properties of scattering and resonant and bound states are related to the band structure of the semiconductor. The form of the impurity potentials and the effect of the dielectric screening and deep levels are also discussed. Applications to the cases of donor acceptor and isoelectronic impurities are described, making use of the effective mass approximation and taking into account interband mixing and central cell corrections. Existing calculations are reviewed and compared with some of the experimentally known levels. Optical processes involving transitions between all types of electronic levels are described and experimental evidence for them is reported. Effects of external perturbations like uniaxial pressure, electric and magnetic fields are finally examined.

A realistic model to discuss resonant states in semiconductors as GaAs and InP is developed. Analytic expressions for the energies and the widths of the resonant states are found and compared with recent experimental optical results in InP. Es wird ein realistisches Modell zur Behandlung resorianter Zustande in Halbleitern wie GaAs und InP entwickelt. Analytische Ausdrucke der Energien und Rasonanzbreiten der Zustande werden berechnet und init neueren Ergebnissen ron optisclien Versuchen an InP verglichen.

The binding energies of exciton states in interaction with longitudinal optical phonons in polar materials are computed by using a phonon coherent state, the distribution function of which is obtained from an exact solution of the functional variational equation. We find an incomplete relaxation of the lattice and an increase of the binding energies with respect to those obtained with static dielectric screening when the polaron radius is comparable to the exciton radius. The case of anisotropic effective masses is also discussed. Transition probabilities are computed in first order for direct excitons with zero phonon and with phonon participation.

A significant correction to the value of the total exciton mass in polar materials results from the interaction of the electron and the hole with the longitudinal optical phonons. A procedure is given for computing this mass renormalization by means of the excitonic-polaron theory; numerical results are obtained for many substances. Evidence for this effect is found from a detailed analysis of experimental polariton dispersion data.

The coupling between the ionic and electronic motion is analysed in an unidimensional exact chemisorption problem. The influence of the ionic motion on the electron resonance and the modification of the bound-state equation of the ion are studied.

A general formulation of the theory of electron impurity states in a lattice in the extended zone scheme is presented. The dependence of the impurity states on the band structure is discussed, and it is shown that the existence of secondary extrema in the band structure may produce additional bound and resonant states. A prescription is given for computing such states and for estimating the probabilities of transitions to them from the ground state; some properties of these transition probabilities are discussed. Solutions of onedimensional models are presented explicitly.

The cross-section and the scattering amplitude from an impurity in a crystal are expressed, through formulae which are similar to the classical ones, in terms of quantities which present many ianalogies and some differences with respect to the usual phase shifts. The relations between these phase shifts and the poles of the Green’s function of the total Hamiltonian and other properties are also discussed.

The realistic model introduced in the previous paper is used to discuss resonant states in an imperfect cubic crystal; we consider resonances associated to the secondary extrema of the band structure located at theX-points of the Brillouin zone. It is shown that the inter-valley impurity interaction splits the threes states, associated to the nonequivalentX-minima into states withГ1 andГ3 symmetries; similarly, the ninep states are split into states withГ4 andГ5 symmetry. The lifetime of these states depends on the density of states of the band structure in the first Brillouin zone. The identification of theL-bands in alkali halides with transitions to such resonant states is discussed, in connection with the experimental results of many authors.

An extended crystal momentum representation is proposed and an alternative form of the Schrodinger equation in the crystal momentum representation (CMR) is given, which can be useful for strong impurity potentials. Moreover, properties of the operators and wave functions, which characterize such a representation, are discussed. Eine nichtreduzierte Kristallimpulsdarstellung wird vorgeschlagen und eine alternative Form der Schrodingergleichung in der Kristallimpulsdarstellung (CMR) gegeben, die fur starke Verunreinigungspotentiale nutzlich sein kann. Daruber hinaus werden die Eigenschaften der Operatoren und Wellenfunktionen, die solch eine Darstellung charakterisieren, diskutiert.

It is shown that exciton states with various total angular momenta (L = 0, 1, 2, 3) are differently affected by the interaction with LO phonons in polar materials. In particular, a dependence is found of the binding energy on the value of L not expected on the basis of the statically screened electron-hole attraction. Calculations for CuCl and other ionic compounds show that the lowest L = 1 state (n = 2) is less bound than the corresponding exciton state with static screening. This effect, which is opposite to the polaronic effect on the ground state, is still present for L ≧ 2 but it decreases with increasing L. The computed binding energies of 2p excitons compare favorably with the available experimental data. The method is also applied to the calculation of bipolaron binding energies. Es wird gezeigt, das in polaren Materialien Exzitonenzustande mit verschiedenen Gesamtdrehimpuls (L = 0, 1, 2, 3) unterschiedlich durch Wechselwirkung mit LO-Phononen beeinflust werden. Insbesondere wird eine Abhangigkeit der Bindungsnergie von der Grose von L gefunden, die aufgrund der statisch abgeschirmten Elektron-Loch-Anziehung nicht erwartet wird. Berechnungen fur CuCl und andere ionische Verbindungen zeigen, das der tiefste L = 1-Zustand (n = 2) schwacher gebunden ist, als der entsprechende Exzitonenzustand mit statischer Abschirmung. Dieser Effekt, der dem Polaroneneffekt im Grundzustand entgegengesetzt ist, ist noch fur L = 2 vorhanden, nimmt jedoch mit wachsendem L ab. Die berechneten Bindungsenergien der 2p-Exzitonen stimmen gut mit vorhandenen experimentellen Werten uberein. Die Methode wird auch auf die Berechnung der Bindungsenergien von Bipolaronen angewendet.

In this paper we study the electron-electron correlation in silicon anisotropic quantum dots. A variational approach to the problem of the quantum confinement of two electrons in an ellipsoidal quantum dot is presented. All the calculations are done as a function of the dot aspect ratio, showing how the Coulomb repulsion and dielectric effects (related to the dielectric mismatch between the dot and the surrounding medium) give rise to shape-dependent correlation effects. The energy needed to add a second electron to the ellipsoidal quantum dot is calculated and discussed as well.

The single particle spectrum of a charged particle in a nanometric ellipsoidal quantum dot is calculated taking also into account the surface polarization effects. Furthermore the optical properties of the absorption coefficient also depending on the light polarisation are discussed and compared with the experimental data.

We present a random-phase approximation calculation of the collective plasmon excitation spectrum of a one-dimensional electron gas confined in cylindrical and rectangular semiconductor quantum wires. The plasmon spectrum for the cylindrical case is calculated considering up to three occupied subbands. Taking into account the twofold angular degeneracy of the single-particle energy spectrum, we derive different expressions for the electron-electron interaction when opposite angular quantum numbers are involved. That occurrence leads, even in a two-subband system, to the presence of new undamped plasmon modes for q → 0 not exhibited in previous work. Comparing plasmon modes between cylindrical and rectangular quantum wires, we find an investigable shape-confinement effect for the intrasubband plasma excitation in the lowest subband.

The internal vibrational states of the large bipolaron are studied by using the strong coupling Bogolyubov-Tyablikov canonical transformation of coordinates, that takes into account the conservation of the total momentum of the system. The complete spectrum is explicitly calculated and the electronic and vibrational properties of the states are discussed. Moreover the comparison of the bipolaron ground state and the binding energies with the results of the path integral and the Lee-Low and Pines methods shows that the proposed approach provides a correct description of the large bipolaron even in the intermediate regime of the electron-phonon interaction.

The coexistence of large and small polarons in perovskitic materials is shown. The consequences on the infrared optical absorption coefficient are also discussed.

A single-particle Hamiltonian approach is used for describing dynamical screening of excitons in optically excited semiconductors. Upon considering a particular electron-hole pair, the excitation spectrum of all the other electrons and holes is replaced by a single plasmon mode omega (q). From a Frohlich-type Hamiltonian, 1s exciton binding energy and wavefunctions are calculated variationally with a generalization of the Lee-Low-Pines transformation. The advantage of the method, beside the simplicity, is that bandgap renormalization is accounted for within the same Hamiltonian so that a consistent comparison with experimental data is possible. In particular, our model reproduces both the remarkable persistence of the 1s GaAs exciton line under strong optical excitation and the measured transition density from bound to unbound states.

A first-principles calculation of the impurity screening in Si and Ge nanocrystals is presented. We show that isocoric screening gives results in agreement with both the linear response and the point-charge approximations. Based on the present ab initio results, and by comparison with previous calculations, we propose a physical real-space interpretation of the several contributions to the screening. Combining the Thomas-Fermi theory and simple electrostatics, we show that it is possible to construct a model screening function that has the merit of being of simple physical interpretation. The main point upon which the model is based is that, up to distances of the order of a bond length from the perturbation, the charge response does not depend on the nanocrystal size. We show in a very clear way that the link between the screening at the nanoscale and in the bulk is given by the surface polarization. A detailed discussion is devoted to the importance of local field effects in the screening. Our first-principles calculations and the Thomas-Fermi theory clearly show that in Si and Ge nanocrystals, local field effects are dominated by surface polarization, which causes a reduction of the screening in going from the bulk down to the nanoscale. Finally, the model screening function is compared with recent state-of-the-art ab initio calculations and tested with impurity activation energies.

The role of local fields in the optical response of silicon nanocrystals is analyzed using a tight binding approach. Our calculations show that, at variance with bulk silicon, local field effects dramatically modify the silicon nanocrystal optical response. An explanation is given in terms of surface electronic polarization and confirmed by the fair agreement between the tight binding results and that of a classical dielectric model. From such a comparison, it emerges that the classical model works not only for large but also for very small nanocrystals. Moreover, the dependence on size of the optical response is discussed, in particular treating the limit of large size nanocrystals., Comment: 4 pages, 4 figures

We report on a theoretical derivation of the electronic dielectric response of semiconductor nanocrystals using a tight-binding framework. Extending to the nanoscale the Hanke and Sham approach [Phys. Rev. B 12, 4501 (1975)] developed for bulk semiconductors, we show how local field effects can be included in the study of confined systems. A great advantage of this scheme is that of being formulated in terms of localized orbitals and thus it requires very few computational resources and times. Applications to the optical and screening properties of semiconductor nanocrystals are presented here and discussed. Results concerning the absorption cross section, the static polarizability and the screening function of InAs (direct gap) and Si (indirect gap) nanocrystals compare well to both first principles results and experimental data. We also show that the present scheme allows us to easily go beyond the continuum dielectric model, based on the Clausius-Mossotti equation, which is frequently used to include the nanocrystal surface polarization. Our calculations indicate that the continuum dielectric model, used in conjunction with a size dependent dielectric constant, underestimates the nanocrystal polarizability, leading to exceedingly strong surface polarization fields., Comment: 9 pages, 5 figures; corrected typos, added references

We introduce a very simple method to study the phase transition from the homogeneous dilute large polaron gas toward the formation of a cubic crystal within the framework of the Vlasov [Many-Particle Theory and its Applications to Plasma (Gordon and Breach, New York, 1962)] nonlinear kinetic equation and the equations for the Bogolyubov [Problems of Dynamic Theory in Statistical Physics. Selected Works on Statistical Physics (Moscow State University, Moscow, 1979)] distribution functions. Two different critical temperatures ${T}_{1}^{\mathrm{cr}}$ and ${T}_{2}^{\mathrm{cr}}$ are introduced, defining the range of stability of the crystal phase $({T}_{2}^{\mathrm{cr}}lTl{T}_{1}^{\mathrm{cr}})$. The existence and properties of the crystal phase are discussed as a function of the ionicity parameters of the medium, the electron-phonon Fr\"ohlich coupling constant and the density of the dilute polaron gas. In particular, the lattice parameter is found to increase when the ionicity of the medium decreases whereas it is independent of the Fr\"ohlich constant $\ensuremath{\alpha}$ and the polaron density. Furthermore, it increases upon decreasing the temperature from ${T}_{1}^{\mathrm{cr}}$ toward ${T}_{2}^{\mathrm{cr}}$, showing a behavior different from that observed for common solids. We find also that a drift velocity of the polaron gas tends to reduce the stability of the crystal. To illustrate the simplicity of the calculation scheme, we apply the same technique to study the formation of the argon (Ar) crystal starting from the atomic gas interacting through a reliable Lennard-Jones potential. We calculate the crystallization temperature and the Ar atom distribution. The lattice parameter is an increasing function of the temperature and the second critical temperature is not defined. We try to relate the different dependence on the temperature of the lattice parameter to the features of the polaron-polaron and atom-atom interactions.

The effect of organic adsorbates on the silicon (001) surface is investigated using first-principles calculations. Ethylene and a class of cyclopentene derivatives, containing different functional groups, are considered, all anchoring to the surface through the same $[2+2]$ cycloaddition mechanism. Because they all show similar bonding properties, any variation in the surface properties must be related to the functional group. The structural relaxation induced by the adsorption is discussed, elucidating the effect of both the adsorbate species and coverage. It turns out that different distortions occur in the molecular geometry, depending on both the species and the surface coverage, while molecule-to-surface bonding does show very similar features for all the considered molecules. We show that the presence of the adsorbate can modify the surface charge density, thus giving rise to an induced dipolar layer that modifies the electrostatic potential outside the surface. Such a dipole layer can, in turn, be related to surface electron affinity and work function changes. A careful analysis of the dipole moment and of the electrostatic potential changes is carried out discussing the correlations with the properties of the isolated molecules. All the results indicate how the surface properties can be tuned through a suitable choice of the adsorbate.

Using first-principle density-functional theory in the GGA approximation we have studied the electronic screening in semiconductor nanocrystals. Combining simple electrostatics and the Thomas-Fermi theory it is shown that an analytical and general form of a model position-dependent screening function can be obtained. Taking as a case study silicon nanocrystals, the relative weights of the nanocrystal core and surface polarization contribution to the screening are thoroughly discussed. The connection between the screening at the nanoscale and in the bulk is clarified.

In this work we show that the polaron effects in cylindrical quantum wires are function of the cylinder radius R-0 through the boundary conditions for both the ionic and the electronic motion and through the size dependence of the static and high frequency dielectric constants. We find that the dielectric constants are increasing functions of R-0. This fact and the different boundary conditions for the ions and the electrons have the final consequence that polaron self-energy can either be an increasing or a decreasing function of R-0.

In this paper we establish criteria of instability of the homogeneous large polaron gas versus the periodic state. We study, in the framework of the Bogolyubov approach of the equilibrium distribution functions, how this transition depends on the parameters of the polar medium (dielectric parameters, electron-phonon coupling constant, polaron density). The temperature dependence of the transition is analyzed, indicating that the stability of the periodic phase can be achieved in a given range of temperatures, depending on the material and the polaron density. The comparison of the total energies of the periodic and homogeneous phases does confirm that the stability of the periodic phase corresponds to the lowest-energy configuration.

The occurrence of polaronic behaviour in real solids is often accompanied by strong exchange and correlation effects in the electron gas besides being strongly entangled to the phononic degrees of freedom. Such effects can be relevant for the instability towards Wigner crystallization or charge density waves, or yet for the polaron role in high-T c superconductors and in manganites. The inclusion of exchange and correlation in the coupled electron-phonon system is thus highly desirable. In this work, we exploit the density functional theory and its time-dependent extension to construct an appropriate effective potential useful for studying the properties of interacting polarons. The validity and the possible developments of this approach are discussed, and future applications are proposed.

The optical properties of anisotropic quantum dots with ellipsoidal shape are investigated and discussed as a function of the dot aspect ratio. The energy spectrum ~ground and many excited states! is calculated and analyzed in comparison with the spherical quantum dot. The optical matrix elements in the dipole approximation and the oscillator strengths for the infrared transitions are shown. The main result is that optical processes significantly depend on the radiation polarization in contrast to nonpolarized processes observed for spherical quantum dots. The dot anisotropy is shown to play a fundamental role in determining the dot properties.

A simple approach to the many-polaron problem for both weak and intermediate electron-phonon coupling and valid for densities much smaller than those typical of metals is presented. Within the model, the collective excitation spectrum is studied pointing out the presence of charge density wave instabilities in a finite range of the electron densities. Finally, preliminary results on the optical absorption of an interacting large polaron gas are presented.

Within a recently proposed variational approach it has been shown that, in $La_{1-x}A_xMnO_3$ perovskites with $0, Comment: 9 figures

The polaron self-energy and the effective mass are studied around the Γ point of the Brillouin zone as a function of the bare electron band width Δ, the electron-phonon coupling constant α, and the density λ of other electrons. It is found that there are ranges of values of Δ, α and λ in which there is coexistence of polarons with small and large masses. The effect of such coexistence on the optical infrared absorbtion coefficient in polar materials is discussed.

We have developed a method, based on the effective mass approximation, for calculating electronic states in an arbitrarily shaped quantum nanostructure. Modelling the average porous silicon nanostructure with a deformed quantum wire, the calculated shallow impurity binding energies are in good agreement with surface photovoltage spectroscopy data. We have also studied a new type of surface carrier localization due to nanostructure surface geometrical irregularities. The implications of the existence of these trapping states are discussed for porous silicon.

The interplay of strong local electron-lattice and electron-electron interaction is analyzed in the two-dimensional Hubbard-Holstein model using an effective single band Hamiltonian. The effect of the strain field acting on the CuO2 plane and the local cooperative pseudo Jahn Teller vibronic electron-lattice coupling appropriate to cuprate superconductors at optimum doping (i.e.; at doping larger than 1/8) are included via the effective next near neighbor electronic hopping integral t′ (determined by the strain field) close to the local vibronic frequency ω0 (involved in the pseudo Jahn Teller electron lattice coupling). The system shows a characteristic feature of the physics of complex systems, the competition and fluctuation between two states: 1) a first phase of charges self trapped in domains with local lattice distortions (a generalization to a many polaron system of the idea of single intermediate polaron) and 2) a second phase of free carriers.

In this paper we investigate quantum confinement and electron-electron correlation in silicon deformed quantum wires. Starting from the single-particle picture, which shows the possibility of localizing one electron inside the wire deformation, we build a variational ansatz for the two-electron ground state. We compare the localizing effect induced by the deformation with the Coulomb repulsion, pointing out the existence of a two-electron confined ground state, depending on the wire geometry. On varying the geometrical parameters characterizing the wire deformation, it is possible to switch from structures dominated by the localization to structures in which the increase of the available volume makes the Coulomb contribution very relevant, as for ordinary quantum dots. The effects induced by the dielectric mismatch between the wire and the surrounding medium are included and discussed.

A new variational technique is developed to investigate the polaronic features of the Holstein Molecular Crystal Model. It is based on a linear superposition of Bloch states that describe large and small polaron wave functions. It is shown that this method provides a very good description of the regime characterized by intermediate values of the electron-phonon coupling constant (the so-called intermediate polaron) for any value of the adiabatic parameter $\omega_0/t$. The polaron ground state energy in one and two dimensions is calculated and successfully compared with the best estimates available providing a clear physical interpretation of the intermediate polaron. The band structure, the spectral weight of the ground state and the lattice displacement associated to the polaron are also calculated and discussed. The new method has the advantage to require a very little computational effort., Comment: 21 pages, 8 figures, to appear on Phys. Rev. B