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We carried out a theoretical study of the rutile TiO2(110) surface using ab initio techniques. We investigate the effects of both surface and subsurface defects. These defects consist of a missing oxygen atom in the crystalline structure, the oxygen vacancy. We show that the defect formation energy of oxygen vacancies strongly depends on the position of the defect in the material. Our results imply that subsurface defects could play a role in the reactivity of the surface. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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.

In this paper we present a variational technique for calculating the energy levels in a confined system with a complex shape and finite boundary conditions. The general method is applied to the case of a deformed cylindrical quantum wire and it is shown that in this case the single particle Schrödinger equation can be reduced to a set of coupled one-dimensional equations. These equations, containing an effective potential depending on the wire geometry and boundary conditions, can be solved by means of a perturbation expansion. It is shown that the calculated perturbation corrections become important only when a sharp deformation is considered.

We report on our effective mass calculations for a particle confined in an ellipsoidal quantum dot. Upon using a curvilinear coordinates system, the single particle exact eigenvalues and eigenfunctions have been numerically calculated. Dielectric image effects have been properly taken into account. It is shown that on keeping the volume constant, the confinement energies depend only on the dot shape. The implications of this shape dependence are analyzed for the infrared optical properties.

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.

Abstract:: 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.

Abstract:: The normal state conductivity, σ(ω), of a system of interacting large polarons is calculated within the Random Phase approximation and some numerical results are presented. The behaviour of the optical absorption as a function of the charge carrier density and of the temperature is analyzed for different values of the electron-phonon coupling constant. It is shown that σ(ω)exhibits features similar to those observed in the infrared spectra of the cuprates.

Abstract:: 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.

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 ω=0. The chemical potential, the entropy and the specific heat are also discussed.

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. Si usa il metodo delle funzioni di Green per studiare il problema degli stati elettronici di impurezza in un cristallo semiinfinito. Si considerano le connessioni tra stati di impurezza e di superficie sia dal punto di vista generale che in modelli specifici. Метод функций Грина используется для исследования проблемы примеси в полубесконечном кристалле. Рассматриваются всязи между примесными и поверхностными состояниями с общей точки зрения и в рамках специальных моделей.

The dielectric function of multivalley conduction electron systems is studied taking into account both the intravalley and the intervalley matrix elements. A direct application is performed for the six-valley silicon case. It is shown that the dielectric function takes the form of a sum of Lindhard-type terms, each one related to a pair of valleys. Analytical approximations for the static and dynamical cases are proposed. It is shown that while in the static case the intervalley contributions are negligible, in the dynamical case they lead to composite plasma dispersion of acoustic type for q → 0. New analytical approximate plasma dispersion formulae are presented and it is shown that the acoustic behavior can be interpreted within a two-component plasma model where to the intervalley contributions an effective mass lighter than the band mass is associated.

We solve exactly and numerically the Schrödinger equation when an atom goes towards a metallic surface in the jellium model. The position of the resonance and its width are discussed in varying the screening of the potential and its distance from the surface. Si risolve esattamente con tecniche numeriche l'equazione di Schrödinger di un atomo di idrogeno che si avvicina ad una superficie metallica in un modello a jellium del solido. Si discutono la posizione e l'ampiezza della risonanza al variare sia della distanza tra impurezza e superficie sia dello schermaggio del potenziale di impurezza. Мы решаем уравнение Шредингера точно и численно, когда атом приближается к металлической поверхности. Обсуждаются положение резонанса и его ширина в зависимости от экранирования потенциала и расстояния атома от поверхности.

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. Si studia l'accoppiamento tra il moto elettronico ed ionico in un esatto modello unidimensionale per il problema del chemiassorbimento. Si studia la modificazione della risonanza elettronica e dell'equazione per gli stati legati dello ione. В рамках точной одномерной модели анализируется связь между движением электронов и ионов в проблеме хемосорбции. Исследуется влияние движения ионов на электронный резонанс. Рассматривается модификация уравнения связанного состояния.

A set of integral equations for the transverse and longitudinal electromagnetic fields is obtained, which describes the evolution of an incoming free field on a spatially dispersive metal. Boundary conditions are discussed when a plasmonic mode too is propagating. Si costruisce un sistema di equazioni integrali per le parti longitudinale e trasversa dei campi elettromagnetici che descrive la propagazione del campo in un metallo spazialmente dispersivo. Si discutono le condizioni al contorno quando è presente anche un modo plasmonico. Получается система интегральных уравнений для поперечного и продольного электромагнитных полей, которые описывают эволюцию падающего свободного поля на металл с пространственной дисперсей. Обсуждаются граничные условия в том случае, когда распространяется и плазмонная мода.

The polaron band theory of Lee, Low and Pines is extended beyond the effective mass approximation to a general form of the electron–phonon interaction within two different self-consistent schemes. In the first one a variational Bloch state depending on the polaron crystalline momentum is used to study polaron features taking into account umklapp processes. In particular, the self-energy and the effective mass at the Γ point of the Brillouin zone are calculated as functions of the electron–phonon coupling constant α. It is found that a sudden transition of these quantities from a large band to a narrow band polaron behaviour occurs at a critical value αc. Such value increases indefinitely with the bare electron band width; moreover the transition becomes sharper. The theory recovers, as particular cases, a) the Lee-Low-Pines regime valid for small α and large electron band width Δ˜(Δ˜ ≫ ħω and b) the Holstein limit for large α and small band width (Δ˜ ≫ ħω). This occurs as result of the competing role of α and Δ˜. In the second scheme, the electron–phonon interaction is considered only in a single elementary cell and the self-trapped polaron state is calculated self-consistently. It is shown that, if only one electronic band is taken into account, such state becomes a Δ function with infinitely negative energy when α is larger than a critical value depending on the electron band width. To avoid this fact, electronic band states of higher energy must be considered. Finally, through the tight-binding method, the polaron band is set up. It is shown that at the Γ point of the Brillouin zone, the contribution of the higher electronic bands prevents the self-energy and the polaron mass to have a sharp increase from the large to the narrow band regime.

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.

The phase-transition phenomenon in an interacting Bose system with a pair Hamiltonian is studied. For fixed density two temperaturesT1

A model, unique for all alkali halides, is built up, which gives energies for theFandKtransitions in good agreement with the experimental results, both in absorption and in emission. In this model theL-bands must correspond to transitions in the conduction band. Viene presentato un modello, unico per tutti gli alogenuri alcalini, che dà energie di transizione per le bandeFeKin buon accordo con i risultati sperimentali, sia in assorbimento che in emissione. In questo modello le bandeLdevono corrispondere a transizioni nella banda di conduzione. Строится единая для всех шелочных галоидов модель, которая дается знергии дляFиKпереходов в хорощем согласии с зкспериментальными реэультатами, как при поглошении, так и при иэлучении. В зтой моделиL-полосы должны соответствовать переходам в эону проводимости.

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. Si esprimono la sezione d’urto e l’ampiezza di scattering da un’impurità in un cristallo, modiante formule simili a quelle classiche, in termini di quantità che sono in parte analoghe, in parte diverse dagli usuali spostamenti di fase. Si discutono anche la relazione fra questi spostamenti di fase ed i poli della funzione di Green della hamiltoniana totale ed altre proprietà. Поперечное сечение и амплитуда рассеяния на примеси в кристалле выражаются через фор мулы, аналогичные кла ссическим выражениям, в термина х величин, которые обес печивают множество а налогий и некоторые различия п о сравнению с обычными сдвигами фаз. Также об суждаются соотношения между этими фазовыми сдвиг ами и полюса функций Г рина полного Гамильтониа на и другие свойства.

A realistic model is set up in order to study the structure of the donor ground states in the semiconducting III-V compounds. The model is also applied to Si and gives results in agreement with those of Baldereschi. The lifting of the degeneracies, which are present in the effective-mass approximation, is shown to be due to the intervalley interaction of the impurity potential between degenerate minima and also between minima at different energy. The impurity states in GaAs are studied in detail as function of the energy separation between thek= 0 minimum and the subsidiary ones located atk= (2π/a)(1, 0, 0) etc. States of the same symmetry originating from those minima strongly interact, according to the noncrossing rule, when the energy separation is small and this produces a strong shift of the impurity states and a mixing of the wave functions. Si studia in un modello realistico la struttura dello stato fondamentale e dei primi stati eccitati di un’impurezza donatore in un semiconduttore cubico del tipo III-V. Si trova che gli elementi di matrice del potenziale di impurezza tra stati legati associati a minimi diversi e degeneri nell’approssimazione delle masse efficaci sono responsabili delle strutture degli stati osservate. Inoltre si studia l’influenza sui primi stati della presenza nella banda di conduzione di un minimo ak= 0 e di tre minimi degeneri nei puntiXa energie differenti. La forma delle funzioni d’onda dei primi stati si studia al variare dell’energia di separazione tra i minimi. Предлагается реалис тическая модель для т ого, чтобы исследоват ь структуру донорных основных со стояний в полупровощ их III-V соединениях. Эта м одель также применяется к Si и дает р езультаты, согласующ иеся с результатами Б алдерески. Показывается, что уве личение вырождений, к оторые присутствуют в приближении эффективных масс, обу словлено взаимодейс твием примесного пот енциала между вырожденными миниму мами, а также между мин имумами при различно й энергии. Подробно исследуютс я примесные состояни я в GaAs, как функция расст ояния между энергетическими уро внями между минимумо м k = 0 и вторичными минимумами, располож енными при k=(2π/а)(1, 0, 0) и т.д. Состояния той же симм етрии, образованные и з этих минимумов, силь но взаимодействуют, сог ласно неперекрестно му правилу, когда расс тояние между энергетическими уро внями мало, и это приво дит к сильному сдвигу примесных состояний и смешиван ию волновых функций.

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 threesstates, associated to the nonequivalentX-minima into states withГ1andГ3symmetries; similarly, the ninepstates are split into states withГ4andГ5symmetry. 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. Si estende il modello del lavoro precedente allo studio degli stati risonanti associati ai minimi secondari degeneri nei puntiXdi una banda di conduzione realistica di un cristallo cubico. Si mostra che i tre statisdi più bassa energia associati ai tre minimi non equivalenti sono separati dagli elementi di matrice del potenziale di impurezza in stati con simmetriaГ1eГ3; i primi nove stati p sono invece separati in due tripletti di simmetriaГ4ed un tripletto con simmetriaГ5. Si discute quindi l’identificazione di questi stati come responsabili delle bande di assorbimentoLnegli alogenuri alcalini. Используя реалистич ескую модель, введенн ую в предыдущей работ е, мы обсуждаем резонансные состоян ия в идеальном кубиче ском кристалле. Мы рас сматриваем резонансы, связанные с вторичными экстрем умами зонной структу ры, расположенными вХточках зоны Брилл юэна. Показывается, чт о примесное взаимоде йствие расщепляет три в сост ояния, связанные с неэ квивалентнымиХмини-мумаму, в состояния сГ1и -Г3си мметриями (**); аналогич но, девятьрсостояний расщепля ются в состоянияГ4, иГ5, симметрии. Время жизн и этих состояний зави сит от плотности сост ояний зонной структуры в первой зо не Бриллюэна. Обсужда ется идентификацияL-зон в щелочных галоидах с п ереходами в такие рез онансные состояния в связи с экспериментальными результатами многих авторов.