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The theory of numbers, the theory of computation and well-known biological and neurological studies on cognition and consciousness all indicate the concept of recursion as their common denominator. Mathematical recursion owes its meaning and properties to a dual relationship between its results, which always constitute a sequence, and the operator that generated them, which is instead invariant. This article proposes that this duality in recursion originates from the duality between the biological homeostatic equilibrium in living systems and the adaptive physico-chemical changes required to sustain such equilibria. Such duality gives order and meaning to the experiences of a living system. One of the many implications of this innovative perspective is that this duality can decouple computational results from our intuitive order relations, and that this can cause a rarefaction of the capacity of digital systems to convey communication and favour adaptation to the environment.

The structural and electronic properties of twisted bilayer graphene are investigated from first principles and tight binding approach as a function of the twist angle (ranging from the first "magic" angle $\theta=1.08^\circ$ to $\theta=3.89^\circ$, with the former corresponding to the largest unit cell, comprising 11164 carbon atoms). By properly taking into account the long-range van der Waals interaction, we provide the patterns for the atomic displacements (with respect to the ideal twisted bilayer). The out-of-plane relaxation shows an oscillating ("buckling") behavior, very evident for the smallest angles, with the atoms around the AA stacking regions interested by the largest displacements. The out-of-plane displacements are accompanied by a significant in-plane relaxation, showing a vortex-like pattern, where the vorticity (intended as curl of the displacement field) is reverted when moving from the top to the bottom plane and viceversa. Overall, the atomic relaxation results in the shrinking of the AA stacking regions in favor of the more energetically favorable AB/BA stacking domains. The measured flat bands emerging at the first magic angle can be accurately described only if the atomic relaxations are taken into account. Quite importantly, the experimental gaps separating the flat band manifold from the higher and lower energy bands cannot be reproduced if only in-plane or only out-of-plane relaxations are considered. The stability of the relaxed bilayer at the first magic angle is estimated to be of the order of 0.5-0.9 meV per atom (or 7-10 K). Our calculations shed light on the importance of an accurate description of the vdW interaction and of the resulting atomic relaxation to envisage the electronic structure of this really peculiar kind of vdW bilayers., Comment: 10 pages, 5 figures

The electronic properties of twisted bilayer graphene are being intensely investigated. The flat bands emerging at the first ``magic angle'' are responsible for anomalous insulating behavior at half-filling and superconductivity. Using state-of-the-art $a\phantom{\rule{0}{0ex}}b\phantom{\rule{0.333em}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ calculations, it is shown that the energy gaps and band dispersion are captured correctly only when the atomic corrugation, arising as a result of the interlayer interaction, is considered. The atomic corrugation shows a wave profile with maximum atomic out-of-plane displacements of about 0.1 angstrom.

The concept of Recursion occurs in several contexts: mathematical reasoning (Poincaré), computability theory (Turing, Church), cybernetics (von Foerster), linguistics (Chomsky), epistemology (Cassirer), sociology (Luhmann) and others. It is remarkable that recursion is also emerging as a fundamental key in unraveling biological processes (Maturana, Varela, Damasio, Edelman). We show that there is an isomorphism between biological recursion and all other type of recursions and it is precisely this isomorphism which gives order and therefore meaning to the multiplicity of our experience.

This article is both a comment on Neyland’s ‘On organizing algorithms’ and a supplementary note to our ‘The concept of algorithm as an interpretative key of modern rationality’. In the first part we discuss the concepts of algorithm and recursive function from a different perspective from that of our previous article. Our cultural reference for these concepts is once again computability theory. We give additional arguments in support of the idea that a culture informed by an algorithmic logic has promoted modern rationality both in science and in society. We stress again the importance of distinguishing between algorithms applied to quantifiable entities such as space, time and value and those applied to ontological entities such as human actions. In the second case, the algorithm is applied outside its domain of definition and leads to social disaggregation.

We show that the central finite difference formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators on discrete coordinate eigenkets |xn〉 defined on a uniform grid. Starting from the discretization of integrals involving canonical commutations, simple closed-form expressions of the matrix elements are obtained. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the derivative approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method. © 2018 Wiley Periodicals, Inc.

Few layer bismuth nanofilms with (111) orientation have shown striking electronic properties, especially as building blocks of novel two-dimensional heterostructures. In this paper we present state-of-the-art first principles calculations, based on both density functional theory and maximally localized Wannier functions, that encompass electronic and structural properties of free-standing Bi(111) nanofilms. We accurately evaluate both the in-plane lattice constant and, by including the van der Waals interaction between bismuth bilayers, the intra/interlayer distances. Interestingly and somehow unexpectedly, the in-plane lattice constant is predicted to shrink by about 5% going from the thickest investigated nanofilm $(\ensuremath{\sim}80\phantom{\rule{0.16em}{0ex}}\AA{})$ to single bilayer Bi(111), entailing a thickness dependent lattice mismatch in complex heterostructures involving ultrathin Bi(111). Moreover, quantum confinement effects, that would be expected to rule the electronic structure at this size range, compete with surface states that appear close to and across the Fermi level. The implication is that not only all but the thinnest films have a metallic band structure but also that such surface states might play a role in either the formation of interfaces with other materials or for sensing applications. Finally, the calculated electronic structure compares extremely well with ARPES measurements.

Focus of the review is on experimental set-ups and theoretical proposals aimed to enhance thermoelectric performances of molecular junctions. In addition to charge conductance, the thermoelectric parameter commonly measured in these systems is the thermopower, which is typically rather low. We review recent experimental outcomes relative to several junction configurations used to optimize the thermopower. On the other hand, theoretical calculations provide estimations of all the thermoelectric parameters in the linear and non-linear regime, in particular of the thermoelectric figure of merit and efficiency, completing our knowledge of molecular thermoelectricity. For this reason, the review will mainly focus on theoretical studies analyzing the role of not only electronic, but also of the vibrational degrees of freedom. Theoretical results about thermoelectric phenomena in the coherent regime are reviewed focusing on interference effects which play a significant role in enhancing the figure of merit. Moreover, we review theoretical studies including the effects of molecular many-body interactions, such as electron-vibration couplings, which typically tend to reduce the efficiency. Since a fine tuning of many parameters and coupling strengths is required to optimize the thermoelectric conversion in molecular junctions, new theoretically proposed set-ups are discussed in the conclusions.

We report on a theoretical study of the nonpolar ZnO (101̅0) and (112̅0) surfaces carried out in the framework of density functional theory, aiming to elucidate the thermodynamic and kinetic stability of the clean surface against the formation and diffusion of oxygen vacancies. At variance with other oxide materials and ZnO surfaces with different orientation, we show that, under exposure to molecular oxygen in the gas phase, no significant amounts of oxygen vacancies can be sustained by the surface, in agreement with recent Scanning Tunnelling Microscope (STM) observations. However, our calculations show also that under ultrahigh vacuum and high-temperature conditions the observation of oxygen vacancies might be possible, as reported in earlier experiments of Göpel and Lampe.(1) We characterize the defected surfaces electronic and structural properties as a function of the position of the defect with respect to the surface and discuss the diffusion paths of such defects both parallel and across the surface.

We have performed first-principles calculations on anatase TiO2 nanowires (NWs) to investigate the dependence of their structural and electronic properties on the size, the surface coverage, and the morphology. We have found that the overall crystallinity of the NWs increases on increasing the diameter size or equivalently upon surface coverage with simple water-derived adsorbates. The NWs grown along the [010] direction are found to be more ordered with respect to the NWs in the [001] direction of the same size, thus highlighting the dependence of the crystallinity on the choice of the morphology. The bare and hydrated NWs do show the band gap blue shift due to the size confinement, but deviations from an ideal trend with the size are found and ascribed to the morphology and the crystallinity. Through the analysis of the valence band maximum and conduction band minimum energies we found that the electrochemical potential variations of the TiO2 NWs profit from the confined size, for example, by favoring the water splitting process. Moreover, the availability of internal channels for an efficient charge transport can be tuned by the surface coverage. The terminal hydroxyl groups of the hydrated NWs cannot be considered as deep hole traps since their related electronic states have binding energies in the same range of the NW oxygen states. The hydrogenated NWs grown along the [001] direction show occupied states at the bottom of the conduction bands, thus we expect that TiO2 NWs can be used as efficient hydrogen sensors. Finally, the surface hydration leads to the most stable NWs among the considered surface configurations with formation energies that are even close to the bulk limit.

The absorption and, for the first time, the emission spectra of doped silicon nanocrystals have been calculated within a first-principles framework including geometry optimization. Starting from hydrogenated silicon nanocrystals, simultaneous n- and p-type doping with boron and phosphorous impurities have been considered. We found that the B-P co-doping results to be easier than simple 13- or P-doping and that the two impurities tend to occupy nearest neighbours sites inside the nanocrystal itself. The co-doped nanocrystals bandstructure presents band edge states that are localized on the impurities and are responsible of the red-shifted absorption threshold with respect to that of pure un-doped nanocrystals in fair agreement with the experimental outcorne. The emission spectra show a Stokes shift with respect to the absorption due to the structural relaxation after the creation of the electron-hole pair. Moreover, the absorption and emission spectra have been calculated for a small co-doped nanocrystal beyond the single particle approach by introducing the self-energy correction and solving the Bethe-Salpeter equation scheme. Our procedure shows the important role played by the many-body effects. (C) 2006 Elsevier B.V. All rights reserved.

The electronic and optical properties of silicon nanocrystals passivated with hydrogen and oxygen have been investigated both in the ground- and in an excited-state configuration, through different ab-initio techniques. The presence of an electron–hole pair leads to a strong interplay between the structural and optical properties of the system. The structural distortion of the nanocrystals induced by an electronic excitation is analysed together with the role of the symmetry constraint during the relaxation. The structural distortion can account for the experimentally observed Stokes Shift. Size-related aspects are also analysed and discussed.

The quantum confinement for a conduction-band electron within a spherical quantum dot is investigated in the framework of the effective-mass approximation. The conduction-band effective-mass anisotropy is fully taken into account. The exact solution for the electronic spectrum is provided, showing how the 'isotropic' mass levels map into the new spectrum which accounts for the anisotropy. The removal of degeneracies typical of the spherical dot, as well as its effects on the infrared transition energies, are discussed.

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.

The thermoelectric properties of a molecular junction model, appropriate for large molecules such as fullerenes, are studied within a non-equilibrium adiabatic approach in the linear regime at room temperature. A self-consistent calculation is implemented for electron and phonon thermal conductance showing that both increase with the inclusion of the electron-vibration coupling. Moreover, we show that the deviations from the Wiedemann-Franz law are progressively reduced upon increasing the interaction between electronic and vibrational degrees of freedom. Consequently, the junction thermoelectric efficiency is substantially reduced by the electron-vibration coupling. Even so, for realistic parameters values, the thermoelectric figure of merit can still have peaks of the order of unity. Finally, in the off-resonant electronic regime, our results are compared with those of an approach which is exact for low molecular electron densities. We give evidence that in this case additional quantum effects, not included in the first part of this work, do not affect significantly the junction thermoelectric properties in any temperature regime., 15 pages, 11 figures, 2 Appendices

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.

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.

Measurements of the nonlinear refractive index n 2 of a high-porosity freestanding porous silicon sample are reported at different laser wavelengths by means of the z-scan technique. The results show a negative below-gap nonlinear refractive index, so that thermal contributions to the observed effects can be reasonably excluded. Values for n 2 of the order of 10−9 esu are here reported. These results are compatible with the hypothesis of an enhancement of optical nonlinearities due to quantum confinement of carriers in nanocrystals present in the material.

We study the motion of a particle confined in an ellipsoidal quantum dot, solving the corresponding Schrodinger equation both numerically, using the appropriate coordinate system, and variationally. The results from the two methods are compared, varying the ellipsoid semi-axes. We find that the confined-state energies split with respect to those of the spherical quantum dot and this can be explained as a consequence of both a volume-induced deformation effect and a geometry-induced one. The role of the dot geometry is shown to be relevant also for the formation of topological surface states.

A z-scan measurement of the nonlinear refractive index of porous silicon (PS) is performed at a photon energy well below the effective bandgap of the sample. The measure gives ReX (3) ≈−10−8 esu, that is four orders of magnitude larger than the bulk value. We also present a calculation of the enhancement of X (3) in PS due to the spatial auantum confinement of the exciton in the quasi-one-dimensional nanostructure. The calculated enhancement is in very good agreement with the experimental data. Finally, we performed a perturbative calculation of nonlinear absorption δα in a auantum wire, obtaining the material-independent dispersive scaling of the quantum wire nonlinear refractive index. The calculation suggests the presence of a ‘auantum-confinement-enhanced’ auadratic Stark effect in the quasi-one-dimensional structure that gives a Iow and almost constant value of Reχ (3) at photon energy around half-bandgap and large negative values in the range Egap/2 < hw < Egap . As we discuss, this predict...

We show that the optical absorption and emission energies in porous silicon can be accounted for in a quantum wire confinement model where both the electron and the hole are localized by lateral surface wire undulations. Localization energies for both the particles have been numerically calculated within the effective mass approximation showing that there exists a limited class of wire geometries which are consistent with porous silicon optical and structure analysis data.

Measurements of the nonlinear refractive index of free-standing porous silicon samples by means of the Z-scan technique are reported. A sensitive enhancement of the optical nonlinearity is found with respect to bulk silicon. The results are in agreement with a simple theoretical model which is also presented and discussed, that attributes the enhancement to quantum confinement of carriers. The negative sign of nonlinear refractive index suggests that optical Stark effect gives the dominating contribution to the nonlinearity. It is also found that the nonlinearity is mainly refractive, which is very promising in order to use porous silicon for nonlinear optical applications such as power limiting or optical switching.

According to Ernst Cassirer, the transition from the concept of substance to that of mathematical function as a guide of knowledge coincided with the end of ancient and the beginning of modern theoretical thought. In the first part of this article we argue that a similar transition has also taken place in the practical sphere, where mathematical function occurs in one of its specific forms, which is that of the algorithm concept. In the second part we argue that with the rise of modernity the idea of substance and the related concepts of category and classification, which are deeply embedded in western culture, have not been totally supplanted by that of function. The intertwining of the concepts of substance and function has generated contradictory hybrids. These hybrids are used as a key for the understanding of the different repercussions of algorithmic logic on society in terms of social integration.

The linear thermoelectric properties of molecular junctions are theoretically studied close to room temperature within a model including electron-electron and electron-vibration interactions on the molecule. A nonequilibrium adiabatic approach is generalized to include large Coulomb repulsion through a self-consistent procedure and applied to the investigation of large molecules, such as fullerenes, within the Coulomb blockade regime. The focus is on the phonon thermal conductance which is quite sensitive to the effects of strong electron-electron interactions within the intermediate electron-vibration coupling regime. The electron-vibration interaction enhances the phonon and electron thermal conductance, and it reduces the charge conductance and the thermopower inducing a decrease of the thermoelectric figure of merit. For realistic values of junction parameters, the peak values of the thermoelectric figure of merit are still of the order of unity since the phonon thermal conductance can be even smaller than the electron counterpart., Comment: 8 pages, 1 Appendix, 12 pages. arXiv admin note: substantial text overlap with arXiv:1406.3771

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 α c . 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 >> hw) and b) the Holstein limit for large α and small band width (Δ << hω). 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.

Large polaron and bipolaron formation is reviewed with particular emphasis on the screening effects which become important at relatively high carrier density (plasma frequency, ωp, larger than longitudinal optical frequency, ω1). At high density polarons are mobile particles even at very high electron-phonon coupling constant (a»l) and bipolaron binding energy tends to vanish giving evidence of the existence of metastable bipolaron states. The coexistence of metastable bipolarons (bosons) and polarons (fermions) supports the so-called boson-fermion model of superconductivity. This model can be generalized in order to take into account the dependence on the carrier density given in the polaron-bipolaron framework. The results are in good agreement with the density dependence of the critical temperature exhibited by many high-Tc superconductors.

In this paper we report on the frequency dependence of the AC conductivity of porous silicon in the range 10 Hz-100 kHz. Two types of testing devices have been fabricated on three different series of samples formed electrochemically using as a starting material ptype, n −-type and n +-type silicon substrates. For frequencies less than 20-40 kHz the conductivity is found to follow a sublinear frequency dependence. This behaviour is typical of a carrier transport mechanism determined by an anomalous diffusion process. At higher frequencies we find that surface states influence the transport mechanism. This suggests a double-channel transport mechanism: one related to porous-silicon “volume” properties and the other more connected to the “surface” itself.

We address the structural and electronic properties of graphene nanoribbons (GNRs) covalently immobilized on a metallic substrate by means of an organic layer. The GNR–organic layer and organic layer–metal interfaces can be thought of as constituents of a nanodevice and have been accurately studied using large-scale density functional theory calculations. Our results demonstrate the possibility of combining nanopatterned metal–organic layer substrates with selected GNRs to obtain well ordered and stable structures while preserving the GNR energy band gap, an essential requirement for any switching nanodevice.

A novel class of heteroacene molecules, benzodifuroxazin-4-ones, has been effectively synthesized by means of a thermally activated double cyclization reaction starting from amidic precursors. The new molecules were thermally and optically characterized, revealing an outstanding thermal stability to oxidation and an uncommon enhancement of fluorescent properties in solid state as compared to solution. As shown by single-crystal XRD analysis, the molecules crystallize in a face-to-face (π-stack) arrangement instead of the herringbone structure typical of the most acene derivatives. The electronic properties of both molecules and crystals have been investigated by means of a detailed Density Functional Theory computational analysis: very stable HOMO energies have been calculated and, from the band structure analysis, it is possible to suggest a preferential direction of charge transport along the π-stacking direction. All the reported properties indicate this new class of heteroacene derivatives as interesting candidates for a possible application in organic electronics.

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 Hamiltonian for two interacting electrons coupled with longitudinal phonons and plasmons is set up. The phonons are treated in the Fr\"ohlich scheme and the plasmons in the single-pole approximation. We are interested in systems with low electron density (n\ensuremath{\le}${10}^{20}$--${10}^{21}$) such as high-${\mathit{T}}_{\mathit{c}}$ superconductors. It is shown that, in this density range, the electron dynamics do not simply screen the electrostatic interaction but, also, cooperates to the bipolaron formation. Furthermore we find that the binding energies and the effective mass depend on the electronic density. The features of the effective electron-electron potential are discussed, mainly for what concerns the self-energy terms and the long-range tail; the former depends on the pair state and the second shows that the plasmon field tends to screen all the electrostatic interactions, even the electron-phonon one. It is also shown that the Hamiltonian formulation is equivalent to a dielectric formulation where the total dielectric function of the system is the sum of the dielectric function appropriate for an ionic of the system is the sum of the dielectric function appropriate for an ionic material and that appropriate for the electron gas. Within this model we calculate the Bose-condensation critical temperature of a system of correlated pairs and free carriers in a two-fluid model at thermodynamical equilibrium.

The propagation of the acoustic and the electromagnetic signals is studied in materials with tetragonal and hexagonal symmetries that are piezoelectric, piezomagnetic, or magnetoelectric. Three magnetic spatial symmetries are considered: 622 for hexagonal crystals and 422 and 4(')22(') for tetragonal crystals. The equations for the five modes (three mainly acoustic and two mainly electromagnetic) are solved both in the general case and in specific cases in which the material is only piezoelectric, piezomagnetic, or magnetoelectric. It is found that the piezomagnetic and the magnetoelectric coefficients and the magnetic permeability renormalize the elastic constants, the piezoelectric coefficients, and the dielectric tensor. The acoustic frequencies depend on the angle theta that the component of the wave vector in the a-b plane forms with the a axis. The main contribution to the electromagnetic modes derives only from the dielectric tensor and the magnetoelectric coefficients and it is independent of theta and of the piezoelectric and the piezomagnetic coefficients. Starting from the general equations, a method has been devised to study separately the acoustic and the electromagnetic solutions. It is found that a number of relations must be verified in order to have stability of the electromagnetic and the acoustic modes.

The impurity screening in silicon nanocrystals is analyzed using a first-principles approach based on density functional theory. The electron density induced by a positively charged impurity is evaluated as a function of the nanocrystal size. From our calculations we found that the impurity is responsible for an electron density accumulation around the impurity site, fully compensated by a positive charge accumulation at the surface (electron depletion). The results are sound and shed new light on the most recent findings in this field. On the basis of the present first-principles results, we propose a Thomas–Fermi model of the impurity screening in silicon nanocrystals. The model gives reliable estimations of the screening function, that well compares to recent ab-initio calculations.

Nowadays we live in the so-called "Silicon Era", in which devices based on the silicon technology permeate all aspects of our daily life. One can simply think how much silicon is in the everyday household objects, gadgets and appliances. The impact of silicon technology has been very relevant in photodetection as well. it enables designing large or very large-scale integration devices, in particular microchips and pixelled detectors like the Silicon Photo Multiplier made of micrometric channels grouped in mm(2) pixels. However, on the horizon, the recent development of nanotechnologies is opening a new direction in the design of sub-micron photodevices, owing to the capability to deal with individual molecules of compounds or to chemically grow various kinds of materials. Among them, carbon compounds appear to be the most promising materials being chemically very similar to silicon, abundant and easy to handle. In particular, carbon nanotubes (CNT) are a very intriguing new form of material, whose properties are being studied worldwide providing important results. The photoelectric effects observed on carbon nanotubes indicate the possibility to build photodetectors based on CNTs inducing many people to claim that we are at the beginning of a Post Silicon Era or of the Carbon Era. In this paper, we report on the most important achievements obtained on the application of nanotechnologies to photodetection and medical imaging, as well as to the development of radiation detectors for astro-particle physics experiments.

Molecular materials with a polar arrangement of the constituent dipoles are good candidates for exhibiting piezoelectric properties directly related to the strain-induced polarization. We assess, from first principles, the properties of the metal-organic molecular crystal (4-dimethylaminopyridyl)bis(acetylacetato)zinc(II) in presence of strain. The spontaneous polarization and the piezoelectric properties are studied by means of the modern theory of polarization. The cooperative interaction among molecular chains is shown to lead to a collective polarization enhancement effect. Some theoretical issues concerning the multivalued behavior of the Berry phase are also illustrated.

The titanium dioxide (TiO2) complexes are widely investigated for their striking and multipurpose capabilities. The TiO2 key feature lies in its photocatalytic activity for several reactions of social (bioengineering, environmental and artistic protection, pollution containment) and commercial (photovoltaic, alternative-energy, gas sensing) interests. The possibility to enhance specific reactions at the nanoscale by a fine tuning of the nano-sized single crystals properties boosted in the last decade the scientific research. Thus a theoretical understanding of the fundamental properties of TiO2 nanocrystals became necessary to predict and expedite the experimental effords. We present here a characterization of TiO2 0D nanoclusters and 1D nanowires in the framework of ab initio DFT calculations. Based on both theoretical and experimental evidences we defined a stoichiometric TiO2 NC by modifying a perfect bipyramidal morphology and then used this NC as a chain repetition unit in the NW. We analyzed the effect of the surface coverage by functionalizing dangling bonds with simple adsorbates (dissociated water and hydrogens) modeling two acidic environments. These terminations are important to model the basical interactions of TiO2 nanosystems with the hydration sphere, which is always found to surround the nanosamples and toaffect their photocatalytic activity. We thus address the electronic reorganization and the surface weight in determining the global features of the nanostructures. The structural reconstruction is found to depend on the surface coverage and the experimental evidences on the structural variations can be explained by a topological analysis of the Ti-O bonds. Quantum confinement effects in the electronic properties are observed through the bandgap widening and the discretization of the energy distribution, but the surface competes to determine the energy dispersion of the electronic levels. The hydrogenated nanocrystals do show occupied levels at the bottom of the coduction bands, thus leading to metallic nanowires in one dimension. Whereas in the hydrogenated cluster such levels present a localized charge distribution with respect to the whole structure and they are also similar for the atomic orbital character and energy position to the defect states obtained by oxygens desorption. From the analysis of the electronic density of states we found that Ti-H bonds induce in-gap states above the valence bands, whereas hydration leads to occupied states that shift the valence bands to lower binding energies. Formation energy calculations reveal that surface hydration leads to the most stable nanocrystals, in agreement with the experimental findings that water coverage stabilizes the surface.

The effects of the incorporation of group-III (B and Al), group-IV (C and Ge), and group-V (N and P) impurities on the formation energies, electronic density of states, optical absorption spectra, and radiative lifetimes of Si nanocrystallites of different shape and with diameters up to 2 nm are studied by means of an ab initio pseudopotential method that takes into account spin polarization. The single doping with group-III or group-V impurities leads to significant changes on the onsets of the absorption spectra that are related to the minority-spin states. In contrast to the optical absorption spectra, the radiative lifetimes are sensitively influenced by the shape of the nanocrystallites, though this influence tends to disappear as the size of the nanocrystallites increase. Codoping is investigated for pairs of group-III and group-V impurities. We show that the impurity formation energies decrease significantly when the nanocrystallites are codoped with B and P or with Al and P. Additional peaks are introduced in the absorption spectra due to codoping, giving rise to a redshift of the absorption onset with respect to the undoped nanocrystallites. Those additional peaks are more intense when codoping is performed with two different species either of the group III or of the group V. The values of radiative lifetimes for the codoped nanocrystallites are mostly in between the values for the nanocrystallites doped with the impurities separately.

The structural and electronic properties of anatase ${\text{TiO}}_{2}$ nanocrystals (NCs) are investigated through first-principles calculations. The dependence of the structural properties (e.g., NC volume variations) on the surface chemistry is discussed by considering two different surface coverages (dissociated water and hydrogens). Both prevent a pronounced reconstruction of the surface, thus ensuring a better crystalline organization of the atoms with respect to the bare NC. In particular, the results for the hydrated NC do show the largest overlap with the experimental findings. The band-gap blueshift with respect to the bulk shows up for both the bare and the hydrated NC, whereas hydrogen coverage or oxygen desorption from the bare NCs induce occupied electronic states below the conduction levels thus hindering the gap opening due to quantum confinement. These states are spatially localized in a restricted region and can be progressively annihilated by oxygen adsorption on undercoordinated surface titanium atoms. Formation energy calculations reveal that surface hydration leads to the most stable NC, in agreement with the experimental finding that the truncated bipyramidal morphology is typical of the moderate acidic environment. Oxygen desorption from the bare NC is unfavorable, thus highlighting the stabilizing role of surface oxygen stoichiometry for ${\text{TiO}}_{2}$. Available experimental data on the electronic and structural properties of ${\text{TiO}}_{2}$ NCs are summarized and compared with our results.

Oxygen vacancies at the SnO2(110) and (101) surface and subsurface sites have been studied in the framework of density functional theory by using both all-electron Gaussian and pseudopotential plane-wave methods. The all-electron calculations have been performed using the B3LYP exchange-correlation functional with accurate estimations of energy gaps and density of states. We show that bulk oxygen vacancies are responsible for the appearance of a fully occupied flat energy level lying at about 1 eV above the top valence band, and an empty level resonant with the conduction band. Surface oxygen vacancies strongly modify the surface band structures with the appearance of intragap states covering most of the forbidden energy window, or only a small part of it, depending on the vacancy depth from the surface. Oxygen vacancies can account for electron affinity variations with respect to the stoichiometric surfaces as well. A significant support to the present results is found by comparing them to the available experimental data.

Well-oriented thin films of methyl-ammonium trihalogenostannates $\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Sn}{X}_{3}$ compounds $(X=\mathrm{Cl},\mathrm{Br})$ are grown by the single source thermal ablation technique. Optical absorption and structural analysis of $\mathrm{C}{\mathrm{H}}_{3}\mathrm{N}{\mathrm{H}}_{3}\mathrm{Sn}{X}_{3}$ thin films are combined with ab initio calculations in order to clarify their electronic properties and the role of the organic cation. The structural calculations reproduce well the measured lattice parameters, and optical measurements reveal a direct gap absorption onset for both compounds, in agreement with the calculated band structures. It turns out from projected density of states analysis that the valence and conduction bands take negligible contribution from the methylammonium. It is inferred that the band gap mainly depends on the ionicity and size of the inorganic cage $\mathrm{Sn}{X}_{3}$.