Erio Tosatti

National Academy of Sciences of Ukraine, Kiev, Misto Kyyiv, Ukraine

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Publications (505)2055.31 Total impact

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    ABSTRACT: The surface of a crystal made of roughly spherical molecules exposes, above its bulk rotational phase transition at T= Tr, a carpet of freely rotating molecules, possibly functioning as “nanobearings” in sliding friction. We explored by extensive molecular dynamics simulations the frictional and adhesion changes experienced by a sliding C60 flake on the surface of the prototype system C60 fullerite. At fixed flake orientation both quantities exhibit only a modest frictional drop of order 20% across the transition. However, adhesion and friction drop by a factor of 2 as the flake breaks its perfect angular alignment with the C60 surface lattice suggesting an entropy-driven aligned-misaligned switch during pull-off at Tr. The results can be of relevance for sliding Kr islands, where very little frictional differences were observed at Tr, but also to the sliding of C60 -coated tip, where a remarkable factor 2 drop has been reported.
    Nanoscale 09/2014; · 6.73 Impact Factor
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    ABSTRACT: Oxygen, one of the most common and important elements in nature, has an exceedingly well-explored phase diagram under pressure, up to and beyond 100 GPa. At low temperatures, the low-pressure antiferromagnetic phases below 8 GPa where O2 molecules have spin S = 1 are followed by the broad apparently nonmagnetic ε phase from about 8 to 96 GPa. In this phase, which is our focus, molecules group structurally together to form quartets while switching, as believed by most, to spin S = 0. Here we present theoretical results strongly connecting with existing vibrational and optical evidence, showing that this is true only above 20 GPa, whereas the S = 1 molecular state survives up to about 20 GPa. The ε phase thus breaks up into two: a spinless ε0 (20-96 GPa), and another ε1 (8-20 GPa) where the molecules have S = 1 but possess only short-range antiferromagnetic correlations. A local spin liquid-like singlet ground state akin to some earlier proposals, and whose optical signature we identify in existing data, is proposed for this phase. Our proposed phase diagram thus has a first-order phase transition just above 20 GPa, extending at finite temperature and most likely terminating into a crossover with a critical point near 30 GPa and 200 K.
    Proceedings of the National Academy of Sciences of the United States of America. 07/2014;
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    ABSTRACT: In standard nucleation theory, the nucleation process is characterized by computing ΔΩ(V), the reversible work required to form a cluster of volume V of the stable phase inside the metastable mother phase. However, other quantities besides the volume could play a role in the free energy of cluster formation, and this will in turn affect the nucleation barrier and the shape of the nucleus. Here we exploit our recently introduced mesoscopic theory of nucleation to compute the free energy cost of a nearly spherical cluster of volume V and a fluctuating surface area A, whereby the maximum of ΔΩ(V) is replaced by a saddle point in ΔΩ(V, A). Compared to the simpler theory based on volume only, the barrier height of ΔΩ(V, A) at the transition state is systematically larger by a few kBT. More importantly, we show that, depending on the physical situation, the most probable shape of the nucleus may be highly non-spherical, even when the surface tension and stiffness of the model are isotropic. Interestingly, these shape fluctuations do not influence or modify the standard Classical Nucleation Theory manner of extracting the interface tension from the logarithm of the nucleation rate near coexistence.
    The Journal of Chemical Physics 03/2014; 140(9):094501. · 3.12 Impact Factor
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    ABSTRACT: Recent highly idealized model studies of lubricated nanofriction for two crystalline sliding surfaces with an interposed thin solid crystalline lubricant layer showed that the overall relative velocity of the lubricant $v_{\rm lub} / v_{\rm slider}$ depends only on the ratio of the lattice spacings, and retains a strictly constant value even when system parameters are varied within a wide range. This peculiar "quantized" dynamical locking was understood as due to the sliding-induced motion of misfit dislocations, or soliton structures. So far, the practical relevance of this concept to realistic sliding three dimensional crystals has not been demonstrated. In this work, by means of classical molecular dynamics simulations and theoretical considerations, we realize a realistic three-dimensional crystal-lubricant-crystal geometry. Results show that the flux of lubricant particles associated to the advancing soliton lines gives rise here too to a quantized velocity ratio. Moreover, depending on the interface lattice spacing mismatch, both forward and backward quantized motion of the lubricant is predicted. The persistence under realistic conditions of the dynamically pinned state and quantized sliding is further investigated by varying sliding speed, temperature, load, and lubricant film thickness. The possibilities of experimental observation of quantized sliding are also discussed.
    02/2014; 89(9).
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    ABSTRACT: Pt is known to show spontaneous formation of monatomic chains upon breaking a metallic contact. From model calculations, these chains are expected to be spin polarized. However, direct experimental evidence for or against magnetism is lacking. Here, we investigate shot noise as a potential source of information on the magnetic state of Pt atomic chains. We observe a remarkable structure in the distribution of measured shot-noise levels, where the data appear to be confined to the region of nonmagnetic states. While this suggests a nonmagnetic ground state for the Pt atomic chains, from calculations we find that the magnetism in Pt chains is due to 'actor' electron channels, which contribute very little to ballistic conductance and noise. On the other hand, there are weakly polarized 'spectator' channels, which carry most of the current and are only slightly modified by the magnetic state.
    01/2014;
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    ABSTRACT: Low-temperature electronic conductance in nanocontacts, scanning tunneling microscopy (STM), and metal break junctions involving magnetic atoms or molecules is a growing area with important unsolved theoretical problems. While the detailed relationship between contact geometry and electronic structure requires a quantitative ab initio approach such as density functional theory (DFT), the Kondo many-body effects ensuing from the coupling of the impurity spin with metal electrons are most properly addressed by formulating a generalized Anderson impurity model to be solved with, for example, the numerical renormalization group (NRG) method. Since there is at present no seamless scheme that can accurately carry out that program, we have in recent years designed a systematic method for semiquantitatively joining DFT and NRG. We apply this DFT-NRG scheme to the ideal conductance of single wall (4,4) and (8,8) nanotubes with magnetic adatoms (Co and Fe), both inside and outside the nanotube, and with a single carbon atom vacancy. A rich scenario emerges, with Kondo temperatures generally in the Kelvin range, and conductance anomalies ranging from a single channel maximum to destructive Fano interference with cancellation of two channels out of the total four. The configuration yielding the highest Kondo temperature (tens of Kelvins) and a measurable zero-bias anomaly is that of a Co or Fe impurity inside the narrowest nanotube. The single atom vacancy has a spin, but a very low Kondo temperature is predicted. The geometric, electronic, and symmetry factors influencing this variability are all accessible, which makes this approach methodologically instructive and highlights many delicate and difficult points in the first-principles modeling of the Kondo effect in nanocontacts.
    01/2014;
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    ABSTRACT: Molecular contacts are generally poorly conducting because their energy levels tend to lie far from the Fermi energy of the metal contact, necessitating undesirably large gate and bias voltages in molecular electronics applications. Molecular radicals are an exception because their partly filled orbitals undergo Kondo screening, opening the way to electron passage even at zero bias. Whereas that phenomenon has been experimentally demonstrated for several complex organic radicals, quantitative theoretical predictions have not been attempted so far. It is therefore an open question whether and to what extent an ab initio-based theory is able to make accurate predictions for Kondo temperatures and conductance lineshapes. Choosing nitric oxide (NO) as a simple and exemplary spin 1/2 molecular radical, we present calculations based on a combination of density functional theory and numerical renormalization group (DFT+NRG), predicting a zero bias spectral anomaly with a Kondo temperature of 15 K for NO/Au(111). A scanning tunneling spectroscopy study is subsequently carried out to verify the prediction, and a striking zero bias Kondo anomaly is confirmed, still quite visible at liquid nitrogen temperatures. Comparison shows that the experimental Kondo temperature of about 43 K is larger than the theoretical one, whereas the inverted Fano lineshape implies a strong source of interference not included in the model. These discrepancies are not a surprise, providing in fact an instructive measure of the approximations used in the modeling, which supports and qualifies the viability of the density functional theory and numerical renormalization group approach to the prediction of conductance anomalies in larger molecular radicals.
    Proceedings of the National Academy of Sciences 12/2013; · 9.81 Impact Factor
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    ABSTRACT: Understanding nanoscale friction and dissipation is central to nanotechnology. The recent detection of the electronic-friction drop caused by the onset of superconductivity in Nb (ref. ) by means of an ultrasensitive non-contact pendulum atomic force microscope (AFM) raised hopes that a wider variety of mechanical-dissipation mechanisms become accessible. Here, we report a multiplet of AFM dissipation peaks arising a few nanometres above the surface of NbSe2-a layered compound exhibiting an incommensurate charge-density wave (CDW). Each peak appears at a well-defined tip-surface interaction force of the order of a nanonewton, and persists up to 70 K, where the short-range order of CDWs is known to disappear. Comparison of the measurements with a theoretical model suggests that the peaks are associated with local, tip-induced 2π phase slips of the CDW, and that dissipation maxima arise from hysteretic behaviour of the CDW phase as the tip oscillates at specific distances where sharp local slips occur.
    Nature Material 12/2013; · 35.75 Impact Factor
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    ABSTRACT: A simple device of three laterally coupled quantum dots, the central one contacted by metal leads, provides a realization of the ferromagnetic Kondo model, which is characterized by interesting properties like a nonanalytic inverted zero-bias anomaly and an extreme sensitivity to a magnetic field. Tuning the gate voltages of the lateral dots allows us to study the transition from a ferromagnetic to antiferromagnetic Kondo effect, a simple case of a Berezinskii-Kosterlitz-Thouless transition. We model the device by three coupled Anderson impurities that we study by numerical renormalization group. We calculate the single-particle spectral function of the central dot, which at zero frequency is proportional to the zero-bias conductance, across the transition, both in the absence and in the presence of a magnetic field.
    Physical Review Letters 07/2013; 111(4):047201. · 7.73 Impact Factor
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    ABSTRACT: The Gutzwiller technique has long been known as a method to include correlations in electronic structure calculations. Here we implement an ab-initio Gutzwiller+LDA calculation, and apply it to a classic problem, the ferromagnetism of bulk bcc Fe, whose nature has attracted recent interest. In the conventional Stoner-Wohlfarth model, the ferromagnetic ordering of iron sets in so that the electrons can reduce their mutual Coulomb repulsion at the extra cost of some increase of electron kinetic energy. Density functional theory within the spin polarized local density approximation (LDA) has long supported that picture, showing that ferromagnetic alignment causes band narrowing and a corresponding wavefunction localization, whence a kinetic energy increase. However, because of its inadequate treatment of strong intra-site correlations for localized d orbitals, LDA cannot be relied upon, particularly when it comes to separately describing fine potential and kinetic energy imbalances. With ab-initio Gutzwiller+LDA, we indeed find that the effect of correlations is to dramatically reverse the balance, the ferromagnetic ordering of Fe in fact causing a decrease of kinetic energy, at the cost of some increase of potential energy. The underlying physical mechanism, foreshadowed long ago by Goodenough and others, and more recently supported by LDA+DMFT calculations, is that correlations cause eg and t2g 3d orbitals to behave very differently. Weakly dispersive eg states are spin-polarized and almost localized, while, more than half filled, the t2g are broad band, fully delocalized states. Owing to intra-atomic Hund's rule exchange which aligns eg and t2g spins, the propagation of itinerant t2g holes is only allowed when different atomic spins are ferromagnetically aligned. We thus conclude that double exchange is at work already in the most popular ferromagnetic metal.
    07/2013;
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    ABSTRACT: Several examples of metallic electron doped polycyclic aromatic hydrocarbons (PAHs) molecular crystals have recently been experimentally proposed. Some of them have superconducting components, but most other details are still unknown beginning with structure and the nature of metallicity. We carried out ab-initio density functional calculations for La-Phenanthrene (La-PA), here meant to represent a generic case of three-electron doping, to investigate structure and properties of a conceptually simple case. To our surprise we found first of all that the lowest energy state is not metallic but band insulating, with a disproportionation of two inequivalent PA molecular ions and a low P1 symmetry, questioning the common assumption that three electrons will automatically metallize a PAH crystal. Our best metallic structure is metastable and slightly higher in energy, and retains equivalent PA ions and a higher P21 symmetry -- the same generally claimed for metallic PAHs. We show that a "dimerizing" periodic distortion opens very effectively a gap in place of a symmetry related degeneracy of all P21 structures near the Fermi level, foreshadowing a possible role of that special intermolecular phonon in superconductivity of metallic PAHs. A Hubbard-Frohlich model describing that situation is formulated for future studies.
    Physical Review B 06/2013; 88(11). · 3.66 Impact Factor
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    ABSTRACT: The physics of sliding friction is gaining impulse from nanoscale and mesoscale experiments, simulations, and theoretical modeling. This Colloquium reviews some recent developments in modeling and in atomistic simulation of friction, covering open-ended directions, unconventional nanofrictional systems, and unsolved problems.
    Review of Modern Physics 04/2013; 85(2). · 44.98 Impact Factor
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    ABSTRACT: Stick-slip -- the sequence of mechanical instabilities through which a slider advances on a solid substrate -- is pervasive throughout sliding friction, from nano to geological scales. Here we suggest that trapped cold ions in an optical lattice can also be of help in understanding stick-slip friction, and also the way friction changes when one of the sliders undergoes structural transitions. For that scope, we simulated the dynamical properties of a 101-ions chain, driven to slide back and forth by a slowly oscillating electric field in an incommensurate periodic "corrugation" potential of increasing magnitude U0. We found the chain sliding to switch, as U0 increases and before the Aubry transition, from a smooth-sliding regime with low dissipation to a stick-slip regime with high dissipation. In the stick-slip regime the onset of overall sliding is preceded by precursor events consisting of partial slips of few ions only, leading to partial depinning of the chain, a nutshell remnant of precursor events at the onset of motion also observed in macroscopic sliders. Seeking to identify the possible effects on friction of a structural transition, we reduced the trapping potential aspect ratio until the ion chain shape turned from linear to zigzag. Dynamic friction was found to rise at the transition, reflecting the opening of newer dissipation channels.
    Physical review. B, Condensed matter 03/2013; 87(19). · 3.77 Impact Factor
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    ABSTRACT: Trapped cold ions are known to form linear or planar zigzag chains, helices or clusters depending on trapping conditions. They may be forced to slide over a laser induced corrugated potential, a mimick of sliding friction [1,2]. We present MD simulations of an incommensurate 101 ions chain sliding subject to an external electric field. As expected with increasing corrugation, we observe the transition from a smooth-sliding, highly lubric regime to a strongly dissipative stick-slip regime. Owing to inhomogeneity the dynamics shows features reminiscent of macroscopic frictional behaviors [3]. While the chain extremities are pinned, the incommensurate central part is initially free to slide. The onset of global sliding is preceded by precursor events consisting of partial slips of chain portions further from the center. We also look for frictional anomalies expected for the chain sliding across the linear-zigzag structural phase transition. Although the chain is too short for a proper critical behavior, the sliding friction displays a frank rise near the transition, due to opening of a new dissipative channel via excitations of transverse modes.[4pt] [1] A. Benassi et al, Nature Comm. 2, 236;[0pt] [2] T. Pruttivarasin et al, New Jour. of Phys. 13, 075012;[0pt] [3] S.M. Rubinstein et al, Nature 4, 1005.
    03/2013;
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    ABSTRACT: The experimentally known fact that coaxial carbon nanotubes can be forced to slide one inside the other stimulated in the past much detailed modelling of the dynamical sliding process. Molecular dynamics simulations of sliding coaxial nanotubes showed the existence of strong frictional peaks when, at large speed, one tube excites the other with a ‘washboard’ frequency that happens to resonate with some intrinsic vibration frequency. At some of these special speeds we discover a striking example of dynamical symmetry breaking taking place at the nanoscale. Even when both nanotubes are perfectly left–right symmetric and nonchiral, precisely in correspondence with the large peaks of sliding friction occurring at a series of critical sliding velocities, a nonzero angular momentum spontaneously appears. A detailed analysis shows that this internal angular momentum is of phonon origin, in particular arising from preferential excitation of a right polarized (or, with equal probability, of a left polarized) outer-tube ‘pseudorotation’ mode, thus spontaneously breaking their exact twofold right–left degeneracy. We present and discuss a detailed analysis of nonlinear continuum equations governing this phenomenon, showing the close similarity of this phenomenon with the well-known rotational instability of a forced string, which takes place under sufficiently strong periodic forcing of the string. We also point out new elements appearing in the present problem which are ‘nano’, in particular the involvement of Umklapp processes and the role of sliding nanofriction.
    Philosophical Magazine A 03/2013; 93(8):922-948.
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    ABSTRACT: Recently, polycyclic aromatic hydrocarbon (PAH) molecular solids: picene, coronene, dibenzopentacene, phenanthrene among them, have been reported to turn from insulating to metallic and superconducting upon intercalation of electron-donating atoms, such as K, Ba, La. Despite experimental uncertainties, understanding these novel light-element based superconductors is important since both electron phonon coupling and electron electron correlations seem important, as indicated by early theory work. Choosing La-Phenanthrene (La-PA) as our working case, we first search for the theoretical optimal crystal structure and electronic properties by first principles density functional calculations. We single out a stable insulating phase with P1 symmetry and, slightly higher in energy, a metastable metallic P21 phase--the same (higher) symmetry of pristine PA, also proposed for La-PA. A tight binding model representing the metallic La-PA electronic structure, its dominant electron phonon coupling with an intermolecular dimerizing mode, and an intramolecular Coulomb U is formulated and discussed. In that model it can be argued that BCS pairing may be essentially unhindered by the Coulomb repulsion. Being symmetry-based, the mechanism could apply to other PAH superconductors as well.
    03/2013;
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    O M Braun, Nicola Manini, Erio Tosatti
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    ABSTRACT: Sliding friction across a thin soft lubricant film typically occurs by stick slip, the lubricant fully solidifying at stick, yielding and flowing at slip. The static friction force per unit area preceding slip is known from molecular dynamics (MD) simulations to decrease with increasing contact area. That makes the large-size fate of stick slip unclear and unknown; its possible vanishing is important as it would herald smooth sliding with a dramatic drop of kinetic friction at large size. Here we formulate a scaling law of the static friction force, which for a soft lubricant is predicted to decrease as f_{m}+Δf/A^{γ} for increasing contact area A, with γ>0. Our main finding is that the value of f_{m}, controlling the survival of stick slip at large size, can be evaluated by simulations of comparably small size. MD simulations of soft lubricant sliding are presented, which verify this theory.
    Physical Review Letters 02/2013; 110(8):085503. · 7.73 Impact Factor
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    ABSTRACT: We focus on the Gibbs free energy ΔG for nucleating a droplet of the stable phase (e.g., solid) inside the metastable parent phase (e.g., liquid), close to the first-order transition temperature. This quantity is central to the theory of homogeneous nucleation, since it superintends the nucleation rate. We recently introduced a field theory describing the dependence of ΔG on the droplet volume V, taking into account besides the microscopic fuzziness of the droplet-parent interface, also small fluctuations around the spherical shape whose effect, assuming isotropy, was found to be a characteristic logarithmic term. Here we extend this theory, introducing the effect of anisotropy in the surface tension, and show that in the limit of strong anisotropy ΔG(V) once more develops a term logarithmic on V, now with a prefactor of opposite sign with respect to the isotropic case. Based on this result, we argue that the geometrical shape that large solid nuclei mostly prefer could be inferred from the prefactor of the logarithmic term in the droplet free energy, as determined from the optimization of its near-coexistence profile.
    The Journal of Chemical Physics 02/2013; 138(6):064508. · 3.12 Impact Factor
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    ABSTRACT: The increase of sliding friction upon increasing load is a classic in the macroscopic world. Here we discuss the possibility that friction rise might sometimes turn into a drop when, at the mesoscale and nanoscale, a confined lubricant film separating crystalline sliders undergoes strong layering and solidification. Under pressure, transitions from N to N-1 layers may imply a change of lateral periodicity of the crystallized lubricant sufficient to alter the matching of crystal structures, influencing the ensuing friction jump. A pressure-induced friction drop may occur as the shear gradient maximum switches from the lubricant middle, marked by strong stick-slip with or without shear melting, to the crystalline slider-lubricant interface, characterized by smooth superlubric sliding. We present high pressure sliding simulations to display examples of frictional drops, suggesting their possible relevance to the local behavior in boundary lubrication.
    Physical review. B, Condensed matter 01/2013; 87(4). · 3.77 Impact Factor
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    Andrea Vanossi, Nicola Manini, Erio Tosatti
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    ABSTRACT: In a pioneer experiment, Bohlein et al. realized the controlled sliding of two-dimensional colloidal crystals over laser-generated periodic or quasi-periodic potentials. Here we present realistic simulations and arguments that besides reproducing the main experimentally observed features give a first theoretical demonstration of the potential impact of colloid sliding in nanotribology. The free motion of solitons and antisolitons in the sliding of hard incommensurate crystals is contrasted with the soliton-antisoliton pair nucleation at the large static friction threshold F(s) when the two lattices are commensurate and pinned. The frictional work directly extracted from particles' velocities can be analyzed as a function of classic tribological parameters, including speed, spacing, and amplitude of the periodic potential (representing, respectively, the mismatch of the sliding interface and the corrugation, or "load"). These and other features suggestive of further experiments and insights promote colloid sliding to a unique friction study instrument.
    Proceedings of the National Academy of Sciences 09/2012; 109(41):16429-33. · 9.81 Impact Factor

Publication Stats

7k Citations
2,055.31 Total Impact Points

Institutions

  • 2005–2013
    • National Academy of Sciences of Ukraine
      • Institute of Physics
      Kiev, Misto Kyyiv, Ukraine
    • University of Udine
      Udine, Friuli Venezia Giulia, Italy
    • Università degli Studi dell'Aquila
      • Department of Chemistry, Chemical Engineering and Materials
      Aquila, Abruzzo, Italy
  • 2001–2013
    • Università degli Studi di Messina
      • Dipartimento di Fisica e di Scienze della Terra
      Messina, Sicily, Italy
  • 1982–2013
    • Scuola Internazionale Superiore di Studi Avanzati di Trieste
      Trst, Friuli Venezia Giulia, Italy
  • 2009–2012
    • Georgia Institute of Technology
      • School of Physics
      Atlanta, GA, United States
    • Ruhr-Universität Bochum
      Bochum, North Rhine-Westphalia, Germany
  • 2003–2009
    • University of Milan
      • Department of Physics
      Milano, Lombardy, Italy
    • Universidad del País Vasco / Euskal Herriko Unibertsitatea
      • Departamento de Física de Materiales
      Leioa, Basque Country, Spain
  • 2008
    • Hebrew University of Jerusalem
      • Fritz Haber Center for Molecular Dynamics Research
      Jerusalem, Jerusalem District, Israel
  • 2006–2007
    • Università degli Studi di Modena e Reggio Emilia
      Modène, Emilia-Romagna, Italy
  • 1977–2006
    • Abdus Salam International Centre for Theoretical Physics
      Trst, Friuli Venezia Giulia, Italy
  • 2004
    • Pierre and Marie Curie University - Paris 6
      Lutetia Parisorum, Île-de-France, France
    • Centro FERMI
      Roma, Latium, Italy
  • 1994–2003
    • Forschungszentrum Jülich
      Jülich, North Rhine-Westphalia, Germany
  • 2002
    • DEMOCRITOS
      Trst, Friuli Venezia Giulia, Italy
    • Sapienza University of Rome
      • Department of Physics
      Roma, Latium, Italy
    • Rosario National University
      • Institute of Physics (IFIR)
      Rosario, Santa Fe, Argentina
    • University of California, Davis
      • Department of Physics
      Davis, CA, United States
  • 1968–2001
    • Scuola Normale Superiore di Pisa
      Pisa, Tuscany, Italy
  • 2000
    • Università degli Studi di Milano-Bicocca
      • Department of Materials Science
      Milano, Lombardy, Italy
  • 1978–2000
    • Università degli Studi di Trieste
      Trst, Friuli Venezia Giulia, Italy
    • Stanford University
      Palo Alto, California, United States
  • 1997–1998
    • University of Padova
      Padua, Veneto, Italy
  • 1994–1995
    • University of Geneva
      • Department of Physical Chemistry
      Genève, GE, Switzerland
  • 1990
    • University of Naples Federico II
      • Department of Physical Sciences
      Napoli, Campania, Italy
  • 1985
    • University of Groningen
      Groningen, Groningen, Netherlands
  • 1977–1985
    • University of Pavia
      • Department of Physics
      Ticinum, Lombardy, Italy
  • 1981
    • Università della Calabria
      • Department of Physics
      Rende, Calabria, Italy
  • 1972–1977
    • National Research Council
      • Institute of Biophysics IBF
      Roma, Latium, Italy
  • 1976
    • University of Rome Tor Vergata
      Roma, Latium, Italy
  • 1970
    • Università Degli Studi Roma Tre
      Roma, Latium, Italy
  • 1969
    • Università di Pisa
      Pisa, Tuscany, Italy