Peerreviewed Publications 
Bergeron, H., Curado, E. M. F., Gazeau, J. P., & Rodrigues, L. M. C. S. (2012). Generating functions for generalized binomial distributions. JOURNAL OF MATHEMATICAL PHYSICS, 53(10), 103304.
Résumé: In a recent article generalization of the binomial distribution associated with a sequence of positive numbers was examined. The analysis of the nonnegativeness of the formal probability distributions was a key point to allow to give them a statistical interpretation in terms of probabilities. In this article we present an approach based on generating functions that solves the previous difficulties. Our main theorem makes explicit the conditions under which those formal probability distributions are always nonnegative. Therefore, the constraints of nonnegativeness are automatically fulfilled giving a complete characterization in terms of generating functions. A large number of analytical examples becomes available. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4757601]


Bergeron, H., Siegl, P., & Youssef, A. (2012). New SUSYQM coherent states for PoschlTeller potentials: a detailed mathematical analysis. JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL, 45(24).
Résumé: In a recent short note (Bergeron et al 2010 Europhys. Lett. 92 60003), we have presented the good properties of a new family of semiclassical states for PoschlTeller potentials. These states are built from a supersymmetric quantum mechanics (SUSYQM) approach and the parameters of these 'coherent' states are points in the classical phase space. In this paper, we develop all the mathematical aspects that have been left out of the previous paper (proof of the resolution of unity, detailed calculations of the quantized version of classical observables and mathematical study of the resulting operators: problems of domains, selfadjointness or selfadjoint extensions). Some additional questions such as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of PoschlTeller potentials. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Coherent states: mathematical and physical aspects'.


Borisov, A. G., Echenique, P. M., & Kazansky, A. K. (2012). Attostreaking with metallic nanoobjects. NEW JOURNAL OF PHYSICS, 14, 023036.
Résumé: The application of attosecond streaking spectroscopy (ASS) to direct timedomain studies of the plasmonic excitations in metallic nanoobjects is addressed theoretically. The streaking spectrograms for a rectangular gold nanoantenna and spherical gold clusters are obtained within strong field approximation using classical electron trajectory calculations. The results reported here for spherical clusters are also representative of spherical nanoshells. This study demonstrates that ASS allows for detailed characterization of plasmonic modes, including nearfield enhancement, frequency and decay rate. The role of the inhomogeneity of the induced electric fields is also demonstrated.


Chaabouni, H., Bergeron, H., Baouche, S., Dulieu, F., Matar, E., Congiu, E., Gavilan, L., & Lemaire, J. L. (2012). Sticking coefficient of hydrogen and deuterium on silicates under interstellar conditions. ASTRONOMY & ASTROPHYSICS, 538, A128.
Résumé: Context. Sticking of H and D atoms on interstellar dust grains is the first step in molecular hydrogen formation, which is a key reaction in the interstellar medium. Isotopic properties of the sticking can have an incidence on the observed HD molecule. Aims. After studying the sticking coefficients of H2 and D2 molecules on amorphous silicate surfaces experimentally and theoretically, we extrapolate the results to the sticking coefficient of atoms and propose a formulae that gives the sticking coefficients of H and D on both silicates and icy dust grains. Methods. In our experiments, we used the King and Wells method for measuring the sticking coefficients of H2 and D2 molecules on a silicate surface held at 10 K. It consists of measuring with a QMS (quadrupole mass spectrometer) the signals of H2 and D2 molecules reflected by the surface during the exposure of the sample to the molecular beam at a temperature ranging from 20 K to 340 K. We tested the efficiency of a physical model, developed previously for sticking on waterice surfaces. We applied this model to our experimental results for the sticking coefficients of H2 and D2 molecules on a silicate surface and estimated the sticking coefficient of atoms by a single measurement of atomic recombination and propose an extrapolation. Results. Sticking of H, D, HD, H2, and D2 on silicates grains behaves the same as on icy dust grains. The sticking decreases with the gas temperature, and is dependent on the mass of the impactor. The sticking coefficient for both surfaces and impactors can be modeled by an analytical formulae S (T) = S0(1 + beta T/ T0)/(1 + T/T0)(beta), which describes both the experiments and the thermal distribution expected in an astrophysical context. The parameters S0 and T0 are summarized in a table. Conclusions. Previous estimates for the sticking coefficient of H atoms are close to the new estimation; however, we find that, when isotopic effects are taken into account, the sticking coefficient variations can be as much as a factor of 2 at T = 100 K.


Esteban, R., Borisov, A. G., Nordlander, P., & Aizpurua, J. (2012). Bridging quantum and classical plasmonics with a quantumcorrected model. NATURE COMMUNICATIONS, 3, 825.
Résumé: Electromagnetic coupling between plasmonic resonances in metallic nanoparticles allows for engineering of the optical response and generation of strong localized nearfields. Classical electrodynamics fails to describe this coupling across subnanometer gaps, where quantum effects become important owing to nonlocal screening and the spillout of electrons. However, full quantum simulations are not presently feasible for realistically sized systems. Here we present a novel approach, the quantumcorrected model (QCM), that incorporates quantummechanical effects within a classical electrodynamic framework. The QCM approach models the junction between adjacent nanoparticles by means of a local dielectric response that includes electron tunnelling and tunnelling resistivity at the gap and can be integrated within a classical electrodynamical description of large and complex structures. The QCM predicts optical properties in excellent agreement with fully quantum mechanical calculations for small interacting systems, opening a new venue for addressing quantum effects in realistic plasmonic systems.


GarciaGil, S., Garcia, A., & Ordejon, P. (2012). Calculation of core level shifts within DFT using pseudopotentials and localized basis sets. EUROPEAN PHYSICAL JOURNAL B, 85(7), 239.
Résumé: The calculation of core level shifts can be done in the context of density functional theory (DFT) using different approaches and physical approximations to the photoemission process. The initial state and the Delta SCF approximations are the most commonly used ones. Here, we describe the details of their implementation in the context of DFT using pseudopotentials and localized atomic orbitals as a basis set, and in particular as applied to the Siesta code. We give a full account of the technicalities involved in these calculations, including the details of the ionic pseudopotential generation, basis sets, charge states and reference potential. We test the method by computing the core level shifts of the Si 2p level for a series of molecules and the p(2x2) asymmetric dimer reconstruction of the Si(001) surface.


Gauyacq, J.  P., Lorente, N., & Dutilh Novaes, F. (2012). Excitation of local magnetic moments by tunneling electrons. PROGRESS IN SURFACE SCIENCE, 87(58), 63–107.
Résumé: The advent of millikelvin scanning tunneling microscopes (STM) with inbuilt magnetic fields has opened access to the study of magnetic phenomena with atomic resolution at surfaces. In the case of single atoms adsorbed on a surface, the existence of different magnetic energy levels localized on the adsorbate is due to the breaking of the rotational invariance of the adsorbate spin by the interaction with its environment, leading to energy terms in the meV range. These structures were revealed by STM experiments in IBM Almaden in the early 2000s for atomic adsorbates on CuN surfaces. The experiments consisted in the study of the changes in conductance caused by inelastic tunneling of electrons (IETS, inelastic electron tunneling spectroscopy). Manganese and Iron adatoms were shown to have different magnetic anisotropies induced by the substrate. More experiments by other groups followed up, showing that magnetic excitations could be detected in a variety of systems: e.g. complex organic molecules showed that their magnetic anisotropy was dependent on the molecular environment, piles of magnetic molecules showed that they interact via intermolecular exchange interaction, spin waves were excited on ferromagnetic surfaces and in Mn chains, and magnetic impurities have been analyzed on semiconductors. These experiments brought up some intriguing questions: the efficiency of magnetic excitations was very high, the excitations could or could not involve spin flip of the exciting electron and singularlike behavior was sometimes found at the excitation thresholds. These facts called for extended theoretical analysis: perturbation theories, suddenapproximation approaches and a strong coupling scheme successfully explained most of the magnetic inelastic processes. In addition, manybody approaches were also used to decipher the interplay between inelastic processes and the Kondo effect. Spin torque transfer has been shown to be effective in changing spin orientations of an adsorbate in theoretical works, and soon after it was shown experimentally. More recently, the previously mentioned strong coupling approach was extended to treat the excitation of spin waves in atomic chains and the ubiquitous role of electronhole pair creation in deexciting spins on surfaces has been analyzed. This review article expounds these works, presenting the theoretical approach by the authors while trying to thoroughly review parallel theoretical and experimental works. (C) 2012 Elsevier Ltd. All rights reserved.


Gauyacq, J. P., & Lorente, N. (2012). Lifetime of magnetic excitations in supported ferromagnetic and antiferromagnetic spin1/2 Heisenberg chains. PHYSICAL REVIEW B, 85(11), 115420.
Résumé: The lifetime of magnetic excitations in finite 1Dsupported Heisenberg chains of magnetic atoms is studied theoretically for a model system formed of S = 1/2 spins. Both ferromagnetic and antiferromagnetic cases are considered as well as open chains and rings of atoms. Different chain lengths are considered allowing extrapolation to infinite chains. All the excited magnetic states in the finite chains and rings are studied, not only the spinwave mode. The magnetic excitations decay by electronhole pair creation in the substrate. As the main result, for all the systems considered, the decay rate appears to vary approximately proportionally to the excitation energy of the state, with a proportionality constant independent of the strength of the Heisenberg exchange term. In certain finite systems, a stable state is evidenced at low energy, associated with a special spin coupling structure.


Kaiser, F., Coudreau, T., Milman, P., Ostrowsky, D. B., & Tanzilli, S. (2012). EntanglementEnabled DelayedChoice Experiment. Science, 338(6107), 637–640.
Résumé: Waveparticle complementarity is one of the most intriguing features of quantum physics. To emphasize this measurement apparatus–dependent nature, experiments have been performed in which the output beam splitter of a MachZehnder interferometer is inserted or removed after a photon has already entered the device. A recent extension suggested using a quantum beam splitter at the interferometer’s output; we achieve this using pairs of polarizationentangled photons. One photon is tested in the interferometer and is detected, whereas the other allows us to determine whether wave, particle, or intermediate behaviors have been observed. Furthermore, this experiment allows us to continuously morph the tested photon’s behavior from wavelike to particlelike, which illustrates the inadequacy of a naive wave or particle description of light.


Korytar, R., Lorente, N., & Gauyacq, J.  P. (2012). Manybody effects in magnetic inelastic electron tunneling spectroscopy. PHYSICAL REVIEW B, 85(12), 125434.
Résumé: Magnetic inelastic electron tunneling spectroscopy (IETS) shows sharp increases in conductance when a new conductance channel associated with a change in magnetic structure is open. Typically, the magnetic moment carried by an adsorbate can be changed by collision with a tunneling electron; in this process the spin of the electron can flip or not. A previous oneelectron theory [Phys. Rev. Lett. 103, 176601 (2009)] successfully explained both the conductance thresholds and the magnitude of the conductance variation. The elastic spin flip of conduction electrons by a magnetic impurity leads to the wellknown Kondo effect. In the present work, we compare the theoretical predictions for inelastic magnetic tunneling obtained with a oneelectron approach and with a manybody theory including Kondolike phenomena. We apply our theories to a singlettriplet transition model system that contains most of the characteristics revealed in magnetic IETS. We use two selfconsistent treatments (noncrossing approximation and selfconsistent ladder approximation). We show that, although the oneelectron limit is properly recovered, new intrinsic manybody features appear. In particular, sharp peaks appear close to the inelastic thresholds; these are not localized exactly at thresholds and could influence the determination of magnetic structures from IETS experiments. Analysis of the evolution with temperature reveals that these manybody features involve an energy scale different from that of the usual Kondo peaks. Indeed, the manybody features perdure at temperatures much larger than the one given by the Kondo energy scale of the system.


Koval, N. E., SanchezPortal, D., Borisov, A. G., & Diez Muino, R. (2012). Dynamic screening of a localized hole during photoemission from a metal cluster. NANOSCALE RESEARCH LETTERS, 7(1), 1–9.
Résumé: Recent advances in attosecond spectroscopy techniques have fueled the interest in the theoretical description of electronic processes taking place in the subfemtosecond time scale. Here we study the coupled dynamic screening of a localized hole and a photoelectron emitted from a metal cluster using a semiclassical model. Electron density dynamics in the cluster is calculated with timedependent density functional theory, and the motion of the photoemitted electron is described classically. We show that the dynamic screening of the hole by the cluster electrons affects the motion of the photoemitted electron. At the very beginning of its trajectory, the photoemitted electron interacts with the cluster electrons that pile up to screen the hole. Within our model, this gives rise to a significant reduction of the energy lost by the photoelectron. Thus, this is a velocitydependent effect that should be accounted for when calculating the average losses suffered by photoemitted electrons in metals.


Marinica, D. C., Kazansky, A. K., Nordlander, P., Aizpurua, J., & Borisov, A. G. (2012). Quantum Plasmonics: Nonlinear Effects in the Field Enhancement of a Plasmonic Nanoparticle Dimer. NANO LETTERS, 12(3), 1333–1339.
Résumé: A fully quantum mechanical investigation using timedependent density functional theory reveals that the field enhancement in a coupled nanoparticle dimer can be strongly affected by nonlinear effects. We show that both classical as well as linear quantum mechanical descriptions of the system fail even for moderate incident light intensities. An interparticle current resulting from the strong field photo emission tends to neutralize the plasmoninduced surface charge densities on the opposite sides of the nanoparticle junction. Thus, the coupling between the two nanoparticles and the field enhancement is reduced as compared to linear theory. A substantial nonlinear effect is revealed already at incident powers of 10(9) W/cm(2) for interparticle separation distances as large as 1 nm and down to the touching limit.


Savage, K. J., Hawkeye, M. M., Esteban, R., Borisov, A. G., Aizpurua, J., & Baumberg, J. J. (2012). Revealing the quantum regime in tunnelling plasmonics. NATURE, 491(7425), 574–577.
Résumé: When two metal nanostructures are placed nanometres apart, their optically driven free electrons couple electrically across the gap. The resulting plasmons have enhanced optical fields of a specific colour tightly confined inside the gap. Many emerging nanophotonic technologies depend on the careful control of this plasmonic coupling, including optical nanoantennas for highsensitivity chemical and biological sensors(1), nanoscale control of active devices(24), and improved photovoltaic devices(5). But for subnanometre gaps, coherent quantum tunnelling becomes possible and the system enters a regime of extreme nonlocality in which previous classical treatments(614) fail. Electron correlations across the gap that are driven by quantum tunnelling require a new description of nonlocal transport, which is crucial in nanoscale optoelectronics and singlemolecule electronics. Here, by simultaneously measuring both the electrical and optical properties of two gold nanostructures with controllable subnanometre separation, we reveal the quantum regime of tunnelling plasmonics in unprecedented detail. All observed phenomena are in good agreement with recent quantumbased models of plasmonic systems(15), which eliminate the singularities predicted by classical theories. These findings imply that tunnelling establishes a quantum limit for plasmonic field confinement of about 10(8) lambda(3) for visible light (of wavelength lambda). Our work thus prompts new theoretical and experimental investigations into quantumdomain plasmonic systems, and will affect the future of nanoplasmonic device engineering and nanoscale photochemistry.


Schubert, K., Damm, A., Eremeev, S. V., Marks, M., Shibuta, M., Berthold, W., Guedde, J., Borisov, A. G., Tsirkin, S. S., Chulkov, E. V., & Hoefer, U. (2012). Momentumresolved electron dynamics of imagepotential states on Cu and Ag surfaces. PHYSICAL REVIEW B, 85(20), 205431.
Résumé: The dependence of the inelastic lifetime of electrons in the first n = 1 imagepotential state of clean and raregas covered Ag(111), Cu(111), and Cu(100) surfaces on their momentum parallel to the surface has been studied experimentally by means of timeand angleresolved twophoton photoemission spectroscopy (2PPE) and theoretically by calculations based on the manybody theory within the selfenergy formalism. Similar to the previously studied clean Cu(100) surface, the theoretical results are in excellent agreement with the experiment findings for Cu(111). For Ag(111), the theory overestimates the decay rate and its momentum dependence, which is attributed to the neglect of surface plasmon excitations. With increasing parallel momentum, the n = 1 state shifts out of the projected bulk band gap on both surfaces and turns into an imagepotential resonance. This opens an additional decay channel by resonant electron transfer into the bulk, which is theoretically treated by the application of the wave packet propagation approach. The expected stronger increase of the decay rate upon crossing the edge of the band gap, however, is not observed in the experiment. The decoupling of the imagepotential states from the metal surface upon adsorption of raregas layers results in a decrease of the decay rate as well as of its momentum dependence by a similar factor, which can be successfully explained by the change of interband and intraband contributions to the total decay rate.


Zugarramurdi, A., & Borisov, A. G. (2012). Transition from fast to slow atom diffraction. PHYSICAL REVIEW A, 86(6), 062903.
Résumé: For energetic atomic beams grazingly incident at a surface along lowindex directions, the fast motion of the projectile in the surface plane and the slow motion in the direction perpendicular to the surface appear nearly decoupled. Fastatom diffraction (FAD) experiments reveal twodimensional (2D) diffraction patterns associated with exchange of the reciprocal vector perpendicular to the lowindex direction of fast motion. These results are usually interpreted within the axialchanneling approximation, where the effective 2D potential experienced by the projectile is set as an average of the 3D surface potential along the atomic strings forming the channel. In this work, using the example of grazing scattering of He atoms at a LiF(001) surface, we address theoretically the range of validity of the axialchanneling approximation. Full quantum wavepacketpropagation calculations are used to study the transition from the 2D (fast atom) to the 3D diffraction pattern characteristic for lowenergy atomic and molecular projectiles scattered from surfaces. Along with exact calculations, a semianalytical perturbative treatment based on the LippmannSchwinger equation allows an explanation of why the diffraction processes involving the exchange of reciprocallattice vectors along the fastmotion direction are exponentially small in typical FAD conditions.


Zugarramurdi, A., Zabala, N., Silkin, V. M., Chulkov, E. V., & Borisov, A. G. (2012). Quantumwell states with image state character for Pb overlayers on Cu(111). PHYSICAL REVIEW B, 86(7), 075434.
Résumé: We study theoretically the quantum well states (QWSs) localized in Pb overlayers on Cu(111) surface. Particular emphasis is given to the states with energies close to the vacuum level. Inclusion of the longrange image potential tail into the model potential description of the system allows us to show the effect of hybridization between QWSs and image potential states (ISs). The particleinabox energy sequence characteristic for QWSs evolves into the Rydberg series converging towards the vacuum level. The electron density of the corresponding states is partially moved from inside the metal overlayer into the vacuum. The decay rates due to the inelastic electronelectron scattering decrease with increasing energy, opposite to “conventional” QWSs and similar to the ISs. Manybody and wave packet propagation calculations of the inelastic decay rates are supplemented by simple analysis based on the phase accumulation model and wavefunction penetration approximation. This allows an analytical description of the dependence of the QWS/ISs hybridization on different parameters and, in particular, on the overlayer thickness.

