The characterization of transport properties of nanostructures is central to numerous works in condensed matter physics. This is particularly true in fundamental research works on quantum properties of electronic transport across nano-objects (quantum dots, nanotubes), or in the field of molecular electronics or molecular spintronics. The main theme of this project is to study the quantum electronic transport properties of materials with strong electronic correlations in the regime of strong spatial confinement. When the size of a metallic or semi-conducting nanoparticle is reduced, the confinement of electronic wave functions in a tiny volume leads to a discrete electronic spectrum. As this electronic spectrum can be studied with tremendous precision by tunneling spectroscopy, it becomes possible to determine the energy levels distribution. This distribution can then be compared to theoretical predictions or numerical simulations. The study of quantum dots or nanoparticles with only a few electrons is particularly interesting because of the existing analogies with other many-body systems such as the electronic cloud surrounding individual atoms, atoms nucleus and cold atomic traps, which have defined several paradigms of many-body physics. Thus, the possibility to probe electronic energy levels distributions in materials with strong correlations provides us a mean to characterize these electronic correlations. Numerous progresses achieved in the synthesis of nanocrystals of various shapes and compositions provide us the opportunity to probe the discrete spectrum of nanoparticles with strong electronic correlations. This project will imply three partners who provide together all the required competences to achieve the tunneling spectroscopy of chemically-synthesized nanocrystals. Partner 1 and 3 are localized in Laboratoire Photons et Matière (LPEM), which is on the campus of ESPCI (Paris) and partner 2 is localized in Laboratoire de Physique des Solides (LPS) in Orsay. Partner 1, who is the coordinator of this project, is expert in the field of strongly correlated electronic systems and also has expertise in the synthesis and manipulation of metallic nanocrystals. Parter 2 is expert in mesoscopic physics, hybrids systems, Josephson junctions. Partner 3 is a group of physic-chemists, experts in the synthesis and characterization of nanocrystals of different shapes and composition, as well as in ligands exchange. A first part of the project is to study the statistical distribution of electronic levels of metallic (Au) and superconducting nanocrystals (Pb) obtained by chemical synthesis methods. A second part of this project is about the study of out of equilibrium transport properties of Mott nanocrystal, i.e. nanocrystals made from materials with characteristics properties of Mott insulators, in particular, NiO and VO2. A third part of this project is to measure the tunnel magnetoresistance of spinel nanocrystals MFe2O4 (M=Co,Ni), in order to test the spin-filtering abilities of these junctions. Finally, the fourth and last part of this project is to characterize the transport properties perpendicularly to thin films of insulating oxides such as VO2 and the spinels MFe2O4, using a n AFM/STM, working at low temperature and high magnetic field.

This project addresses one of the major open problems in theoretical physics: to give a theoretical description of the gravitational field in the regimes where its quantum properties cannot be disregarded. The problem is addressed within the framework on one of the main tentative quantum gravity theories: loop quantum gravity (LQG). Two recent developments define the context of this project. The first is theoretical, the second is observational: (i) The ANR project BLAN06-3_139436, to which the present project is partially a continuation, has lead to an unexpected theoretical success. The project has lead to the definition of a vertex amplitude that defines the dynamics of quantum gravity, circumventing the complications of the old canonical theory, and merging the covariant (spinfoam) and canonical approaches [Engle et al 2007a, Freidel-Krasnov 2008, Engle et al 2008]. The resulting theory appears to have a simple and manageable form, that can be used to compute transitions amplitude in quantum gravity explicitly. Thanks to these advances, we have today a manageable tentative background-independent theory of quantum gravity. This theory deserves to be explored in depth, in order to asses its viability as a candidate solution to the problem of quantum gravity. (ii) Contrary to what was almost universally assumed only short time ago, the possibility of measurements testing Planck-scale physics with current technology does not appear entirely impossible anymore. An example of this change is given by the recent announce of the MAGIC telescope collaboration of a preliminary observation of an energy-dependent time delay in the signals from the active galaxy Markarian 501, with a best fit of the parameter governing this dependence being M = 0.30 x 1018 GeV, which is precisely at the Planck scale [Albert et al 2008]. Such dependence was predicted by some quantum gravity theories. This particular observed phenomenon is probably not of quantum-gravitational origin, and it admits different explanations [Wagner 2008]. Nevertheless, the measurement shows clearly that Planck-scale effects are in principle observable, under appropriate observational condition (the amplification factor is given here by the cosmological distance traveled by the signal). Similar observational results may appear soon. The '-rays space telescope GLAST should be able to measure similar effects in '-rays [Norris et al 1999]. The AUGER cosmic ray observatory has already reported a detailed study of the Greisen, Zatsepin and Kuzmin (GZK) threshold [Greisen 1966; Zatsepin-Kuzmin 1966], apparently already in measure of ruling out a proposed quantum-gravity violation of the GZK threshold [Abraham et al 2007]. The possibility of such measurements testing the Planck scale should strongly motivate all tentative theories of quantum gravity to make a resolute effort to produce precise quantitative predictions in all areas that have a chance, even slim, to be enter the reach of our observational means. The present project aims at realizing this objective within LQG. The collaboration that forms the present project is in the ideal position for addressing this task. Its core is formed by the members of the BLAN06-3_139436 ANR project, and brings together the best specific expertise available worldwide. In addition, it includes a new member and a new partner. The new member is Simone Speziale, who has actively collaborated with the previous project, and has been hired this year in France by the CNRS. The new partner is the mathematical physics group of Orsay, lead by Vincent Rivasseau. The joining of the project by Orsay is motivated by the realization that in order to achieve the goals of the project, it is essential to understand the scaling properties of the theory and its behavior under the renormalization group. The Orsay group has a world-renowned expertise in this matter and has the wide understanding of quantum field theory needed to generalize the tools developed in the context of conventional quantum field theory to the novel context of a background-independent theory. The project includes also a numerical calculus component, for which a specific technical expertise is under development in Marseille, taking also advantage of the presence of Laurent Lellouch' lattice QCD group, present in the same research center. The partners of the project have close collaborations with all the other major research centers in nonperturbative quantum gravity. In this larger context, the results of the previous ANR project have given the French collaboration a leading role internationally, role that we intend to maintain and strengthen with the present project.