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** Systèmes électroniques corrélés, supraconductivité et magnétisme **

*Strongly correlated systems are characterized by the fact that their electronic structure is not dominated by the kinetic energy as in simpler weakly interacting systems. Consequences are twofold. First, charge, spin, orbital, lattice etc. degrees of freedom are not hindered by the delocalization and thus can express their interaction or competition, resulting in a large diversity of ground states and exotic properties. Second, their electronic struc- ture can no more be described using mean field type of methods and requires the superposition of many elec- tronic configurations on an equal footing. This is why simple effective models such as the Hubbard model or its extensions are often used to generically describe such systems. In our group we tackle different aspects of the correlation problem going from methodological developments, to the study of realistic systems involving the integration between ab initio methods and models, via the study of the generic properties of the effective models involving the interplay between different degrees of freedom.*

Among the most archetypal strongly correlated systems are the Kondo model and the heavy fermions systems. In several of the latter, abrupt changes of the Fermi surface (often called Lifshitz transitions) have been observed under applied pressure or magnetic field. We explored several models that could lead to such instabilities. In Kondo alloys, and for large Kondo interaction, we revealed the existence of a drastic change in electronic structure, when the number of available conduction electrons is exactly equal to the number of Kondo impurities. At the critical point the system evolves from a local to a coherent Fermi liquid, with a discontinuous change of microscopic characteristics (effective mass, number of carriers, etc., see Scientific achievements). In frustrated lattices, different types of non-magnetic ground states can be stabilized when the absence of long range mag- netic order may result either from local screening (Kondo effect) or from strong intersite frustration. We showed that in a Shastry-Sutherland lattice, these two different phases can be found and differentiated from their Fermi surface, since in the case of Kondo screening the f-electrons participate to the Fermi surface, while in the other case the frustration dominates.

The combination of frustration and electronic correlations also plays an important role in multiferroic materials. However to understand the relative roles of the different degrees of freedom on the coupling between the elec- tric properties (polarization, dielectric constant) and magnetic orders or excitations, it is necessary to quantify the amplitudes of the different degrees of freedom and their interactions. For this purpose one needs to relate quantitatively the effective models to different types of real systems. This is why we developed a methodology integrating ab initio calculations, the determination and study of material specific effective models, symmetry analysis and Landau theory (see Scientific achievements). Using this methodology we conduced a complete study of an archetypal multiferroic system (YMnO3). We were successful not only to compute the macroscopic magneto-electric tensor measured experimentally, but also the contribution of each layer, the evolution of the magnetic coupling under an applied electric field, the relative importance of the Dzyloshinskii-Moriya interac- tion versus the exchange striction or the magneto-striction, and the latter microscopic origin. Integrating these informations within a Landau analysis we were able to explain experimental results such as the polarization and dielectric constant measurements, neutrons scattering and second harmonic generation results. Of course such type of studies are conducted in close collaboration with experimentalist groups.

**Correlations, charge order and frustration**

Using a variety of methods, we look for novel, exotic phases or anomalous electronic properties in correlated lattice models, more specifically when there is an interplay between correlations and charge ordering. In this respect, a fruitful line of research concerns the interplay between charge ordering and the Mott metal- insulator transition in electronic systems where the lattice structure frustrates the insulating charge ordered state. This is for example the case in the superconducting organic salts of the θ − (BEDT − TTF)2X family, or in the transition metal dichalcogenides, which both present layered triangular lattice structures. Studying the extended Hubbard model appropriate to these materials, we were able to show that the presence of charge or- dering fluctuations leads to a strong renormalization of the electron liquid, even far from the integer band fillings where Mott physics is commonly observed. Upon approaching the quantum critical point, such fluctuations were shown to lead to a total destruction of the quasiparticles. Even more exotic properties have been found in the so- called pinball liquid phase. This is a charge ordered metallic phase akin to a supersolid, where Wigner crystallized electrons (pins) coexist with itinerant electrons (balls). In this quantum phase, which is realized in order to lift the massive degeneracy of the classical interacting problem, the coupling between localized and itinerant electrons induces an emergent “heavy-fermion” behavior. The proposed theoretical scenario indicates strong analogies between strongly interacting electron systems as diverse as the heavy fermions, transition metal oxides, organic conductors, as well as the two-dimensional electron gas (2DEG) on the verge of Wigner crystallization.

Our studies focus on the magnetic phases resulting from the frustration of spin-spin interactions and their dynamics : presence or absence of broken symmetries (classical or quantum “spin liquid”), effects of local constraints (eg Ising anisotropy in “spin ices”), phase transitions induced by a strong magnetic field (Bose-Einstein condensation or magnetization steps and their classification). Some of these studies are motivated by experiences taking place at various places including locally (Institut NEEL, National High Magnetic Field Laboratory, Institute Laue Langevin) ; others are mainly theoretical and involve the development of novel simulation algorithms.

Concerning classical spin ices, which can be found in condensed matter or artificial lithographed structures, our goal is to understand the thermodynamic properties of these model systems, their athermal modelling for artificial structures, and the non-equilibrium as well as temporal behaviors. These systems allow to observe interest- ing phases with emerging degrees of freedom like classical magnetic monopoles, or exotic phenomena like the fragmentation of spin degrees of freedom. We are also interested in the dynamics of classical spins in equilibrium and non-equilibrium models in localized spins frustrated systems. These models sustain unconventional excitations, such as coherent motion of loops, which are built on massively degenerate frustrated magnetic manifolds. Understanding the development of these excitations and their signatures in the dynamic structure factors allows in particular to understand or inter- pret many experimental results.

**Superconductivity and superfluidity**

A variety of strongly correlated electron systems present superconducting phases, however correlation is mostly known for its relation with high Tc superconductors (cuprates or pnictides).

In cuprates, we tackle this subject according to different angles such as the link between the pseudo-gap physics and the quasiparticles destruction, the transport properties in the pseudo-gap phase described by a phenom- enological model of the Fermi arcs, or the influence of interband pairing in 2-band models. We were able to show that while in 1-band models, superconductivity appears at infinitesimal attractive interaction, in 2-band models, a Quantum Critical point appears and the superconducting order is resilient to strong repulsion. Another point of view is the use the intrinsic crystalline metastability of the cuprates. Indeed, we showed that local dynamical lattice instability favours large critical temperatures. It is controlled by the density of superfluid charge carriers rather than the energy of Cooper-pairing. The pairing in such a system is dynamical rather than static, whereby itinerant charge carriers are trapped in a Feshbach resonance pair exchange coupling (triggered by dynamically fluctuating ligand environments). It correlates amplitude and phase fluctuations, which is respon- sible for the superconducting state to emerge out of an insulator via a doping induced quantum phase transition.

In pnictides, a major challenge is to understand the interplay between structural, magnetic and superconduct- ing phase transitions. As is the case for multiferroics, these systems present a strong magnetoelastic coupling. The latter appears to be behind the salient features the phase diagram. Besides establishing a universal phase diagram for the magneto-structural phase transitions, we identified the structural instability as a precursor to the magnetic transition and explained the origin of the sensitivity of the magneto-structural transition temperature to uniaxial stress. In iron-chalcogenides we showed that the structural deformations are due to the magnetic order and that the origin of the magnetic instability at a non-nesting wave-vector (in FeTe) is due to the magne- toelastic interaction. Taken together, these works demonstrate the importance of these interactions in the iron based superconducting systems.

On more conventional superconductivity (phonon-mediated BCS, in weakly correlated systems) of highly-doped group IV semiconductors and insulators, ab initio methods have been developed in a modified density functional scheme. Using such a method we showed that for a doping range of a few per cent, the picture is a degenerate system with the Fermi level entering valence bands. This picture was found quite resilient both under system change (diamond, silicon, silicon carbide) and disorder, a theoretical prediction later confirmed by ARPES experi- ments. Let us note that this technique also allowed us to compute both the electron–phonon coupling and the value of the critical temperature.

Close to superconductivity is superfluidity. We obtained rather strong and direct evidence for the existence of an exotic superfluid phase in doped Resonating Valence Bond (RVB) models expected to be realized in quantum spin systems with strong frustration. Such systems exhibit a novel type of elementary excitation called holon, car- rying an electric charge but no spin. We recently proved the existence of a dynamical statistical transmutation of holons, from fermions to bosons, and the condensation of a superfluid phase. Such transmutations can be moni- tored by studying the nodes of the wave function. One spectacular example is obtained at intermediate values of the doping where the system seems to switch from a Fermi liquid to a (bosonic) charge-e superfluid phase.

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