Centre de Physique Théorique

A review of the basic ideas and techniques of the spectral density-functional theory is presented. This method is currently used for electronic structure calculations of strongly correlated materials where the one-electron description breaks down. The method is illustrated with several examples where interactions play a dominant role: systems near metal-insulator transitions, systems near volume collapse transitions, and systems with local moments.

Almost all theories of fundamental interactions are nowadays based on the gauge concept. Starting with the historical example of quantum electrodynamics, we have been led to the successful unified gau

We present a new continuous-time solver for quantum impurity models such as those relevant to dynamical mean field theory. It is based on a stochastic sampling of a perturbation expansion in the impurity-bath hybridization parameter. Comparisons with Monte Carlo and exact diagonalization calculations confirm the accuracy of the new approach, which allows very efficient simulations even at low temperatures and for strong interactions. As examples of the power of the method we present results for the temperature dependence of the kinetic energy and the free energy, enabling an accurate location of the temperature-driven metal-insulator transition.

The charge separation effects in the collisionless plasma expansion into a vacuum are studied in great detail. Accurate results are obtained concerning the structure of the ion front, the resultant ion energy spectrum, and more specifically the maximum ion energy. These are of crucial importance for the interpretation of recent experiments, where high-energy ion jets were produced from short pulse interaction with solid targets.

Strong electronic correlations are often associated with the proximity of a Mott-insulating state. In recent years however, it has become increasingly clear that the Hund’s rule coupling (intra-atomic exchange) is responsible for strong correlations in multiorbital metallic materials that are not close to a Mott insulator. Hund’s coupling has two effects: It influences the energetics of the Mott gap and strongly suppresses the coherence scale for the formation of a Fermi liquid. A global picture has emerged recently, which emphasizes the importance of the average occupancy of the shell as a control parameter. The most dramatic effects occur away from half-filling or single occupancy. We review the theoretical understanding and physical properties of these Hund’s metals, together with the relevance of this concept to transition-metal oxides (TMOs) of the 3d, and especially 4d, series (such as ruthenates), as well as to the iron-based superconductors (iron pnictides and chalcogenides).

We propose a systematic procedure for constructing effective models of strongly correlated materials. The parameters, in particular the on-site screened Coulomb interaction $U$, are calculated from first principles, using the random-phase approximation. We derive an expression for the frequency-dependent $U(\ensuremath{\omega})$ and show, for the case of nickel, that its high-frequency part has significant influence on the spectral functions. We propose a scheme for taking into account the energy dependence of $U(\ensuremath{\omega})$, so that a model with an energy-independent local interaction can still be used for low-energy properties.

A theory of the metal-insulator transition in vanadium dioxide from the high- temperature rutile to the low- temperature monoclinic phase is proposed on the basis of cluster dynamical mean-field theory, in conjunction with the density functional scheme. The interplay of strong electronic Coulomb interactions and structural distortions, in particular, the dimerization of vanadium atoms in the low-temperature phase, plays a crucial role. We find that VO2 is not a conventional Mott insulator, but that the formation of dynamical V-V singlet pairs due to strong Coulomb correlations is necessary to trigger the opening of a Peierls gap.

Synchronization properties of fully connected networks of identical oscillatory neurons are studied, assuming purely excitatory interactions. We analyze their dependence on the time course of the synaptic interaction and on the response of the neurons to small depolarizations. Two types of responses are distinguished. In the first type, neurons always respond to small depolarization by advancing the next spike. In the second type, an excitatory postsynaptic potential (EPSP) received after the refractory period delays the firing of the next spike, while an EPSP received at a later time advances the firing. For these two types of responses we derive general conditions under which excitation destabilizes in-phase synchrony. We show that excitation is generally desynchronizing for neurons with a response of type I but can be synchronizing for responses of type II when the synaptic interactions are fast. These results are illustrated on three models of neurons: the Lapicque integrate-and-fire model, the model of Connor et al., and the Hodgkin-Huxley model. The latter exhibits a type II response, at variance with the first two models, that have type I responses. We then examine the consequences of these results for large networks, focusing on the states of partial coherence that emerge. Finally, we study the Lapicque model and the model of Connor et al. at large coupling and show that excitation can be desynchronizing even beyond the weak coupling regime.

We present here a general framework to produce quasiperiodic tilings and more general quasiperiodic patterns in $n$ dimensions corresponding to a finite number of local neighborings around each point. In particular, we give simple descriptions of the Penrose tilings of the plane and of a tiling of the three-dimensional space which exhibits an icosahedral symmetry. The Fourier transform of this last pattern is derived and shows a striking similarity with the electron-diffraction images obtained for a recently discovered alloy of Al and Mn.

Light upconverting nanostructures employing lanthanide ions constitute an emerging research field recognized with wide ramifications and impact in many areas ranging from healthcare, to energy and, to security. The core-shell design of these nanostructures allows us to deliberately introduce a hierarchy of electronic energy states, thus providing unprecedented opportunities to manipulate the electronic excitation, energy transfer and upconverted emissions. The core-shell morphology also causes the suppression of quenching mechanisms to produce efficient upconversion emission for biophotonic and photonic applications. Using hierarchical architect, whereby each shell layer can be defined to have a specific feature, the electronic structure as well as the physiochemical structure of the upconverting nanomaterials can be tuned to couple other electronic states on the surface such as excitations of organic dye molecules or localized surface plasmons from metallic nanostructures, or to introduce a broad range of imaging or therapeutic modalities into a single conduct. In this review, we summarize the key aspects of nanophotonic control of the light upconverting nanoparticles through governed design and preparation of hierarchical shells in the core-shell nanostructures, and review their emerging applications in the biomedical field, solar energy conversion, as well as security encoding.

Femtosecond time-resolved photoemission is used to investigate the time evolution of electronic structure in the Mott insulator 1T-TaS2. A collapse of the electronic gap is observed within 100 femtoseconds after optical excitation. The photoemission spectra and the spectral function calculated by dynamical mean field theory show that this insulator-metal transition is driven solely by hot electrons. A coherently excited lattice displacement results in a periodic shift of the spectra lasting for 20 ps without perturbing the insulating phase. This capability to disentangle electronic and phononic excitations opens new directions to study electron correlation in solids.

We present an integrability criterion for discrete-time systems that is the equivalent of the Painlev\'e property for systems of a continuous variable. It is based on the observation that for integrable mappings the singularities that may appear are confined, i.e., they do not propagate indefinitely when one iterates the mapping. Using this novel criterion we show that there exists a family of nonautonomous integrable mappings which includes the discrete Painlev\'e equations by ${\mathit{P}}_{\mathrm{I}}$, recently derived in a model of two-dimensional quantum gravity, and ${\mathit{P}}_{\mathrm{II}}$, obtained as a similarity reduction of the integrable modified Korteweg--de Vries lattice. These systems possess Lax pairs, a well-known integrability feature.

Using t(2g) Wannier functions, a low-energy Hamiltonian is derived for orthorhombic 3d(1) transition-metal oxides. Electronic correlations are treated with a new implementation of dynamical mean-field theory for noncubic systems. Good agreement with photoemission data is obtained. The interplay of correlation effects and cation covalency (GdFeO3-type distortions) is found to suppress orbital fluctuations in LaTiO3 and even more in YTiO3, and to favor the transition to the insulating state.

Bulk damage induced by fs IR laser pulses in silica is investigated both experimentally and numerically. In a strong focusing geometry, a first damage zone is followed by a narrow track with submicron width, indicating a filamentary propagation. The shape and size of the damage tracks are shown to correspond to the zone where the electron density created by optical field ionization and avalanche is close to ${10}^{20}\text{ }\text{ }{\mathrm{c}\mathrm{m}}^{\ensuremath{-}3}$. The relative role of avalanche and photoionization is studied. The plasma density produced in the wake of the pulse is shown to saturate around $2--4\ifmmode\times\else\texttimes\fi{}{10}^{20}\text{ }\text{ }{\mathrm{c}\mathrm{m}}^{\ensuremath{-}3}$.

The stability criterion of the internal kink mode is given in toroidal geometry for plasmas with circular cross sections. Contrary to known results in cylindrical geometry, the internal kink mode can be stable if the pressure gradient is sufficiently low.

Essentially all high temperature superconductors display a ``strange metal'' regime above their critical temperatures, where electrical and thermal transport cannot be explained within the traditional Fermi liquid paradigm of quasiparticle excitations. This paper focuses on the first, and newly discovered, solvable theory of a disordered metal without quasiparticle excitations, obtained by extending the Sachdev-Ye-Kitaev (SYK) models to finite spatial dimensions. The complete thermoelectric conductivity matrix is computed, and a surprising exact relation is found between the Seebeck coefficient and the derivative of the thermodynamic entropy with respect to the density. These computations are then compared with holographic theories which map strange metals onto black holes in theories of quantum gravity with one extra spatial dimension.

By comparison with fully kinetic Fokker-Planck calculations, a nonlocal macroscopic formula has been derived for the thermal heat flux. This formula leads in a physically relevant way to the saturation and the delocalization of the heat flux. Its introduction in a fluid code is straightforward and gives to some extent results comparable with classical flux-limited transport calculations with $f=0.1$. However, it also describes a significant level of preheating.

We review, extend, and give some further applications of a method recently suggested to solve the renormalization-scheme-dependence problem in perturbative field theories. The use of a coupling constant as a universal expansion parameter is abandoned. Instead, to each physical quantity depending on a single scale variable is associated an effective charge, whose corresponding St\"uckelberg---Peterman---Gell-Mann---Low function is identified as the proper object on which perturbation theory applies. Integration of the corresponding renormalization-group equations yields renormalization-scheme-invariant results free of any ambiguity related to the definition of the kinematical variable, or that of the scale parameter $\ensuremath{\Lambda}$, even though the theory is not solved to all orders. As a by-product, a renormalization-group improvement of the usual series is achieved. Extension of these methods to operators leads to the introduction of renormalization-group-invariant Green's function and Wilson coefficients, directly related to effective charges. The case of nonzero fermion masses is discussed, both for fixed masses and running masses in mass-independent renormalization schemes. The importance of the scale-invariant mass $\stackrel{^}{m}$ is emphasized. Applications are given to deep-inelastic phenomena, where the use of renormalization-group-invariant coefficient functions allows to perform the factorization without having to introduce a factorization scale. The Sudakov form factor of the electron in QED is discussed as an example of an extension of the method to problems involving several momentum scales.

Fast time averaged equations are derived for the motion of particles and the generation of electromagnetic wake fields under the action of the ponderomotive potential of an ultraintense laser pulse propagating through a tenuous plasma. Based on these averaged equations, a new particle code is designed which calculates the particle trajectories on the plasma period time scale. The regime of total cavitation of the plasma is investigated. It is found that stable propagation over a long distance is possible in this regime, and that energetic electrons are produced with a simple characteristic dependence of their angle of deflection on energy. This new code allows for computationally efficient modeling of pulse propagation over great distances.

We present a new approach to the theory of large-scale solar eruptive phenomena such as coronal mass ejections and two-ribbon flares, in which twisted flux tubes play a crucial role. We show that it is possible to create a highly nonlinear three-dimensional force-free configuration consisting of a twisted magnetic flux rope representing the magnetic structure of a prominence (surrounded by an overlaying, almost potential, arcade) and exhibiting an S-shaped structure, as observed in soft X-ray sigmoid structures. We also show that this magnetic configuration cannot stay in equilibrium and that a considerable amount of magnetic energy is released during its disruption. Unlike most previous models, the amount of magnetic energy stored in the configuration prior to its disruption is so large that it may become comparable to the energy of the open field.