Antoine Georges

Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications

Abstract The subject of this paper is the evolution of Brownian particles in disordered environments. The “Ariadnes clew” we follow is understanding of the general statistical mechanisms which may generate “anomalous” (non-Brownian) diffusion laws; this allows us to develop simple arguments to obtain a qualitative (but often quite accurate) picture of most situations. Several analytical techniques-such as the Green function formalism and renormalization group methods-are also exposed. Care is devoted to the problem of sample to sample fluctuations, particularly acute here. We consider the specific effects of a bias on anomalous diffusion, and discuss the generalizations of Einsteins relation in the presence of disorder. An effort is made to illustrate the theoretical models by describing many physical situations where anomalous diffusion laws have been-or could be-observed.

Dynamical singlets and correlation-assisted Peierls transition in VO2.

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.

Two energy scales and two distinct quasiparticle dynamics in the superconducting state of underdoped cuprates

The superconducting temperature Tc of hole-doped high-temperature superconductors has a dome-like shape as a function of hole concentration, with a maximum Tc at ‘optimal’ doping. On the underdoped side, the superconducting state is often described in terms of one energy scale, associated with the maximum of the d-wave gap (at the antinodes), which increases as the doping decreases. Here, we report electronic Raman scattering experiments that show a second energy scale in the gap function: the slope of the gap at the nodes, which decreases with decreasing doping. Our measurements also reveal two distinct quasiparticle dynamics; electronic coherence persists down to low doping levels at the nodes, whereas antinodal quasiparticles become incoherent. Using a sum-rule, we find that the low-frequency Raman response and the temperature dependence of the superfluid density, both controlled by nodal excitations, behave in a qualitatively similar manner with doping variation.

Universality and Critical Behavior at the Mott Transition

We report conductivity measurements of Cr-doped V2O3 using a variable pressure technique. The critical behavior of the conductivity near the Mott-insulator to metal critical endpoint is investigated in detail as a function of pressure and temperature. The critical exponents are determined, as well as the scaling function associated with the equation of state. The universal properties of a liquid-gas transition are found. This is potentially a generic description of the Mott critical endpoint in correlated electron materials.

Frequency-dependent local interactions and low-energy effective models from electronic structure calculations

We propose a systematic procedure for constructing effective models of strongly correlated materials. The parameters, in particular the on-site screened Coulomb interaction

Mott transition and suppression of orbital fluctuations in orthorhombic 3d(1) perovskites

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Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography

, are calculated from first principles, using the random-phase approximation. We derive an expression for the frequency-dependent

Classical diffusion of a particle in a one-dimensional random force field

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Electronic Correlations in Transport through Coupled Quantum Dots

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

Strong Correlations from Hund’s Coupling

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