On the application of Mattis-Bardeen theory in strongly disordered superconductors

The low energy optical conductivity of conventional superconductors is usually well described by Mattis-Bardeen (MB) theory which predicts the onset of absorption above an energy corresponding to twice the superconducing (SC) gap parameter Delta. Recent experiments on strongly disordered superconductors have challenged the application of the MB formulas due to the occurrence of additional spectral weight at low energies below 2Delta. Here we identify three crucial items which have to be included in the analysis of optical-conductivity data for these systems: (a) the correct identification of the optical threshold in the Mattis-Bardeen theory, and its relation with the gap value extracted from the measured density of states, (b) the gauge-invariant evaluation of the current-current response function, needed to account for the optical absorption by SC collective modes, and (c) the inclusion into the MB formula of the energy dependence of the density of states present already above Tc. By computing the optical conductvity in the disordered attractive Hubbard model we analyze the relevance of all these items, and we provide a compelling scheme for the analysis and interpretation of the optical data in real materials.Comment: 11 pages, 6 figure

Electron-phonon Interaction close to a Mott transition

The effect of Holstein electron-phonon interaction on a Hubbard model close to a Mott-Hubbard transition at half-filling is investigated by means of Dynamical Mean-Field Theory. We observe a reduction of the effective mass that we interpret in terms of a reduced effective repulsion. When the repulsion is rescaled to take into account this effect, the quasiparticle low-energy features are unaffected by the electron-phonon interaction. Phonon features are only observed within the high-energy Hubbard bands. The lack of electron-phonon fingerprints in the quasiparticle physics can be explained interpreting the quasiparticle motion in terms of rare fast processes.Comment: 4 pages, 3 color figures. Slightly revised text and references. Kondo effect result added in Fig. 2 for comparison with DMFT dat

Phase Separation close to the density-driven Mott transition in the Hubbard-Holstein model

The density driven Mott transition is studied by means of Dynamical Mean-Field Theory in the Hubbard-Holstein model, where the Hubbard term leading to the Mott transition is supplemented by an electron-phonon (e-ph) term. We show that an intermediate e-ph coupling leads to a first-order transition at T=0, which is accompanied by phase separation between a metal and an insulator. The compressibility in the metallic phase is substantially enhanced. At quite larger values of the coupling a polaronic phase emerges coexisting with a non-polaronic metal.Comment: 4 pages, 3 figures. Slightly revised text. More details in Fig.1 and 2. Smaller size version of Fig.

Electron-phonon interaction and antiferromagnetic correlations

We study effects of the Coulomb repulsion on the electron-phonon interaction (EPI) in a model of cuprates at zero and finite doping. We find that antiferromagnetic correlations strongly enhance EPI effects on the electron Green's function with respect to the paramagnetic correlated system, but the net effect of the Coulomb interaction is a moderate suppression of the EPI. Doping leads to additional suppression, due to reduced antiferromagnetic correlations. In contrast, the Coulomb interaction strongly suppresses EPI effects on phonons, but the suppression weakens with doping.Comment: 4 pages and 5 figure

Doping-driven transition to a time-reversal breaking state in the phase diagram of the cuprates

Motivated by recent tunnelling and Andreev-reflection experiments, we study the conditions for a quantum transition within the superconducting phase of the cuprates,in which a bulk imaginary (time-reversal breaking) $id_{xy}$component appears in addition to the $d_{x^2 - y^2}$ order parameter. We examine in detail the role of some important physical features of the cuprates.In particular we show that a closed Fermi surface,a bilayer splitting, an orthorhombic distortion,and the proximity to a quantum critical point around optimal doping favor the appearance of the imaginary component. These findings could explain why the mixed $d_{x^2 - y^2}+ id_{xy}$ order parameter is observed in YBCO and LSCO, and suggest that it could appear also in Bi2212. We also predict that, in all cuprates, the mixed state should be stable only in a limited doping region all contained beneath the $d_{x^2 - y^2}$ dome. The behavior of the specific heat at the secondary transition is discussed.Comment: 8 pages, 3 figures. Expanded text, 1 extra figur

Unconventional Hall effect in pnictides from interband interactions

We calculate the Hall transport in a multiband systems with a dominant interband interaction between carriers having electron and hole character. We show that this situation gives rise to an unconventional scenario, beyond the Boltzmann theory, where the quasiparticle currents dressed by vertex corrections acquire the character of the majority carriers. This leads to a larger (positive or negative) Hall coefficient than what expected on the basis of the carrier balance, with a marked temperature dependence. Our results explain the puzzling measurements in pnictides and they provide a more general framework for transport properties in multiband materials.Comment: 5 pages, 2 figure

Spectral properties of incommensurate charge-density wave systems

The concept of frustrated phase separation is applied to investigate its consequences for the electronic structure of the high T_c cuprates. The resulting incommensurate charge density wave (CDW) scattering is most effective in creating local gaps in k-space when the scattering vector connects states with equal energy. Starting from an open Fermi surface we find that the resulting CDW is oriented along the (10)- and (or) (01)-direction which allows for a purely one-dimensional or a two-dimensional ``eggbox type'' charge modulation. In both cases the van Hove singularities are substantially enhanced, and the spectral weight of Fermi surface states near the M-points, tends to be suppressed. Remarkably, a leading edge gap arises near these points, which, in the eggbox case, leaves finite arcs of the Fermi surface gapless. We discuss our results with repect to possible consequences for photoemission experiments

Cluster Dynamical Mean-Field Theory of the density-driven Mott transition in the one-dimensional Hubbard model

The one-dimensional Hubbard model is investigated by means of two different cluster schemes suited to introduce short-range spatial correlations beyond the single-site Dynamical Mean-Field Theory, namely the Cluster-Dynamical Mean-Field Theory and its periodized version. It is shown that both cluster schemes are able to describe with extreme accuracy the evolution of the density as a function of the chemical potential from the Mott insulator to the metallic state. Using exact diagonalization to solve the cluster impurity model, we discuss the role of the truncation of the Hilbert space of the bath, and propose an algorithm that gives higher weights to the low frequency hybridization matrix elements and improves the speed of the convergence of the algorithm.Comment: 6 pages, 4 figures, minor corrections in v

Optical excitation of phase modes in strongly disordered superconductors

According to the Goldstone theorem the breaking of a continuous U(1) symmetry comes along with the existence of low-energy collective modes. In the context of superconductivity these excitations are related to the phase of the superconducting (SC) order parameter and for clean systems are optically inactive. Here we show that for strongly disordered superconductors phase modes acquire a dipole moment and appear as a subgap spectral feature in the optical conductivity. This finding is obtained with both a gauge-invariant random-phase approximation scheme based on a fermionic Bogoliubov-de Gennes state as well as with a prototypical bosonic model for disordered superconductors. In the strongly disordered regime, where the system displays an effective granularity of the SC properties, the optically active dipoles are linked to the isolated SC islands, offering a new perspective for realizing microwave optical devices

Networks from gene expression time series: characterization of correlation patterns

This paper describes characteristic features of networks reconstructed from gene expression time series data. Several null models are considered in order to discriminate between informations embedded in the network that are related to real data, and features that are due to the method used for network reconstruction (time correlation).Comment: 10 pages, 3 BMP figures, 1 Table. To appear in Int. J. Bif. Chaos, July 2007, Volume 17, Issue