We analyze the behavior of the dynamic scattering amplitude between Fermi liquid quasiparticles at the Fermi surface in the proximity of a charge instability, which may occur in the high temperature superconducting cuprates. Within the infinite-U Hubbard-Holstein model in the slave-boson large-N technique we find that, in the absence of long-range Coulomb forces the scattering amplitude is strongly singular at zero momentum transfer close to the phase separation instability and it has the same form provided by gauge-field theories. In the presence of long-range Coulomb forces the charge instability occurs at finite wavevectors and concomitantly the scattering is still singular but anisotropic. Nevertheless it remains strong over extended regions of the momentum space. In both cases we show how normal state properties are largely affected by this scattering. 71.27.+a, It is generally accepted that the understanding of the pairing mechanism in high T c superconductors is related to the understanding of the anomalous behaviour of the normal phase.The anomalous properties of the normal phase have been interpreted along two distinct theoretical lines. One possible explanation is that the low dimensionality of these highly anisotropic systems and their correlated nature are at the origin of a breakdown of the Fermi liquid (FL).In particular the proposal of a Luttinger liquid formation in two dimension [1] has been intensively investigated [2]. The alternative aptitude has been to accept the Landau theory of normal FL's as a suitable starting point. The anomalous properties would then arise as a consequence of strong scattering processes at low energy between the quasiparticles. Along this line magnetic scattering has been considered to be responsible for both the anomalous properties of the normal phase and for the superconducting pairing [3]. Strong scattering may even lead to a complete disruption of the FL phase. In particular it was proposed that excitonic scattering could give rise to the so called marginal FL [4], and could also provide a pairing mechanism. Singular scattering can also be provided by gauge fields [5], which arise by implementing the resonating-valence-bond idea in the t-J model.In this letter we want to understand whether phase separation (PS) or the incommensurate charge density wave (ICDW) instability are sources of strong scattering besides the above mechanisms. Indeed the complex nature of the phase diagram as a function of doping and temperature indicates that various energy scales of different nature (magnetic, excitonic,...) of the same order of magnitude compete to determine the low-energy physics and may lead to various instabilities, among which PS or charge instabilities may play a relevant role.After PS was shown to be present in the phase diagram of the t-J model [6,7], we pointed out that PS commonly occurs in models with short range interaction [8][9][10][11][12][13][14][15], provided the strong local e-e repulsion inhibits the stabilizing role of the kinetic energy. We therefor...

The crossover from weak to strong coupling for a three dimensional continuum model of fermions interacting via an attractive contact potential is studied above the superconducting critical temperature Tc. The pair-fluctuation propagator, the one-loop self-energy, and the spectral function are investigated in a systematic way from the superconducting fluctuation regime (weak coupling) to the bosonic regime (strong coupling). Analytic and numerical results are reported. In the strongcoupling regime, where the pair fluctuation propagator has bosonic character, two quite different peaks appear in the spectral function at a given wave vector, a broad one at negative frequencies and a narrow one at positive frequencies. The broad peak of the spectral function at negative frequencies is asymmetric about its maximum, with its spectral weight decreasing by increasing coupling and temperature. In this regime, two crossover temperatures T * 1 (at which the two peaks in the spectral function merge in one peak) and T * 0 (at which the maximum of the lower peak crosses zero frequency) can be identified, with Tc ≪ T * 0 < T * 1 . By decreasing coupling, the two-peak structure evolves smoothly. In the weak-coupling regime, where the fluctuation propagator has diffusive Ginzburg-Landau character, the overall line-shape of the spectral function is more symmetric and the two crossover temperatures approach Tc. The systematic analysis of the spectral function identifies specific features which allow one to distinguish by ARPES whether a system is in the weak-or strong-coupling regime. Connection of the results of our analysis with the phenomenology of cuprate superconductors is also attempted and rests on the recently introduced two-gap model , according to which a crossover from weak to strong coupling is realized when moving in the Brillouin zone away from the nodal points toward the M points where the d-wave gap acquires its maximum value.PACS numbers: 74.25.Jb

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The recent observation of a transmitted Thz pulse oscillating at three times the frequency of the incident light paves the way to a new protocol to access resonant excitations in a superconductor. Here we show that this non-linear optical process is dominated by light-induced excitation of Cooper pairs, in analogy with a standard Raman experiment. The collective amplitude (Higgs) fluctuations of the superconducting order parameter give in general a smaller contribution, unless one designs the experiment by combining properly the light polarization with the lattice symmetry.PACS numbers: 74.25.Gz,The enormous technological advances made in the last two decades in the time-domain spectroscopy[1, 2] pose several challenges for our understanding of the interaction of the light with the matter. The use of low-energy THz waves[3] to first excite (pump) and then measure (probe) the system is particularly interesting for superconductors, since they can access the region ω < 2∆ 0 of the optical spectrum where linear-response absorption is suppressed by the opening of a superconducting (SC) gap ∆ 0 in the quasiparticle spectrum. For example, recent [4,5] THz pump-THz probe experiments have shown that the probe field displays a periodic oscillation, whose possible connection to amplitude (Higgs) fluctuations of the SC order parameter has been investigated theoretically [7][8][9][10][11]. An interesting additional effect made possible by the use of intense electromagnetic (e.m.) THz field is the experimental observation [5] of the so-called third-harmonic generation (THG), i.e. the appearance below T c in the transmitted pulse of a component oscillating three times faster then the incident light. This effect appears only below T c with a maximum intensity at the temperature where the light frequency ω matches the SC gap value ∆ 0 (T ), and has been attributed [5,6] to a resonant excitation of the Higgs mode. However, we show here that THG is dominated by the resonant excitations of Cooper pairs (CP), (see Fig. 1), overlooked in previous theoretical work [5,6].In contrast to pump-probe experiments [4,5], where the description of the intermediate relaxation processes of the photoexcited states becomes relevant [7][8][9][10][11], the THG effect can be understood as an equilibrium, non-linear optical process. In this paper we compute microscopically the non-linear optical response of a superconductor and we show that the THG essentially measures latticemodulated density correlations, that in the SC state diverge at the threshold 2∆ 0 above which Cooper pairs (CP) proliferate. This effect induces a resonant enhancement of the THG intensity when the frequency 2ω of the incoming electric field coincides with 2∆ 0 , as observed experimentally. Once identified the relevant non-linear optical response function, we also find that the Higgsmode contribution is largely subleading, due to symmetry reasons. Indeed, even if the Higgs mode can be excited by the THz field, as discussed previously [5,6], it essentially decouples from the opti...

High-temperature superconductivity in doped Mott insulators such as the cuprates contradicts the conventional wisdom that electron repulsion is detrimental to superconductivity. Because doped fullerene conductors are also strongly correlated, the recent discovery of high-critical-temperature, presumably s-wave, superconductivity in C60 field effect devices is even more puzzling. We examine a dynamical mean-field solution of a model for electron-doped fullerenes that shows how strong correlations can indeed enhance superconductivity close to the Mott transition. We argue that the mechanism responsible for this enhancement could be common to a wider class of strongly correlated models, including those for cuprate superconductors.