arXiv subjects

C. Castellani

Publications and source records attributed to C. Castellani.

At least 55 records · Page 3Linked to original sources

arXiv2006

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.

cond-mat.str-el↗

arXiv2005

Quasi-particle dephasing time in disordered d-wave superconductors

We evaluate the low-temperature cutoff for quantum interference 1/tf induced in a d-wave superconductor by the diffusion enhanced quasiparticle interactions in the presence of disorder. We carry out our analysis in the framework of the non-linear sigma-model which allows a direct calculation of 1/tf, as the mass of the transverse modes of the theory. Only the triplet amplitude in the particle-hole channel and the Cooper amplitude with is pairing symmetry contribute to 1/tf. We discuss the possible relevance of our results to the present disagreement between thermal transport data in cuprates and the localization theory for d-wave quasiparticles.

cond-mat.supr-con↗

arXiv2005

Temperature dependence of the optical spectral weight in the cuprates: Role of electron correlations

We compare calculations based on the Dynamical Mean-Field Theory of the Hubbard model with the infrared spectral weight $W(Ω,T)$ of La$_{2-x}$Sr$_x$CuO$_4$ and other cuprates. Without using fitting parameters we show that most of the anomalies found in $W(Ω,T)$ with respect to normal metals, including the existence of two different energy scales for the doping- and the $T$-dependence of $W(Ω,T)$, can be ascribed to strong correlation effects.

cond-mat.str-el↗

arXiv2005

Energetic balance of the superconducting transition across the BCS-Bose E instein crossover in the attractive Hubbard model

We investigate by means of Dynamical Mean-Field Theory the crossover from BCS superconductivity to Bose-Einstein (BE) condensation of preformed pairs in the attractive Hubbard model. We follow the evolution of the two energy scales underlying the superconducting phenomenon, the gap $Δ_0$ and the superfluid stiffness $D_S$, which controls the phase coherence. The BCS-BE crossover is clearly mirrored in a change in the hierarchy of these two scales, the smallest of the two controlling the critical temperature. In the whole intermediate-to-strong coupling region $T_c$ scales with $D_S$, while $T_C$ is proportional to $Δ_0$ only in the BCS regime. This evolution as a function of the interaction qualitatively resembles what happens in the cuprates when the doping is decreased towards the Mott insulator. This continuous change reflects also in the energetic balance at the superconducting transition. While superconductivity is stabilized by a potential energy gain in the BCS regime, the strong-coupling superconductivity is made stable by a reduction of kinetic energy. Interestingly the intermediate-coupling region, where the maximum $T_c$ is achieved, behaves similarly to the strong-coupling regime. The above finding implies that the attractive Hubbard model can account qualitatively for the anomalous behavior of optical spectra around $T_c$, where an increase of spectral weight is observed in under and optimally doped cuprates, while the overdoped samples have a more standard behavior. This qualitative agreement is lost in the normal phase, specifically at strong-coupling, calling for the inclusion of strong correlation effects in the theoretical description.

cond-mat.str-el↗

arXiv2005

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.

cond-mat.str-el↗

arXiv2004

Pairing and Superconductivity from weak to strong coupling in the Attractive Hubbard model

The finite-temperature phase diagram of the attractive Hubbard model is studied by means of the Dynamical Mean Field Theory. We first consider the normal phase of the model by explicitly frustrating the superconducting ordering. In this case we obtain a first-order pairing transition between a metallic phase and a paired phase formed by strongly coupled incoherent pairs. The transition line ends in a finite temperature critical point, but a crossover between two qualitatively different solutions still occurs at higher temperature. Comparing the superconducting and the normal phase solutions, we find that the superconducting instability always occurs before the pairing transition in the normal phase takes place, i.e., $T_c > T_{pairing}$. Nevertheless, the high-temperature phase diagram at $T > T_c$ is still characterized by a crossover from a metallic phase to a preformed pair phase. We characterize this crossover by computing different observables that can be used to identify the pseudogap region, like the spin susceptibility, the specific heat and the single-particle spectral function.

cond-mat.supr-con↗

arXiv2004

Strongly Correlated Superconductivity and Pseudogap Phase near a multi-band Mott Insulator

Near a Mott transition, strong electron correlations may enhance Cooper pairing. This is demonstrated in the Dynamical Mean Field Theory solution of a twofold-orbital degenerate Hubbard model with inverted Hund's rules on-site exchange, which favors local spin-singlet configurations. Close to the Mott insulator, which is a local version of a valence bond insulator, a pseudogap non-Fermi-liquid metal, a superconductor, and a normal metal appear, in striking similarity with the physics of the cuprates. The strongly correlated superconducting state has a larger Drude weight than the corresponding normal state. The role of the impurity Kondo problem is underscored.

cond-mat.str-el↗

arXiv2004

Effect of mesoscopic inhomogeneities on local tunnelling density of states

We carry out a theoretical analysis of the momentum dependence of the Fourier-transformed local density of states (LDOS) in the superconducting cuprates within a model considering the interference of quasiparticles scattering on quenched impurities. The impurities introduce an external scattering potential, which is either nearly local in space or it can acquire a substantial momentum dependence due to a possible strong momentum dependence of the electronic screening near a charge modulation instability. The key new effect that we introduce is an additional mesoscopic disorder aiming to reproduce the inhomogeneities experimentally observed in scanning tunnelling microscopy. The crucial effect of this mesoscopic disorder is to give rise to point-like spectroscopic features, to be contrasted with the curve-like shape of the spectra previously calculated within the interfering-quasiparticle schemes. It is also found that stripe-like charge modulations play a relevant role to correctly reproduce all the spectral features of the experiments.

cond-mat.supr-con↗

arXiv2004

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.

cond-mat.str-el↗

arXiv2004

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.

cond-mat.str-el↗

arXiv2004

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.

cond-mat.supr-con↗

arXiv2003

Renormalization Group Approach to the Infrared Behavior of a Zero-Temperature Bose System

We exploit the renormalization-group approach to establish the {\em exact} infrared behavior of an interacting Bose system at zero temperature. The local-gauge symmetry in the broken-symmetry phase is implemented through the associated Ward identities, which reduce the number of independent running couplings to a single one. For this coupling the $ε$-expansion can be controlled to all orders in $ε$ ($=3-d$). For spatial dimensions $1 < d \leq 3$ the Bogoliubov fixed point is unstable towards a different fixed point characterized by the divergence of the longitudinal correlation function. The Bogoliubov linear spectrum, however, is found to be independent from the critical behavior of this correlation function, being exactly constrained by Ward identities. The new fixed point properly gives a finite value of the coupling among transverse fluctuations, but due to virtual intermediate longitudinal fluctuations the effective coupling affecting the transverse correlation function flows to zero. As a result, no transverse anomalous dimension is present. This treatment allows us to recover known results for the quantum Bose gas in the context of a unifying framework and also to reveal the non-trivial skeleton structure of its perturbation theory.

cond-mat.stat-mech↗

arXiv2002

Strongly Correlated Superconductivity

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 C$_{60}$ field effect devices is even more puzzling. We examine a dynamical-mean-field solution of a model for electron doped fullerenes which 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.

cond-mat.str-el↗

arXiv2002

First-Order Pairing Transition and Single-Particle Spectral Function in the Attractive Hubbard Model

A Dynamical Mean Field Theory analysis of the attractive Hubbard model is carried out. We focus on the normal state upon restricting to solutions where superconducting order is not allowed. Nevertheless a clear first-order pairing transition as a function of the coupling takes place at all the electron densities out of half-filling. The transition occurs between a Fermi liquid, stable for $U < U_c$, and an insulating bound pairs phase for $U > U_c$. The spectral function in the Fermi liquid phase is constituted by a low energy structure around the Fermi level (similar to the Kondo resonance of the repulsive half-filled model), which disappears discontinuously at $U=U_c$, and two high energy features (lower and upper Hubbard bands), which persist in the insulating phase.

cond-mat.str-el↗

arXiv2002

Pseudogap and spectral function from superconducting fluctuations to the bosonic limit

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. 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 strong-coupling regime, where the pair fluctuation propagator has bosonic character, two quite different peaks appear in the spectral function, a broad one at negative frequencies and a narrow one at positive frequencies. 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. 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.

cond-mat.supr-con↗

arXiv2001

Coherence length in superconductors from weak to strong coupling

We study the evolution of the superconducting coherence length $ξ_0$ from weak to strong coupling, both within a s-wave and a d-wave lattice model. We show that the identification of $ξ_0$ with the Cooper-pair size $ξ_{pair}$ in the weak-coupling regime is meaningful only for a fully-gapped (e.g., s-wave) superconductor. Instead in the d-wave superconductor, where $ξ_{pair}$ diverges, we show that $ξ_0$ is properly defined as the characteristic length scale for the correlation function of the modulus of the superconducting order parameter. The strong-coupling regime is quite intriguing, since the interplay between particle-particle and particle-hole channel is no more negligible. In the case of s-wave pairing, which allows for an analytical treatment, we show that $ξ_0$ is of order of the lattice spacing at finite densities. In the diluted regime $ξ_0$ diverges, recovering the behavior of the coherence length of a weakly interacting effective bosonic system. Similar results are expected to hold for d-wave superconductors.

cond-mat.supr-con↗

arXiv2001

Phase fluctuations in superconductors: from Galilean invariant to quantum XY models

We analyze the corrections to the superfluid density due to phase fluctuations within both a continuum and a lattice model for $s$- and d-wave superconductors. We expand the phase-only action beyond the Gaussian level and compare our results with the quantum XY model both in the quantum and in the classical regime. We find new dynamic anharmonic vertices, absent in the quantum XY model, which are responsible for the vanishing of the correction to the superfluid density at zero temperature in a continuum (Galilean invariant) model. Moreover the phase-fluctuation effects are reduced with respect to the XY model by a factor at least of order $1/(k_Fξ_0)^2$.

cond-mat.supr-con↗

arXiv2001

Phase separation frustrated by the long range Coulomb interaction I: Theory

We analyze the combined effect of the long range Coulomb (LRC) interaction and of surface energy on first order density-driven phase transitions in the presence of a compensating rigid background. We study mixed states formed by regions of one phase surrounded by the other in the case in which the scale of the inhomogeneities is much larger than the interparticle distance. Two geometries are studied in detail: spherical drops of one phase into the other and a layered structure of one phase alternating with the other. We find the optimum density profile in an approximation in which the free energy is a functional of the local density (LDA). It is shown that an approximation in which the density is assumed to be uniform (UDA) within each phase region gives results very similar to those of the more involved LDA approach. Within the UDA we derive the general equations for the chemical potential and the pressures of each phase which generalize the Maxwell construction to this situation. The equations are valid for a rather arbitrary geometry. We find that the transition to the mixed state is quite abrupt i.e. inhomogeneities of the first phase appear with a finite value of the radius and of the phase volume fraction. The maximum size of the inhomogeneities is found to be on the scale of a few electric field screening lengths. Contrary to the ordinary Maxwell construction, the inverse specific volume of each phase depends here on the global density in the coexistence region and can decrease as the global density increases. The range of densities in which coexistence is observed shrinks as the LRC interaction increases until it reduces to a singular point. We argue that close to this singular point the system undergoes a lattice instability as long as the inverse lattice compressibility is finite.

cond-mat.str-el↗