arXiv subjects

E. Cappelluti

Publications and source records attributed to E. Cappelluti.

At least 73 records · Page 4Linked to original sources

arXiv2002

Spin susceptibility in small Fermi energy systems: effects of nonmagnetic impurities

In small Fermi energy metals, disorder can deeply modify superconducting state properties leading to a strong suppression of the critical temperature $T_c$. In this paper, we show that also normal state properties can be seriously influenced by disorder when the Fermi energy $E_{\rm F}$ is sufficiently small. We calculate the normal state spin susceptibility $χ$ for a narrow band electron-phonon coupled metal as a function of the non-magnetic impurity scattering rate $γ_{\rm imp}$. We find that as soon as $γ_{\rm imp}$ is comparable to $E_{\rm F}$, $χ$ is strongly reduced with respect to its value in the clean limit. The effects of the electron-phonon interaction including the nonadiabatic corrections are discussed. Our results strongly suggest that the recent finding on irradiated MgB$_2$ samples can be naturally explained in terms of small $E_{\rm F}$ values associated with the $σ$-bands of the boron plane, sustaining therefore the hypothesis that MgB$_2$ is a nonadiabatic metal.

cond-mat.supr-con↗

arXiv2002

Magnetic and lattice polaron in Holstein-t-J model

We investigate the interplay between the formation of lattice and magnetic polaron in the case of a single hole in the antiferromagnetic background. We present an exact analytical solution of the Holstein-t-J model in infinite dimensions. Ground state energy, electron-lattice correlation function, spin bag dimension as well as spectral properties are calculated. The magnetic and hole-lattice correlations sustain each other, i.e. the presence of antiferromagnetic correlations favors the formation of the lattice polaron at lower value of the electron-phonon coupling while the polaronic effect contributes to reduce the number of spin defects in the antiferromagnetic background. The crossover towards a spin-lattice small polaron region of the phase diagram becomes a discontinuous transition in the adiabatic limit.

cond-mat.str-el↗

arXiv2002

High $T_c$ superconductivity in MgB$_2$ by nonadiabatic pairing

The evidence for the key role of the $σ$ bands in the electronic properties of MgB$_2$ points to the possibility of nonadiabatic effects in the superconductivity of these materials. These are governed by the small value of the Fermi energy due to the vicinity of the hole doping level to the top of the $σ$ bands. We show that the nonadiabatic theory leads to a coherent interpretation of $T_c = 39$ K and the boron isotope coefficient $α_{\rm B} = 0.30$ without invoking very large couplings and it naturally explains the role of the disorder on $T_c$. It also leads to various specific predictions for the properties of MgB$_2$ and for the material optimization of these type of compounds.

cond-mat.supr-con↗

arXiv2001

Nonadiabatic Superconductivity and Vertex Corrections in Uncorrelated Systems

We investigate the issue of the nonadiabatic superconductivity in uncorrelated systems. A local approximation is employed coherently with the weak dependence on the involved momenta. Our results show that nonadiabatic vertex corrections are never negligible, but lead to a strong suppression of $T_c$ with respect to the conventional theory. This feature is understood in terms of the momentum-frequency dependence of the vertex function. In contrast to strongly correlated systems, where the small ${\bf q}$-selection probes the positive part of vertex function, vertex corrections in uncorrelated systems are essentially negative resulting in an effective reduction of the superconducting pairing. Our analysis shows that vertex corrections in nonadiabatic regime can be never disregarded independently of the degree of electronic correlation in the system.

cond-mat.supr-con↗

arXiv2001

Breakdown of Migdal-Eliashberg Theory in Rb$_3$C$_{60}$

This paper has been withdrawn. An extended version of this work can be found in E. Cappelluti, C. Grimaldi, L. Pietronero, S. Straessler: Phys. Rev. Lett. 85, 4771 (2000) [cond-mat/0105560] and E. Cappelluti, C. Grimaldi, L. Pietronero, S. Straessler, G.A. Ummarino: Eur. Phys. J. B 21, 383 (2001) [cond-mat/0104457]

cond-mat.supr-con↗

arXiv2001

Nonadiabatic Channels in the Superconducting Pairing of Fullerides

We show the intrinsic inconsistency of the conventional phonon mediated theory of superconductivity in relation to the observed properties of Rb$_3$C$_{60}$. The recent, highly accurate measurement of the carbon isotope coefficient $α_{\rm C}=0.21$, together with the high value of $T_c$ (30 K) and the very small Fermi energy $E_{\rm F}$ (0.25 eV), unavoidably implies the opening of nonadiabatic channels in the superconducting pairing. We estimate these effects and show that they are actually the key elements for the high value of $T_c$ in these materials compared to the very low values of graphite intercalation compounds.

cond-mat.supr-con↗

arXiv2001

Superconductivity of Rb$_3$C$_{60}$: breakdown of the Migdal-Eliashberg theory

In this paper, through an exhaustive analysis within the Migdal-Eliashberg theory, we show the incompatibility of experimental data of Rb$_3$C$_{60}$ with the basic assumptions of the standard theory of superconductivity. For different models of the electron-phonon spectral function $α^2F(Ω)$ we solve numerically the Eliashberg equations to find which values of the electron-phonon coupling $λ$, of the logarithmic phonon frequency $Ω_{ln}$ and of the Coulomb pseudopotential $μ^*$ reproduce the experimental data of Rb$_3$C$_{60}$. We find that the solutions are essentially independent of the particular shape of $α^2F(Ω)$ and that, to explain the experimental data of Rb$_3$C$_{60}$, one has to resort to extremely large couplings: $λ=3.0\pm 0.8$. This results differs from the usual partial analyses reported up to now and we claim that this value exceeds the maximum allowed $λ$ compatible with the crystal lattice stability. Moreover, we show quantitatively that the obtained values of $λ$ and $Ω_{ln}$ strongly violate Migdal's theorem and consequently are incompatible with the Migdal-Eliashberg theory. One has therefore to consider the generalization of the theory of superconductivity in the nonadiabatic regime to account for the experimental properties of fullerides.

cond-mat.supr-con↗

arXiv2001

Nonadiabatic Pauli susceptibility in fullerene compounds

Pauli paramagnetic susceptibility $χ$ is unaffected by the electron-phonon interaction in the Migdal-Eliashberg context. Fullerene compounds however do not fulfill the adiabatic assumption of Migdal's theorem and nonadiabatic effects are expected to be relevant in these materials. In this paper we investigate the Pauli spin susceptibility in nonadiabatic regime by following a conserving approach based on Ward's identity. We find that a sizable renormalization of $χ$ due to electron-phonon coupling appears when nonadiabatic effects are taken into account. The intrinsic dependence of $χ$ on the electron-phonon interaction gives rise to a finite and negative isotope effect which could be experimentally detected in fullerides. In addition, we find an enhancement of the spin susceptibility with temperature increasing, in agreement with the temperature dependence of $χ$ observed in fullerene compounds. The role of electronic correlation is also discussed.

cond-mat.supr-con↗

arXiv2000

s- and d-wave Symmetries in Nonadiabatic Theory of Superconductivity

High-$T_c$ superconductors have Fermi energies $E_F$ much smaller than conventional metals comparable to phonon frequencies. In such a situation nonadiabatic effects are important. A generalization of Eliashberg theory in the nonadiabatic regime has previously been shown to reproduce some anomalous features of the high-$T_c$ superconductors as for istance the enhancement of $T_c$ or the isotopic effects on $T_c$ and $m^*$. In this contribution we address the issue of the symmetry of the gap in the context of nonadiabatic superconductivity. We show that vertex corrections have a momentum structure which favours d-wave superconductivity when forward scattering is predominant. An additional increase of $T_c$ is also found.

cond-mat.supr-con↗

arXiv2000

A survey of nonadiabatic superconductivity in cuprates and fullerides

High-$T_c$ superconductors are characterized by very low carrier densities. This feature leads to two fundamental consequences: on one hand the Fermi energies are correspondingly small and they can be of the same order of phonon frequencies. In such a situation nonadiabatic corrections arising from the breakdown of Migdal's theorem can not be longer neglected. In addition, small carrier densities imply poor screening and correlation effects have to be taken into account. We present a comprehensive overview of the theory of superconductivity generalized into the nonadiabatic regime which is qualitatively different from the conventional one. In this framework some of the observed properties of the cuprates and the fullerene compounds can be naturally accounted for, and a number of theoretical predictions are proposed that can be experimentally tested.

cond-mat.supr-con↗

arXiv2000

Effect of Strong Correlation on the Electron-Phonon Interaction

High-$T_c$ superconductors are usually described as strongly correlated electronic systems. This feature deeply affects the one-particle and two-particle properties of the system. In particular, a large incoherent background developes on the top of a narrow quasi-particle peak in the one-electron spectral function. We schematize this structure with a simple phenomenological form. The corresponding Green's function is employed to calculate the charge response of the system taking into account in a proper way strong correlation effects. The effective charge interaction acquires a structure in the exchanged momentum space with a predominance of forward scattering, in agreement with previous numerical calculations. The consequences of the momentum dependence of the interaction are discussed in the framework of the nonadiabatic theory of superconductivity proposed for the high-$T_c$ materials.

cond-mat.supr-con↗

arXiv2000

Nonadiabatic theory of the superconducting state

Fermi energies in fullerene compounds and cuprates are extremely small as consequence of the small number of charge carriers and are comparable to the phonon frequency scale. In this situation the conventional Migdal-Eliashberg theory does not hold anymore and nonadiabatic effects need to be taken into account. In previous studies, a generalization of Eliashberg theory in the nonadiabatic regime has been proposed to calculate normal state properties and the onset temperature $T_c$ of the superconductive phase. Here we extend the nonadiabatic theory below $T_c$ where the opening of the superconducting order parameter affects the nonadiabatic correction. The superconducting gap $Δ$ is calculated in a self-consistent way. We find that large values of the ratio $2 Δ/T_c$ are obtained in the nonadiabatic theory by smaller electron-phonon coupling $λ$ than in Migdal-Eliashberg theory. This agrees with the picture that strong-coupling phenomenology can be achieved in nonadiabatic theory by ``reasonable'' values of $λ$. We apply our analysis to the case of the fullerene compounds.

cond-mat.supr-con↗

arXiv2000

Failure of the Migdal-Eliashberg Theory of Superconductivity in Rb_3C_60

We discuss the compatibility of the most accurate experimental data with the ordinary Migdal-Eliashberg theory of superconductivity in the fullerene compound Rb_3C_60. By using different model phonon spectra we conclude that the experimental data can be fitted only by invoking an electron-phonon coupling of order λ\simeq 3. This exceedingly high value is unphysical and it is not consistent with the basic assumptions of the Migdal-Eliashberg theory. On the contrary, by relaxing the adiabatic hypothesis on which the Migdal-Eliashberg theory rests, the experimental data can be fitted by much more realistic values of λ. This generalized theory predicts also characteristic features absent in the Migdal-Eliashberg framework which can be experimentally tested.

cond-mat.supr-con↗

arXiv2000

Interplay of superconductivity with structural phases in a generalized t-J model

The phase diagram of the t-J-V model is discussed using a 1/N expansion in terms of X operators. It is shown that a flux phase of d-wave symmetry is stabilized by the Coulomb interaction V at intermediate dopings and competes with d-wave superconductivity. Since the flux wave instability is stronger than the superconducting one optimal doping is essentially determined by the onset of the flux phase. Below optimal doping the flux phase coexists with superconductivity at low and exists as a pseudo gap phase at higher temperatures. It is also found that the flux phase boundary is much less sensitive to impurity scattering than the boundary for superconductivity in agreement with experiments in Zn doped La-214 and (Y,Ca)-123.

cond-mat.supr-con↗

arXiv1999

Impurity Effects on the Flux Phase Quantum Critical Point Scenario

Impurity substitution of Zn in La-214 and (Y,Ca)-123 high-T_c superconductors suppresses T_c but does not affect appreciably the onset of the pseudogap phase in the underdoped region nor optimal doping or the position of the inferred quantum critical point. Based on a 1/N expansion of the t-J model we explain these findings as well as the similar dependence on a magnetic field in terms of a quantum critical point scenario where a flux phase causes the pseudogap.

cond-mat.supr-con↗

arXiv1998

Isotope effect on $m^*$ in high-T_c materials due to the breakdown of Migdal's theorem

We show that the inclusion of effects beyond Migdal's limit in the electron-phonon interaction naturally leads to an isotope effect for the effective mass $m^{*}$ of the charge carriers even much before reaching the polaron limit. This is the situation already considered in our approach to nonadiabatic superconductivity. Such a result provides a scenario different from the polaronic one for the interpretation of the recently observed isotope effect on $m^{*}$ in YBa$_{2}$Cu$_{3}$O$_{6+x}$ and La$_{2-x}$Sr$_{x}$CuO$_{4}$.

cond-mat.supr-con↗

arXiv1998

Interplay between superconductivity and flux phase in the t-J model

We study the phase diagram of the t-J model using a mean field type approximation within the Baym-Kadanoff perturbation expansion for Hubbard $X$-operators. The line separating the normal state from a d-wave flux or bond-order state starts near optimal doping at T=0 and rises quickly with decreasing doping. The transition temperature $T_c$ for d-wave superconductivity increases monotonically in the overdoped region towards optimal doping. Near optimaldoping a strong competition between the two d-wave order parameters sets in leading to a strong suppression of $T_c$ in the underdoped region. Treating for simplicity the flux phase as commensurate the superconducting and flux phases coexist in the underdoped region below $T_c$, whereas a pure flux phase exists above $T_c$ with a pseudo-gap of d-wave symmetry in the excitation spectrum. We also find that incommensurate charge-density-wave ground states due to Coulomb interactions do not modify strongly the above phase diagram near the superconducting phase, at least, as long as the latter exists at all.

cond-mat.supr-con↗

arXiv1998

Role of the superconducting gap opening on vertex corrections

The nonadiabatic effects due to the breakdown of Migdal's theorem in high-$T_c$ superconductors are strongly affected by the opening of the superconducting gap. Here we report how the momentum-frequency dependence of vertex corrections is modified by the gap. A general effect is that the positive region of the vertex corrections is increased leading to an enhancement of their relevance. This has a number of physical consequences that we discuss in details in relation to specific experiments.

cond-mat.supr-con↗