We propose a scenario for superconductivity at strong electron-electron attractive interaction, in the case when the increase of the interaction strength promotes the nucleation of the local Cooper pairs and forms a state with a spatially phase incoherent Cooper pair order parameter. We show that this state can be characterized by a pseudogap which is determined by the electron scattering by phase fluctuations. At low temperatures, however, long-range correlations between the regions with different phases become important and establish global phase coherence and hence superconductivity in the system. We develop a mean-field theory to describe a phase transition between the preformed Cooper pair and superconducting states. This scenario of superconductivity applies not only to conductors with parabolic bands but also to the flat-band systems in which flat and dispersive bands coexist and are responsible for the formation of Cooper pairs as well as their phase synchronization.We propose a scenario for superconductivity at strong electron-electron attractive interaction, in the case when the increase of the interaction strength promotes the nucleation of the local Cooper pairs and forms a state with a spatially phase incoherent Cooper pair order parameter. We show that this state can be characterized by a pseudogap which is determined by the electron scattering by phase fluctuations. At low temperatures, however, long-range correlations between the regions with different phases become important and establish global phase coherence and hence superconductivity in the system. We develop a mean-field theory to describe a phase transition between the preformed Cooper pair and superconducting states. This scenario of superconductivity applies not only to conductors with parabolic bands but also to the flat-band systems in which flat and dispersive bands coexist and are responsible for the formation of Cooper pairs as well as their phase synchronization.

arXiv:2308.04508Aug 8, 20230 citations

Pairing and superconductivity from weak to strong coupling in the attractive Hubbard model

A. Toschi, Paolo Barone, Massimo Capone +1 more

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, 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.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, 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.

arXiv:cond-mat/0411637New Journal of PhysicsJan 14, 2005100 citations

Mechanism for fluctuating pair density wave

Chandan Setty, Laura Fanfarillo, P. J. Hirschfeld

Abstract In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, EF, form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO3 or cold atom condensates where the pairing scale, EB, becomes comparable or even larger than EF. In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature Ti, where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform d-wave super- conductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified microscopic framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.Abstract In weakly coupled BCS superconductors, only electrons within a tiny energy window around the Fermi energy, EF, form Cooper pairs. This may not be the case in strong coupling superconductors such as cuprates, FeSe, SrTiO3 or cold atom condensates where the pairing scale, EB, becomes comparable or even larger than EF. In cuprates, for example, a plausible candidate for the pseudogap state at low doping is a fluctuating pair density wave, but no microscopic model has yet been found which supports such a state. In this work, we write an analytically solvable model to examine pairing phases in the strongly coupled regime and in the presence of anisotropic interactions. Already for moderate coupling we find an unusual finite temperature phase, below an instability temperature Ti, where local pair correlations have non-zero center-of-mass momentum but lack long-range order. At low temperature, this fluctuating pair density wave can condense either to a uniform d-wave super- conductor or the widely postulated pair-density wave phase depending on the interaction strength. Our minimal model offers a unified microscopic framework to understand the emergence of both fluctuating and long range pair density waves in realistic systems.

arXiv:2110.13138Nature CommunicationsJun 1, 202330 citations

Detecting a preformed pair phase: Response to a pairing forcing field

Agnese Tagliavini, Massimo Capone, A. Toschi

The normal state of strongly coupled superconductors is characterized by the presence of ``preformed'' Cooper pairs well above the superconducting critical temperature. In this regime, the electrons are paired, but they lack the phase coherence necessary for superconductivity. The existence of preformed pairs implies the existence of a characteristic energy scale associated with a pseudogap. Preformed pairs are often invoked to interpret systems where some signatures of pairing are present without actual superconductivity, but an unambiguous theoretical characterization of a preformed-pair system is still lacking. To fill this gap, we consider the response to an external pairing field of an attractive Hubbard model, which hosts one of the cleanest realizations of a preformed pair phase, and a repulsive model where $s$ -wave superconductivity cannot be realized. Using dynamical mean-field theory to study this response, we identify the characteristic features which distinguish the reaction of a preformed pair state from a normal metal without any precursor of pairing. The theoretical detection of preformed pairs is associated with the behavior of the second derivative of the order parameter with respect to the external field, as confirmed by analytic calculations in limiting cases. Our findings provide a solid test bed for the interpretation of state-of-the-art calculations for the normal state of the doped Hubbard model in terms of $d$ -wave preformed pairs and, in perspective, of nonequilibrium experiments in high-temperature superconductors.The normal state of strongly coupled superconductors is characterized by the presence of ``preformed'' Cooper pairs well above the superconducting critical temperature. In this regime, the electrons are paired, but they lack the phase coherence necessary for superconductivity. The existence of preformed pairs implies the existence of a characteristic energy scale associated with a pseudogap. Preformed pairs are often invoked to interpret systems where some signatures of pairing are present without actual superconductivity, but an unambiguous theoretical characterization of a preformed-pair system is still lacking. To fill this gap, we consider the response to an external pairing field of an attractive Hubbard model, which hosts one of the cleanest realizations of a preformed pair phase, and a repulsive model where $s$-wave superconductivity cannot be realized. Using dynamical mean-field theory to study this response, we identify the characteristic features which distinguish the reaction of a preformed pair state from a normal metal without any precursor of pairing. The theoretical detection of preformed pairs is associated with the behavior of the second derivative of the order parameter with respect to the external field, as confirmed by analytic calculations in limiting cases. Our findings provide a solid test bed for the interpretation of state-of-the-art calculations for the normal state of the doped Hubbard model in terms of $d$-wave preformed pairs and, in perspective, of nonequilibrium experiments in high-temperature superconductors.

arXiv:1604.08882Physical review. B./Physical review. BOct 10, 201618 citations

Superconductivity from purely repulsive interactions in the strong-coupling approach: Application of SU(2) slave-rotor theory to the Hubbard model

Ki‐Seok Kim, Mun Dae Kim

We propose a mechanism of superconductivity from purely repulsive interactions in the strong-coupling regime, where the Bardeen-Cooper-Schrieffer mechanism such as the spin-fluctuation approach is difficult to apply. Based on the SU(2) slave-rotor representation of the Hubbard model, we find that the single energy scale for the amplitude formation of Cooper pairs and their phase coherence is separated into two energy scales, allowing the so-called pseudogap state where such Cooper pairs are coherent locally but not globally, interpreted as realization of the density-phase uncertainty principle. This superconducting state shows the temperature-linear decreasing ratio of superfluid weight, resulting from strong phase fluctuations.We propose a mechanism of superconductivity from purely repulsive interactions in the strong-coupling regime, where the Bardeen-Cooper-Schrieffer mechanism such as the spin-fluctuation approach is difficult to apply. Based on the SU(2) slave-rotor representation of the Hubbard model, we find that the single energy scale for the amplitude formation of Cooper pairs and their phase coherence is separated into two energy scales, allowing the so-called pseudogap state where such Cooper pairs are coherent locally but not globally, interpreted as realization of the density-phase uncertainty principle. This superconducting state shows the temperature-linear decreasing ratio of superfluid weight, resulting from strong phase fluctuations.

arXiv:0906.0833Physical Review BFeb 25, 20105 citations

Are preformed Cooper pairs the cause for the pseudogap in superconductors?

T. A. Mamedov, MANUEL DE LLANO

A weak-coupling scenario wherein bosonic preformed electron pairs emerge upon cooling from two-electron correlations can explain the pseudogap phase consisting of segments where a Bogoliubov-like energy-momentum relation gapped spectrum alternates with a normal ungapped one. Bose–Einstein condensation (BEC) of preformed pairs interacting with the background fermions leads to either - or -wave-like superconducting gaps, the result being sensitive to the magnitude of the total number density of pairs at which BEC occurs and becomes possible already for a moderately anisotropic -wave pairing of fermions repelling each other via isotropic coulombic forces. The present model is compatible with the coexistence of pseudogap and of superconductivity phenomena.A weak-coupling scenario wherein bosonic preformed electron pairs emerge upon cooling from two-electron correlations can explain the pseudogap phase consisting of segments where a Bogoliubov-like energy-momentum relation gapped spectrum alternates with a normal ungapped one. Bose–Einstein condensation (BEC) of preformed pairs interacting with the background fermions leads to either - or -wave-like superconducting gaps, the result being sensitive to the magnitude of the total number density of pairs at which BEC occurs and becomes possible already for a moderately anisotropic -wave pairing of fermions repelling each other via isotropic coulombic forces. The present model is compatible with the coexistence of pseudogap and of superconductivity phenomena.

The Philosophical Magazine A Journal of Theoretical Experimental and Applied PhysicsNov 14, 20149 citations

s

-wave superconductivity cannot be realized. Using dynamical mean-field theory to study this response, we identify the characteristic features which distinguish the reaction of a preformed pair state from a normal metal without any precursor of pairing. The theoretical detection of preformed pairs is associated with the behavior of the second derivative of the order parameter with respect to the external field, as confirmed by analytic calculations in limiting cases. Our findings provide a solid test bed for the interpretation of state-of-the-art calculations for the normal state of the doped Hubbard model in terms of

d

-wave preformed pairs and, in perspective, of nonequilibrium experiments in high-temperature superconductors.