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 pseudogap state of cuprate high-temperature superconductors has been often viewed as either a yet unknown competing order or a precursor state to superconductivity. While awaiting the resolution of the pseudogap problem in cuprates, we demonstrate that local pairing fluctuations, vortex liquid dynamics, and other precursor phenomena can emerge quite generally whenever fermionic excitations remain gapped across the superconducting transition, regardless of the gap origin. Our choice of a tractable model is a lattice band insulator with short-range attractive interactions between fermions in the s-wave channel. An effective crossover between Bardeen-Cooper-Schrieffer (BCS) and Bose-Einstein condensate (BEC) regimes can be identified in any band insulator above two dimensions, while in two dimensions only the BEC regime exists. The superconducting transition is ``unconventional'' (non-pair-breaking) in the BEC regime, identified by either the bosonic mean field or XY universality class. The insulator adjacent to the superconductor in the BEC regime is a bosonic Mott insulator of Cooper pairs, which may be susceptible to charge density wave ordering. We construct a function of the many-body excitation spectrum whose nonanalytic changes define a sharp distinction between band and Mott insulators. The corresponding ``second-order transition'' can be observed out of equilibrium by driving a Cooper pair laser in the Mott insulator. We explicitly show that the gap for charged bosonic excitations lies below the threshold for Cooper pair breakup in any BEC regime, despite quantum fluctuations. Our discussion ends with a view of possible consequences for cuprates, where antinodal pair dynamics has certain features in common with our simple s-wave picture.
The condensation of paired fermions into superfluid states changes progressively depending on the coupling strength. At the midpoint of the crossover between Bardeen-Cooper-Schrieffer (BCS) weak-coupling and Bose-Einstein condensate (BEC) strong-coupling limits, paired fermions condensate most robustly, thereby leading to the emergence of a pseudogap due to enhanced pairing fluctuations. In the case of electrons in solids, excessively strong interactions often induce competing electronic orders instead of strong-coupling superconductivity, and experimental comprehension of the pseudogap remains incomplete. In this study, we provide experimental evidence demonstrating the opening of a pseudogap, marking the incipient stage of the BCS-BEC crossover in the organic system $\ensuremath{\kappa}\text{\ensuremath{-}}(\mathrm{BEDT}\text{\ensuremath{-}}{\mathrm{TTF})}_{2}X$. By controlling electron correlations, we investigate the thermodynamic properties of the BCS-BEC crossover and pseudogap phase. Since the superconductivity of $\ensuremath{\kappa}\text{\ensuremath{-}}{(\text{BEDT}\text{\ensuremath{-}}\mathrm{TTF})}_{2}X$ arises from a simple Fermi liquid that does not exhibit any other electronic orders, our study sheds light on the inherent nature of the BCS-BEC crossover.
A boson–fermion (BF) quantum-statistical binary gas mixture model of high- T c superconductors (HTSCs) recently introduced consists of resonant bosonic Cooper electron pairs (CPs) in chemical and thermal equilibrium with single unpaired electrons. Here, this model is refined and extended to include: i) the anisotropy of the original BF vertex interaction causing boson formation/disintegration and ii) momentum-independent Coulomb repulsions between electron charge carriers. It is shown that pair breakings due to Coulomb repulsion depend on the separation between boson and fermion spectra. Specifically, as such a separation shrinks, the pair-breaking ability of the Coulomb interaction weakens and disappears altogether at the Bose–Einstein condensation (BEC) T c , i.e., at the temperature at which a complete softening of bosons occurs due to boson self-energy renormalization. Simultaneous inclusion of both effects produces “islands” in momentum space of incoherent CPs above the Fermi sea as temperature is lowered. These islands grow upon further cooling and merge together just before T c is reached. The BF model thusly extended now predicts a pseudogap phase in 2D HTSCs with lines of points on the Fermi surface along which the pseudogap vanishes, hence explaining the origin of the temperature-dependent “Fermi arcs” observed in experiments.
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.
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.
As is known, the 1/q2 theorem of Bogoliubov asserts that the mean density of the fermion pair states with the total momentum q obeys the inequality ${n}_{q}>~{C/q}^{2}(\stackrel{\ensuremath{\rightarrow}}{q}0)$ in the case of the Fermi system taken at nonzero temperature and in the superconducting state provided the interaction term of its Hamiltonian is locally gauge invariant. With the principle of correlation weakening it is proved in this paper that the reason for the mentioned singular behavior of nq is the presence of the bound states of particle pairs with nonzero total momenta. Thus, below the temperature of the superconducting phase transition there always exist the bound states of the fermion couples beyond the pair condensate. If the pseudogap observed in the normal phase of the high-Tc superconductors is stipulated by the presence of the electron bound pairs, then the derived result suggests, in a model-independent manner, that the pseudogap survives below Tc.