The pseudogap phase occurring in cuprate and organic superconductors is analyzed based on the dynamical cluster approximation approach to the Hubbard model. In this method a cluster embedded in a self-consistent bath is studied. With increasing Coulomb repulsion,
U, the antinodal point [$\mathbf{k}=(\ensuremath{\pi},0)$] displays a gradual suppression of spectral density of states around the Fermi energy which is not observed at the nodal point [$\mathbf{k}=(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$]. The opening of the antinodal pseudogap is found to be related to the internal structure of the cluster and the much weaker bath-cluster couplings at the antinodal than nodal point. The role played by internal cluster correlations is elucidated from a simple four-level model. For small
U, the cluster levels form Kondo singlets with their baths leading to a peak in the spectral density. As
U is increased a localized state is formed localizing the electrons in the cluster. If this cluster localized state is nondegenerate, the Kondo effect is destroyed and a pseudogap opens up in the spectra at the antinodal point. The pseudogap can be understood in terms of destructive interference between different paths for electrons hopping between the cluster and the bath. However, electrons at the nodal points remain in Kondo states up to larger
U since they are more strongly coupled to the bath. The strong correlation between the $(\ensuremath{\pi},0)$ and the $(0,\ensuremath{\pi})$ cluster levels in the localized state leads to a large correlation energy gain, which is important for localizing electrons and opening up a pseudogap at the antinodal point. Such a scenario is in contrast with two independent Mott transitions found in two-band systems with different bandwidths in which the localized cluster electron does not correlate strongly with any other cluster electron for intermediate
U. The important intracluster sector correlations are associated with the resonating valence bond character of the cluster ground state containing
d-wave singlet pairs. The low-energy excitations determining the pseudogap have suppressed
d-wave pairing, indicating that the pseudogap can be related to breaking very short-range
d-wave pairs. Geometrical frustration on the anisotropic triangular lattice relevant to $\ensuremath{\kappa}$-(BEDT-TTF)
2X leads to a switch in the character of the ground state of the cluster at intermediate hopping ratios ${t}^{\ensuremath{'}}/t\ensuremath{\sim}0.7$. Electron doping of the frustrated square lattice destroys the pseudogap, in agreement with photoemission experiments on cuprates, due to a larger Schrieffer-Wolff exchange coupling,
JK, and a stronger cluster-bath coupling for the antinodal point.
There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around
xc, the end point of the superconducting dome on the overdoped side, where the cuprate is believed to be well described by the Fermi-liquid theory. This is the most evident in the observed ${\ensuremath{\rho}}_{s}(0)\ensuremath{-}{T}_{c}$ scaling and the large amount of uncondensed optical spectral weight at low energy. The second puzzle concerns the remarkable robustness of the
d-wave pairing against the inevitable disorder effect in such a doped system, which is also totally unexpected from the conventional BCS picture. Here we show that these two puzzles are deeply connected to the origin of a third puzzle about the cuprate superconductors, namely, the mysterious quantum critical behavior observed around
x∗, the so called pseudogap end point. Through a systematic variational Monte Carlo (VMC) study of the disordered 2D $t\ensuremath{-}J$ model from the resonating valence bond (RVB) perspective, we find that the
d-wave pairing in this model is remarkably more robust against the disorder effect than that in a conventional
d-wave BCS superconductor. We find that such remarkable robustness can be attributed to the spin-charge separation mechanism in the RVB picture, through which the
d-wave RVB pairing of the charge-neutral spinons becomes essentially immune to the disorder potential except for the secondary effect related to the modulation of the local doping level by the disorder. We propose that there exists a Mott transition at
x∗, where the RVB pairing in the underdoped regime is transmuted into the increasingly more BCS-like pairing for
x>x∗, whose increasing fragility against the disorder effect leads to the non-BCS behavior and the ultimate suppression of superconductivity around
xc.
We study electronic structure of hole- and electron-doped Mott insulators in the two-dimensional Hubbard model to reach a unified picture for the normal state of cuprate high-
Tc superconductors. By using a cluster extension of the dynamical mean-field theory, we demonstrate that structure of coexisting zeros and poles of the single-particle Green's function holds the key to understand Mott physics in the underdoped region. We show evidence for the emergence of non-Fermi-liquid phase caused by the topological quantum phase transition of Fermi surface by analyzing low-energy charge dynamics. The spectra calculated in a wide range of energy and momentum reproduce various anomalous properties observed in experiments for the high-
Tc cuprates. Our results reveal that the pseudogap in hole-doped cuprates has a
d-wavelike structure only below the Fermi level while it retains non-
d-wave structure with a fully opened gap above the Fermi energy even in the nodal direction due to a zero surface extending over the entire Brillouin zone. In addition to the non-
d-wave pseudogap, the present comprehensive identifications of the spectral asymmetry as to the Fermi energy, the Fermi arc, and the back-bending behavior of the dispersion, waterfall, and low-energy kink, in agreement with the experimental anomalies of the cuprates, do not support that these originate from (the precursors of) symmetry breakings such as the preformed pairing and the
d-density-wave fluctuations, but support that they are direct consequences of the proximity to the Mott insulator. Several possible experiments are further proposed to prove or disprove our zero mechanism.
There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around
xc, the end point of the superconducting dome on the overdoped side, where the cuparte is believed to be well described by the fermi liquid theory. This is the most evident in the observed
ρs(0)−Tc scaling and the large amount of uncondensed optical spectral weight at low energy. The second puzzle concerns the remarkable robustness of the d-wave pairing against the inevitable disorder effect in such a doped system, which is also totally unexpected from the conventional BCS picture. Here we show that these two puzzles are deeply connected to the origin of a third puzzle about the cuprate superconductors, namely, the mysterious quantum critical behavior observed around
x∗, the so-called pseudogap end point. Through a systematic variational optimization of the disordered 2D
t−J model from the resonating valence bond(RVB) perspective, we find that the d-wave pairing in this model is remarkably more robust against the disorder effect than that in a conventional d-wave BCS superconductor. We find that such remarkable robustness can be attributed to the spin-charge separation mechanism in the RVB picture, through which the d-wave RVB pairing of the charge neutral spinons becomes essentially immune to the impurity potential except for the secondary effect related to the modulation of the local doping level by the disorder. We propose that there exists a Mott transition at
x∗, where the RVB pairing in the underdoped regime is transmuted into the increasingly more BCS-like pairing for
x>x∗, whose increasing fragility against the disorder effect leads to the non-BCS behavior and the ultimate suppression of superconductivity around
xc.
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.
Evidence that the pseudogap (PG) in a near-optimally doped Bi
2Sr
2CaCu
2O
8+δ sample destroys the BCS logarithmic pairing instability [1] raises again the question of the role of the PG in the high-temperature superconducting cuprates [2]. The elimination of the BCS instability is consistent with the view that the PG competes with superconductivity. However, as noted in [1], the onset of superconductivity with a
Tc∼90 K suggests an alternative scenario in which the PG reflects the formation of short range pairing correlations. Here, we report results obtained from a dynamic cluster quantum Monte Carlo approximation (DCA) for a 2D Hubbard model and conclude that (1) the PG, like the superconductivity, arises due to short-range antiferromagnetic correlations and (2) contrary to the usual case in which the pairing instability arises from the Cooper instability, here, the strength of the spin-fluctuations increases as the temperature decreases leading to the pairing instability.