superconductors, remains one of the greatest puzzles in condensed matter physics. One possible mechanism is fermionic incoherence, which near a quantum critical point allows pair formation but suppresses superconductivity. Employing quantum Monte Carlo simulations of a model of itinerant fermions coupled to ferromagnetic spin fluctuations, represented by a quantum rotor, we report numerical evidence of pseudogap behavior, emerging from pairing fluctuations in a quantum-critical non-Fermi liquid. Specifically, we observe enhanced pairing fluctuations and a partial gap opening in the fermionic spectrum. However, the system remains non-superconducting until reaching a much lower temperature. In the pseudogap regime the system displays a "gap-filling" rather than "gap-closing" behavior, similar to the one observed in cuprate superconductors. Our results present direct evidence of the pseudogap state, driven by superconducting fluctuations.
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.
Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors is still lacking. An additional puzzle is the unknown connection between the superconducting gap and the so-called pseudogap which is a central property of the most unusual normal state. Angle-resolved photoemission spectroscopy (ARPES) measurements have revealed a gap-like behavior on parts of the Fermi surface, leaving a non-gapped segment known as Fermi arc around the diagonal of the Brillouin zone. Starting from the
t-
J model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase in the framework of a novel renormalization scheme called PRM. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at a renormalized 'free' Hamiltonian for correlated electrons. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: We find well-defined excitation peaks around
ω=0 near the nodal direction, which become strongly suppressed around the antinodal point. The origin of the pseudogap can be traced back to a suppression of spectral weight from incoherent excitations in a small
ω-range around the Fermi energy. In a subsequent paper, also the supercunducting phase at moderate hole doping will be discussed within the PRM approach.
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.
Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high-temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has proven to be highly challenging. However, it has recently been realized that many models used to describe such systems are amenable to numerically exact solution by quantum Monte Carlo (QMC) techniques, without suffering from the fermion sign problem. In this review, we examine the status of the understanding of metallic quantum criticality and the recent progress made by QMC simulations. We focus on the cases of spin-density wave and Ising nematic criticality. We describe the results obtained so far and their implications for superconductivity, non-Fermi liquid behavior, and transport near metallic quantum critical points. Some of the outstanding puzzles and future directions are highlighted.
In this paper, we try to understand the pseudogap phenomenon observed in the cuprate superconductor through a model study. Specifically, we explore the so-called low-temperature pseudogap state by turning off the superconducting (SC) off diagonal long range order in an ansatz state for the t – J model (Weng 2011 New J. Phys. 13 103039 ). Besides strong non-Gaussian SC fluctuations, the resulting state also exhibits a systematic pseudogap behavior in both spin and charge degrees of freedom, manifested in the uniform spin susceptibility, specific heat, non-Drude resistivity, Nernst effect, as well as the quantum oscillation associated with small Fermi pockets emerging in strong magnetic fields, etc. These anomalous 'normal state' properties are found in qualitative consistency with experimental measurements in the cuprates. Such a model study establishes an intrinsic connection between the peculiar pseudogap properties and the non-BCS nature of the SC ground state. A critical comparison with other approaches to the doped Mott insulator is also made.