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Physical review. B./Physical review. B

Origin of the pseudogap end point in high- T c cuprate superconductors

Jianhua Yang, Tao Li

Published Jul 30, 2024• 1 citation
Publisher

Abstract

There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around ${x}_{c}$, 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 ${x}_{c}$.

DOI
10.1103/physrevb.110.024521

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There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around $x_{c}$, 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 $ρ_{s}(0)-T_{c}$ 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 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 $x_{c}$.

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There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around xc{x}_{c}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 \ensuremathρs(0)\ensuremath−Tc{\ensuremath{\rho}}_{s}(0)\ensuremath{-}{T}_{c}\ensuremathρs​(0)\ensuremath−Tc​ scaling and the large amount of uncondensed optical spectral weight at low energy. The second puzzle concerns the remarkable robustness of the ddd-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∗{x}^{*}x∗, the so called pseudogap end point. Through a systematic variational Monte Carlo (VMC) study of the disordered 2D t\ensuremath−Jt\ensuremath{-}Jt\ensuremath−J model from the resonating valence bond (RVB) perspective, we find that the ddd-wave pairing in this model is remarkably more robust against the disorder effect than that in a conventional ddd-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 ddd-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∗{x}^{*}x∗, where the RVB pairing in the underdoped regime is transmuted into the increasingly more BCS-like pairing for x>x∗x>{x}^{*}x>x∗, whose increasing fragility against the disorder effect leads to the non-BCS behavior and the ultimate suppression of superconductivity around xc{x}_{c}xc​.
A tale of two pairs: on the origin of the pseudogap end point in the high-Tc_{c}c​ cuprate superconductors
There are two seemingly unrelated puzzles about the cuprate superconductors. The first puzzle concerns the strong non-BCS behavior around xcx_{c}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)−Tcρ_{s}(0)-T_{c}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∗x^{*}x∗, the so-called pseudogap end point. Through a systematic variational optimization of the disordered 2D t−Jt-Jt−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∗x^{*}x∗, where the RVB pairing in the underdoped regime is transmuted into the increasingly more BCS-like pairing for x>x∗x>x^{*}x>x∗, whose increasing fragility against the disorder effect leads to the non-BCS behavior and the ultimate suppression of superconductivity around xcx_{c}xc​.
A major puzzle in the study of the cuprate superconductivity is the origin of the pseudogap end point. Intriguingly, such a critical doping is also where the superfluid density of the system reaches its maximum. A non-monotonic doping dependence of the superfluid density is rather unusual since the Drude weight of the cuprate system is found to increase monotonically with the doping concentration. It is generally believed that such a peculiar behavior should be attributed to both the strongly correlated nature of the cuprate system and the disorder effect. In this work, we develop a variational theory for the zero temperature superfluid density of the disordered t−Jt-Jt−J model. This is achieved in two steps. First, we perform an unrestricted variational optimization of an RVB variational ground state for the disordered t−Jt-Jt−J model. Second, we construct the variational state that describes the paramagnetic current response on such an RVB state. The zero temperature superfluid density ρs(0)ρ_{s}(0)ρs​(0) is then extracted from the curvature of the variational ground state energy of the system as a function of the external electromagnetic field. We find that ρs(0)ρ_{s}(0)ρs​(0) computed in this way is remarkably robust against the disorder effect. More specifically, we find that ρs(0)ρ_{s}(0)ρs​(0) is a monotonically increasing function of doping concentration xxx and scales linearly with the total optical weight. This is consistent with the observation in the underdoped cuprates but is strongly at odd with the behavior in the overdoped cuprates. The strong contrast between the disorder effect in the underdoped and the overdoped regime lends strong support to our previous proposal that there exist a Mott transition between a doped-Mott-insulating metal in the underdoped regime and a fermi-liquid-like metal in the overdoped regime around the pseudogap end point.
We investigate the microscopic origin of the pseudogap in the weakly doped 2D Hubbard model using Quantum Monte Carlo within the dynamical cluster approximation. We compare our results with proposed scenarios for the pseudogap. All our numerical evidence is in favor of spin-charge separation as described in the resonating valence bond picture as the cause of the pseudogap behavior. Scenarios of "preformed pairs", the coupling of quasiparticles to antiferromagnetic spin-fluctuations and stripes are inconsistent with our results.
Abstract The mysterious metallic phase showing T-linear resistivity and a universal scattering rate 1 / τ = α P k B T / ℏ with a universal prefactor α P ∼ 1 and logarithmic-in-temperature singular specific heat coefficient, the so-called ‘Planckian metal phase’ was observed in various overdoped high- T c cuprate superconductors over a finite range in doping. Revealing the mystery of the Planckian metal state is believed to be the key to understanding the mechanism for high- T c superconductivity. Here, we propose a generic microscopic mechanism for this state based on quantum-critical local bosonic charge Kondo fluctuations coupled to both spinon and a heavy conduction-electron Fermi surface within the heavy-fermion formulation of the slave-boson t–J model. By a controlled perturbative renormalization group analysis, we examine the competition between the pseudogap phase, characterized by Anderson’s Resonating-Valence-Bond spin-liquid, and the Fermi-liquid state, modeled by the electron hopping (effective charge Kondo effect). We find a quantum-critical metallic phase with a universal Planckian ℏ ω / k B T scaling in scattering rate near an extended localized-delocalized (pseudogap-to-Fermi liquid) charge-Kondo breakdown transition. The d-wave superconducting ground state emerges near the transition. Unprecedented qualitative and quantitative agreements are reached between our theoretical predictions and various experiments, including optical conductivity, universal doping-independent field-to-temperature scaling in magnetoresistance, specific heat coefficient, marginal Fermi-liquid spectral function observed in ARPES, and Fermi surface reconstruction observed in Hall coefficients in various overdoped cuprates. Our mechanism offers a microscopic understanding of the quantum-critical Planckian metal phase observed in cuprates and its link to the pseudogap, d-wave superconducting, and Fermi liquid phases. It offers a promising route for understanding how d-wave superconductivity emerges from such a strange metal phase in cuprates–one of the long-standing open problems in condensed matter physics since 1990s–as well as shows a broader implication for the Planckian strange metal states observed in other correlated unconventional superconductors.
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 sss-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\mathit{XY}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 sss-wave picture.
Cooper pairing instability in a Fermi liquid is well understood by the BCS theory, but pairing mechanism for doped Mott insulators still remains elusive. Previously it has been shown by density matrix renormalization group (DMRG) method that a single doped hole is always self-localized due to the quantum destructive interference of the phase string signs hidden in the t-J ladders. Here we report a DMRG investigation of hole binding in the same model, where a novel pairing-glue scheme beyond the BCS realm is discovered. Specifically, we show that, in addition to spin pairing due to superexchange interaction, the strong frustration of the phase string signs on the kinetic energy gets effectively removed by pairing the charges, which results in strong binding of two holes. By contrast, if the phase string signs are "switched off" artificially, the pairing strength diminishes significantly even if the superexchange coupling remains the same. In the latter, unpaired holes behave like coherent quasiparticles with pairing drastically weakened, whose sole origin may be attributed to the resonating-valence-bond (RVB) pairing of spins. Such non-BCS pairing mechanism is therefore beyond the RVB picture and may shed important light on the high-T(c) cuprate superconductors.