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arXiv:cond-mat/9705144 · Physical review. B, Condensed matter

Pseudogap effects induced by resonant pair scattering

Boldizsár Jankó, Jiri Maly, Kathryn Levin

Published Nov 1, 1997• 167 citations
arXivHTMLPDF

Abstract

We demonstrate how resonant pair scattering of correlated electrons above ${T}_{c}$ can give rise to pseudogap behavior. This resonance in the scattering $T$ matrix appears for superconducting interactions of intermediate strength, within the framework of a simple fermionic model. It is associated with a splitting of the single peak in the spectral function into a pair of peaks separated by an energy gap. Our physical picture is contrasted with that derived from other $T$-matrix schemes, with superconducting fluctuation effects, and with preformed pair (boson-fermion) models. Implications for photoemission and tunneling experiments in the cuprates are discussed.

DOI
10.1103/physrevb.56.r11407

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We demonstrate how resonant pair scattering of correlated electrons above Tc{T}_{c}Tc​ can give rise to pseudogap behavior. This resonance in the scattering TTT matrix appears for superconducting interactions of intermediate strength, within the framework of a simple fermionic model. It is associated with a splitting of the single peak in the spectral function into a pair of peaks separated by an energy gap. Our physical picture is contrasted with that derived from other TTT-matrix schemes, with superconducting fluctuation effects, and with preformed pair (boson-fermion) models. Implications for photoemission and tunneling experiments in the cuprates are discussed.
We provide a fresh perspective on the pseudogap physics for attractive fermions as described by the three-dimensional Hubbard model. The pseudogap in the single-particle spectral function, which occurs for temperatures above the critical temperature Tc{T}_{c}Tc​ of the superfluid transition, is often interpreted in terms of preformed uncondensed pairs. Here we show that the occurrence of pseudogap physics can be consistently understood as due to local excitations which lead to a splitting of the quasiparticle peak for sufficiently large interaction. This effect becomes prominent at intermediate and high temperatures when the quantum-mechanical hopping is incoherent. We demonstrate the absence of the conjectured pairing temperature below which pseudogap physics is expected to occur. Our results are based on approximating the physics of the three-dimensional Hubbard model by dynamical mean-field theory calculations and a momentum independent self-energy. Our predictions can be tested with ultracold atoms in optical lattices with currently available temperatures and spectroscopic techniques.
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.
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 ttt-JJJ 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=0ω=0ω=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 ωωω-range around the Fermi energy. In a subsequent paper, also the supercunducting phase at moderate hole doping will be discussed within the PRM approach.
We study the anomalous normal-state properties of a simple two-dimensional model whose ground state is a ddd-wave superconductor. Using a self-consistent, conserving formulation, we show that pairing correlations above Tc{T}_{c}Tc​ lead to the appearance of a highly anisotropic pseudogap in the electronic spectral function and the destruction of the Fermi surface. We discuss the similarities and differences between our results and angle-resolved photoemission spectroscopy experiments on underdoped cuprates.
Despite the intense theoretical and experimental effort, an understanding of the superconducting pairing mechanism of the high-temperature superconductors leading to an unprecedented high transition temperature Tc{T}_{c}Tc​ 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 gaplike behavior on parts of the Fermi surface, leaving a nongapped segment known as Fermi arc around the diagonal of the Brillouin zone. Two main interpretations of the origin of the pseudogap have been proposed: either the pseudogap is a precursor to superconductivity, or it arises from another order competing with superconductivity. Starting from the t-J model, in this paper we present a microscopic approach to investigate physical properties of the pseudogap phase as well as the superconducting phase in the framework of a renormalization scheme called projector-based renormalization method. This approach is based on a stepwise elimination of high-energy transitions using unitary transformations. We arrive at renormalized ``free'' Hamiltonians for correlated electrons for both phases. Our microscopic approach allows us to explain the experimental findings in the underdoped as well as in the optimal hole doping regime. The ARPES spectral function along the Fermi surface turns out to be in good agreement with experiment: For the pseudogap phase we find well-defined excitation peaks around $\ensuremath{\omega}=0$ 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 $\ensuremath{\omega}$ range around the Fermi energy. In the superconducting phase, the order parameter turns out to have ddd-wave symmetry with a coherence length of a few lattice constants. In good agreement with experiments, we find no superconducting solutions for very small hole doping.
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.