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arXiv:cond-mat/9705166 · Physical review. B, Condensed matter

Pseudogap above Tc in a model with dx2−y2 pairing

Jan R. Engelbrecht, Alexander Nazarenko, Mohit Randeria, Elbio R. Dagotto

Published Jun 1, 1998• 105 citations
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Abstract

We study the anomalous normal-state properties of a simple two-dimensional model whose ground state is a $d$-wave superconductor. Using a self-consistent, conserving formulation, we show that pairing correlations above ${T}_{c}$ 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.

DOI
10.1103/physrevb.57.13406

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Physical review. B, Condensed matter•Jan 1, 1997•19 citations
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.
A model with d-wave pairing symmetry is studied by employing a nonperturbative sum-rule approach. At low temperature the magnitude of a normal-state pseudogap shows strong $\stackrel{\ensuremath{\rightarrow}}{k}$ or angle dependence well fitted by $\mathrm{cos}2\ensuremath{\varphi}$ form. With increasing temperature, the pseudogap closes at some critical angle ${\ensuremath{\varphi}}_{c},$ and beyond this angle a single quasiparticlelike peak appears. The resulting Fermi surface is strongly temperature dependent. Both in the spectral function and the density of states, the pseudogap disappears in a manner that the spectral weight fills in the pseudogap instead of closing it with increasing temperature. All these features are qualitatively consistent with angle resolved photoemission spectroscopy for underdoped cuprates.
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 electronic structure within a system of phase-decoupled one-dimensional superconductors coexisting with stripe spin and charge-density-wave order. This system has a nodal Fermi surface (Fermi arc) in the form of a hole pocket and an antinodal pseudogap. The spectral function in the antinodes is approximately particle-hole symmetric contrary to the gapped regions just outside the pocket. We find that states at the Fermi energy are extended whereas states near the pseudogap energy have localization lengths as short as the interstripe spacing. We consider pairing which has either local ddd-wave or sss-wave symmetry and find similar results in both cases, consistent with the pseudogap being an effect of local pair correlations. We suggest that this state is a stripe-ordered caricature of the pseudogap phase in underdoped cuprates with coexisting spin-, charge-, and pair-density-wave correlations. Lastly, we also model a superconducting state which (1) evolves smoothly from the pseudogap state, (2) has a signature subgap peak in the density of states, and (3) has the coherent pair density concentrated to the nodal region.
The line shape of photoemission spectra for underdoped cuprates is studied within the two-dimensional extended Hubbard model. Strong anisotropic scattering along the Fermi surface and the destruction of the Fermi surface near $(0,\ensuremath{\pi})$ are obtained for underdoped cuprates. These features are fully consistent with the recent angle-resolved photoemission experiments for underdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ as well as with the recent QMC calculations.
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.
Recently a pseudogap with d-wave symmetry was observed near the Fermi level in photoemission spectra of normal-state Bi2{\mathrm{Bi}}_{2}Bi2​Sr2{\mathrm{Sr}}_{2}Sr2​CaCu2{\mathrm{CaCu}}_{2}CaCu2​O8{\mathrm{O}}_{8}O8​ crystals. We demonstrate that an analogous pseudogap exists in the energy spectrum of the two-dimensional t-J model of cuprate perovskites. In agreement with experiment the magnitude of the pseudogap is 10--20 meV in underdoped crystals with hole concentration x\ensuremath{\lesssim}0.17 and the pseudogap disappears in optimally and overdoped crystals when x\ensuremath{\gtrsim}0.17. We demonstrate also that in the t-J model the overall energy spectrum near the Fermi level and the Fermi surface agree well with experimental observations.