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arXiv:cond-mat/0110382 · Physical Review Letters

RobustD-Wave Pairing Correlations in a Hole-Doped Spin-Fermion Model

Mohammad Moraghebi, Seiji Yunoki, Adriana Moreo

Published Apr 17, 2002• 20 citations
arXivHTMLPDF

Abstract

Pairing correlations are studied numerically in a hole-doped spin-fermion model. Simulations performed on up to 12 x 12 clusters provide indications of D-wave superconductivity away from half-filling comparable to those of the 2D t-J model. The pairing correlations are the strongest in the direction perpendicular to the dynamic stripes that appear in the ground state at some densities. An optimal doping, where correlations are maximized, was observed at approximately 25% doping with an estimated T(c) approximately 100-200 K, in qualitative agreement with high-T(c) cuprates' phenomenology, while pairing correlations are suppressed by static stripe inhomogeneities.

DOI
10.1103/physrevlett.88.187001

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Pairing correlations are studied numerically in a hole-doped spin-fermion model. Simulations performed on up to 12 x 12 clusters provide indications of D-wave superconductivity away from half-filling comparable to those of the 2D t-J model. The pairing correlations are the strongest in the direction perpendicular to the dynamic stripes that appear in the ground state at some densities. An optimal doping, where correlations are maximized, was observed at approximately 25% doping with an estimated T(c) approximately 100-200 K, in qualitative agreement with high-T(c) cuprates' phenomenology, while pairing correlations are suppressed by static stripe inhomogeneities.
We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-[Formula: see text]-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative [Formula: see text] values ([Formula: see text]) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The [Formula: see text] (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find [Formula: see text] strongly suppresses superconductivity. The [Formula: see text] (electron-doped) region shows the expected circular Fermi pocket of holes around the [Formula: see text] point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector [Formula: see text] induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with [Formula: see text] is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near [Formula: see text] for [Formula: see text], we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.
The optical conductivity and Drude weight of a spin-fermion model for cuprates are studied as a function of electronic density and temperature using Monte Carlo techniques. This model develops stripes and robust D-wave pairing correlations upon hole doping, and it has the advantage that it can be numerically simulated without sign problems. Both static and dynamical information can be obtained. In this work, it was possible to analyze up to $12\ifmmode\times\else\texttimes\fi{}12$ site clusters at low temperatures ranging between 0.01t0.01t0.01t and 0.1t0.1t0.1t (between 50 K and 500 K for a hopping amplitude $t\ensuremath{\sim}0.5\mathrm{eV}).$ As the temperature is reduced, spectral weight is transferred from high to low frequencies in agreement with the behavior observed experimentally. Varying the hole density, the Drude weight has a maximum at the optimal doping for the model, i.e., at the density where the pairing correlations are stronger. It was also observed that the inverse of the Drude weight, roughly proportional to the resistivity, decreases linearly with the temperature at optimal doping, and it is abruptly reduced when robust pairing correlations develop upon further reducing the temperature. The behavior and general form of the optical conductivity are found to be in good agreement with experimental results for the cuprates. Our results also establish the spin-fermion model for cuprates as a reasonable alternative to the $t\ensuremath{-}J$ model, which is much more difficult to study accurately.
The optical conductivity and Drude weight of a spin-fermion model for cuprates are studied as a function of electronic density and temperature using Monte Carlo techniques. This model develops stripes and robust D-wave pairing correlations upon hole doping, and it has the advantage that it can be numerically simulated without sign problems. Both static and dynamical information can be obtained. In this work, it was possible to analyze up to 12312 site clusters at low temperatures ranging between 0.01t and 0.1t ~between 50 K and 500 K for a hopping amplitude t;0.5 eV). As the temperature is reduced, spectral weight is transferred from high to low frequencies in agreement with the behavior observed experimentally. Varying the hole density, the Drude weight has a maximum at the optimal doping for the model, i.e., at the density where the pairing correlations are stronger. It was also observed that the inverse of the Drude weight, roughly proportional to the resistivity, decreases linearly with the temperature at optimal doping, and it is abruptly reduced when robust pairing correlations develop upon further reducing the temperature. The behavior and general form of the optical conductivity are found to be in good agreement with experimental results for the cuprates. Our results also establish the spin-fermion model for cuprates as a reasonable alternative to the t-J model, which is much more difficult to study accurately.
Optical Conductivity σ(ω)σ(ω)σ(ω) and Resistivity ρdcρ_{dc}ρdc​ of a Hole Doped Spin-Fermion Model for Cuprates
The optical conductivity and Drude weight of a Spin-Fermion model for cuprates are studied as a function of electronic density and temperature. This model develops stripes and robust D-wave pairing correlation upon hole doping, and it has the advantage that it can be numerically simulated without sign problems. Both static and dynamical information can be obtained. In this work it was possible to analyze up to 12x12 site clusters at low temperatures ranging between 0.01t and 0.1t (between 50K and 500K for a hopping amplitude t∼0.5eVt \sim 0.5 eVt∼0.5eV). As the temperature is reduced, spectral weight is transferred from high to low frequencies in agreement with the behavior observed experimentally. Varying the hole density, the Drude weight has a maximum at the optimal doping for the model, i.e., at the density where the pairing correlations are stronger. It was also observed that the inverse of the Drude weight, roughly proportional to the resistivity, decreases linearly with the temperature at optimal doping, and it is abruptly reduced when robust pairing correlations develop upon further reducing the temperature. The behavior and general form of the optical conductivity are found to be in good agreement with experimental results for the cuprates. Our results also establish the Spin-Fermion model for cuprates as a reasonable alternative to the t-J model, which is much more difficult to study accurately.
There is growing evidence that the hole-doped single-band Hubbard and t - J models do not have a superconducting ground state reflective of the high-temperature cuprate superconductors but instead have striped spin- and charge-ordered ground states. Nevertheless, it is proposed that these models may still provide an effective low-energy model for electron-doped materials. Here we study the finite temperature spin and charge correlations in the electron-doped Hubbard model using quantum Monte Carlo dynamical cluster approximation calculations and contrast their behavior with those found on the hole-doped side of the phase diagram. We find evidence for a charge modulation with both checkerboard and unidirectional components decoupled from any spin-density modulations. These correlations are inconsistent with a weak-coupling description based on Fermi surface nesting, and their doping dependence agrees qualitatively with resonant inelastic x-ray scattering measurements. Our results provide evidence that the single-band Hubbard model describes the electron-doped cuprates.
Recent experimental results of angle-resolved photoemission spectroscopy suggested that an additional strong nearest neighbor attraction in the Hubbard model might be significant for the doped cuprates. The stripe-ordered patterns, which are formed by the inhomogeneous distribution of spin, charge, and pairing correlations in CuO2{\mathrm{CuO}}_{2}CuO2​ planes, are a well-known feature of the doped cuprates. By employing constrained path quantum Monte Carlo, we examine the effect of the nearest neighbor attraction on a two-dimensional repulsive Hubbard model. Within and across the stripe regions, the ground-state spin correlations and the ddd-wave pairing correlation are calculated. We found that the spin-spin correlation is the largest when the interstripe region is nearly half filled, and we also found the ddd-wave superconducting correlation of the neighboring sites is enhanced in the presence of the stripe pattern. This reveals the crucial effects of the strong nearest neighbor attraction on superconductivity in doped cuprates.