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Physical review. B, Condensed matter

Optical conductivity and resistivity of a hole-doped spin-fermion model for cuprates

Mohammad Moraghebi, Seiji Yunoki, Adriana Moreo

Published Dec 30, 2002• 13 citations
Publisher

Abstract

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 $0.01t$ and $0.1t$ (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.

DOI
10.1103/physrevb.66.214522

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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×\else\texttimes\fi1212\ifmmode\times\else\texttimes\fi{}1212\ifmmode×\else\texttimes\fi12 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∼0.5eV).t\ensuremath{\sim}0.5\mathrm{eV}).t\ensuremath∼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\ensuremath−Jt\ensuremath{-}Jt\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.
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.
The optical conductivity of the 2D t−Jt-Jt−J model and the origin of electron incoherence in the high-Tc_{c}c​ cuprate superconductors: a variational study
Understanding the origin of electron incoherence is the first step toward a theoretical description of the non-Fermi liquid behavior of the high-Tc_{c}c​ cuprate superconductors. Such electron incoherence manifests itself most evidently in the non-Drude behavior of the optical response of the system and the anomalous density fluctuation behavior in the long wave length limit. The spectral weight transfer related to such dissipative response, which is absent in conventional Fermi liquid metal, has direct consequence on the dc transport property of the system in the normal state and the superfluid stiffness in the superconducting state. It is found that such electron incoherence remains significant even in the clean limit and at low temperature and thus must be attributed to the strong electron correlation effect in the cuprate superconductors. Here we study such an intrinsic effect in the 2D t−Jt-Jt−J model through the variational calculation of its optical conductivity σ(ω)σ(ω)σ(ω). We assume a resonating valence bond ground state as our starting point and find that a significant portion of the total optical spectral weight remains incoherent throughout the phase diagram. The optical absorption is found to extend all the way to an energy of the order of the bare band width. We find that both the total optical weight Kˉ\bar{K}Kˉ and the integrated incoherent optical weight III increase monotonically with doping, with their ratio Rincoh=I/KˉR_{incoh}=I/\bar{K}Rincoh​=I/Kˉ decreasing monotonically with doping. Our results indicate that the majority part of electron incoherence in the 2D t−Jt-Jt−J model can be attributed to the electron fractionalization mechanism assumed in such a treatment. We also find that the Drude weight deduced from D=Kˉ−ID=\bar{K}-ID=Kˉ−I scales linearly with hole doping, without any sign of a non-monotonic behavior in the overdoped regime.
Results are for finite-temperature optical conductivity \ensuremath{\sigma}(\ensuremath{\omega}) and dc resistivity \ensuremath{\rho}(T), obtained within the t-J model on a square lattice by a method based on the Lanczos diagonalization. Studying systems with N=16 or 18 sites and hole concentrations ch{\mathit{c}}_{\mathit{h}}ch​\ensuremath{\le}0.25, a thermodynamic behavior is reached for quite low temperatures. \ensuremath{\sigma}(\ensuremath{\omega}) spectra reveal a slow non-Drude falloff at large frequencies and the emergence of a broad midinfrared peak at low doping. At optimum doping \ensuremath{\rho}(T) shows nearly linear variation with T. Both quantities agree well with experimental results in cuprates.
A Monte Carlo maximum-entropy calculation of the optical conductivity of the infinite-dimensional Hubbard model is presented. We show that the optical conductivity displays the anomalies found in the cuprate superconductors, including a Drude width which grows linearly with temperature, a Drude weight which grows linearly with doping, and a temperature and doping-dependent mid-IR peak. These anomalies arise as a consequence of the dynamical generation of a quasiparticle band at the Fermi energy as T\ensuremath{\rightarrow}0, and are a generic property of the strongly correlated Hubbard model in all dimensions greater than one.