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Physical review. B, Condensed matter

Pairing correlations with s* and dx2−y2 symmetry in a disordered Cu4 O8 cluster

Владимир Федорович Елесин, Arkady V. Krasheninnikov, L. А. Openov

Published Dec 1, 1995• 0 citations
Publisher

Abstract

Recently we have shown [V. F. Elesin, A. V. Krasheninnikov, and L. A. Openov, Sov. Phys. JETP 79, 789 (1994)] that in the hole-doped ${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ cluster pairing correlations with ${s}^{*}$ symmetry are nearly twice as strong as those with ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry, while in the electron-doped cluster pairing correlations seem to be present in the ${s}^{*}$ channel only. In this paper the effect of on-site disorder on the pairing correlators with ${s}^{*}$ and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry in the ${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$ cluster is studied numerically through an exact diagonalization of the Emery-Anderson Hamiltonian. It is shown that at a nearly optimal doping level (0.25 excess holes per copper atom) the disorder weakens pairing correlations in the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ channel and has much less influence on pairing correlations in the ${s}^{*}$ channel. Based on the results obtained, the "superconducting" components of pairing correlators are estimated to be 10-30% of their full values, with the remaining parts of correlators being contributions from a finite-size effect. These results indicate that cluster calculations may be relevant for the study of high-${T}_{c}$ superconductivity.

DOI
10.1103/physrevb.52.16187

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Recently we have shown [V. F. Elesin, A. V. Krasheninnikov, and L. A. Openov, Sov. Phys. JETP 79, 789 (1994)] that in the hole-doped {\mathrm{Cu}}_{4}$${\mathrm{O}}_{8} cluster pairing correlations with s∗{s}^{*}s∗ symmetry are nearly twice as strong as those with dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ symmetry, while in the electron-doped cluster pairing correlations seem to be present in the s∗{s}^{*}s∗ channel only. In this paper the effect of on-site disorder on the pairing correlators with s∗{s}^{*}s∗ and dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ symmetry in the {\mathrm{Cu}}_{4}$${\mathrm{O}}_{8} cluster is studied numerically through an exact diagonalization of the Emery-Anderson Hamiltonian. It is shown that at a nearly optimal doping level (0.25 excess holes per copper atom) the disorder weakens pairing correlations in the dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ channel and has much less influence on pairing correlations in the s∗{s}^{*}s∗ channel. Based on the results obtained, the "superconducting" components of pairing correlators are estimated to be 10-30% of their full values, with the remaining parts of correlators being contributions from a finite-size effect. These results indicate that cluster calculations may be relevant for the study of high-Tc{T}_{c}Tc​ superconductivity.
We calculate on-site s, extended s and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing correlation functions in a generalized Hubbard model for the cuprates, for parameters appropriate for electron-doped systems, using numerical diagonalization of a $4\ifmmode\times\else\texttimes\fi{}4$ cluster. We find indications of d-wave superconductivity for small doping $(\ensuremath{\sim}0.1$ electrons per unit cell) and s-wave superconductivity for overdoped systems $(\ensuremath{\sim}0.5$ electrons per unit cell) or small U. The magnitude of the pairing correlation functions and the vertex contributions to them are in general much smaller than in the hole-doped case. We also present results for the spin-structure factor.
We examine the influence of hole doping on superconducting pairing symmetries in the two-dimensional Hubbard model extended by next-nearest-neighbor hopping, nearest-neighbor Coulomb interaction, correlated hopping, exchange interaction and pair-hopping processes. Using Lanczos exact diagonalization supported by projector quantum Monte Carlo method, we calculate superconducting correlation functions corresponding to s-wave, extended s-wave, and d-wave pairing over a broad range of electron concentrations and interaction parameters. We find that hole doping acts as an efficient control parameter of superconducting pairing symmetry, giving rise to robust crossovers between the dominant pairing correlations. While extended s-wave pairing dominates throughout most of the overdoped regime, reducing the hole concentration progressively enhances d-wave correlations over large regions of the ground-state diagram. The critical doping associated with these crossovers depends strongly on the underlying interaction mechanism. In particular, correlated hopping and next-nearest-neighbor hopping substantially modify the location of the pairing-symmetry boundaries, whereas the local Hubbard interaction exhibits a comparatively weaker effect. In contrast to all other interaction channels, a finite nearest-neighbor Coulomb interaction additionally stabilizes conventional s-wave state over a sizeable region of parameter space. Our results demonstrate that superconducting pairing symmetry in the extended Hubbard model is governed by a subtle interplay between carrier concentration and nonlocal electronic interactions.
Using numerical diagonalization of a $4\ifmmode\times\else\texttimes\fi{}4$ cluster, we calculate on-site s, extended-s,s,s, and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing correlation functions (PCF's) in an effective generalized Hubbard model for the cuprates, with nearest-neighbor correlated hopping and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}.$ The vertex contributions to the PCF's are significantly enhanced, relative to the ${t\ensuremath{-}t}^{\ensuremath{'}}\ensuremath{-}U$ model. The behavior of the PCF's and their vertex contributions, and signatures of anomalous flux quantization, indicate superconductivity in the d-wave channel for moderate doping and in the s-wave channel for high doping and small U.
A Monte Carlo world-line algorithm for a CuO2{\mathrm{O}}_{2}O2​ plane based on a breakup of the plane into five-site cells, CuO4{\mathrm{O}}_{4}O4​ has been suggested. The algorithm has fast convergency and gives the possibility of investigating the superconducting state symmetry. The calculation of pairing correlation functions was made with an advent of additional imaginary-time slices to the Monte Carlo scheme. The characteristics of a two-dimensional Cu-O cluster with number of sites Na=768{N}_{a}=768Na​=768 (16\ifmmode\times\else\texttimes\fi{}16 CuO2{\mathrm{O}}_{2}O2​ cells) were calculated. It has been shown within the chosen interval of parameters of the Emery Hamiltonian (Ud=6t{U}_{d}=6tUd​=6t, $\ensuremath{\varepsilon}=1\ensuremath{-}3t$, Up=V=0{U}_{p}=V=0Up​=V=0), temperatures (T> 0.125tT>~0.125tT> 0.125t), and carrier concentrations (0.7< x< 1.50.7<~x<~1.50.7< x< 1.5) that (i) the long-range off-diagonal order associated with the superconducting state was not observed in the thermodynamic limit in any pairing channels and (ii) a tendency to divergence in s∗{s}^{*}s∗ channels and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ channels, which is noted as the temperature decreases, is due to the antiferromagnetic ordering rather than the superconducting pairing. If the carrier concentration xxx is equal to 1.0 (undoped dielectric state) the pairing correlations have maximum amplitude and demonstrate clear antiferromagnetic ordering in the copper sublattice, and the characteristic correlation length is close to the earlier-reported antiferromagnetic length.
Applying a variational Monte Carlo method to a two-dimensional t-J model, we study the nonmonotonic d_{x^2-y^2}-wave superconductivity, observed by Raman scattering and ARPES experiments in the electron-doped cuprates. As a gap function in the trial state, we extend the d-wave form (ext.d) so as to have its maxima located near the hot spots of the system. It is found that, in contrast to the hole-doped case, the ext.d wave is always more stable than the simple d wave in the electron-doped case, and the magnetic correlation of the wave vector (π,π) as well as the pair correlation is enhanced. These results corroborate spin-correlation-mediated superconductivity in cuprates, recently argued from a FLEX calculation. In addition, we confirm that s- and p-wave symmetries are never stabilized even in the over-doped regime.
We have calculated high temperature series to 12th order in inverse temperature for singlet superconducting correlation functions of the 2D $t\mathrm{\text{\ensuremath{-}}}J$ model with sss, ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$, and dxy{d}_{xy}dxy​ symmetry pairs. Our calculations differ from previous work by removing disconnected pieces from the original four-point correlator and by treating the resulting pairing correlator as a matrix. We find the correlation length for ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing grows significantly with decreasing temperature and develops a broad peak as a function of doping around $\ensuremath{\delta}=0.25$ for T/J=0.25T/J=0.25T/J=0.25 at J/t=0.4J/t=0.4J/t=0.4. The correlation lengths for sss and dxy{d}_{xy}dxy​ symmetry remain small and do not display peaks. Antiferromagnetic spin correlations at low doping act to suppress the ${d}_{{x}^{2}\ensuremath{-}{y}^{x}}$ and dxy{d}_{xy}dxy​ superconducting correlation lengths.