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Physical Review B

Binding of charge carriers in the extended t−J model

J. M. Tipper, C. Genert, K. J. E. Vos

Published Feb 25, 2005• 0 citations
Publisher

Abstract

We have examined the effects of extended hopping parameters in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model on the binding and spatial distribution of charge carriers. Previous studies have shown that a negative next-nearest-neighbor hopping in the physical parameter range serves to weaken striped behavior in the model. We show using exact diagonalization that a physically relevant set of parameters for the hole doped cuprates that includes next-next-nearest-neighbor hopping strengthens the binding of the holes and enhances stripe behavior in the underdoped regime.

DOI
10.1103/physrevb.71.054515

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We have examined the effects of extended hopping parameters in the t\ensuremath-t\ensuremath′\ensuremath-t\ensuremath′′\ensuremath-Jt\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}Jt\ensuremath-t\ensuremath′\ensuremath-t\ensuremath′′\ensuremath-J model on the binding and spatial distribution of charge carriers. Previous studies have shown that a negative next-nearest-neighbor hopping in the physical parameter range serves to weaken striped behavior in the model. We show using exact diagonalization that a physically relevant set of parameters for the hole doped cuprates that includes next-next-nearest-neighbor hopping strengthens the binding of the holes and enhances stripe behavior in the underdoped regime.
') neighbor hoppings. Our work investigates the consequences of increasing hole doping on the instauration of stripes and the behavior of the superconducting order parameter, with a discussion on how the two phenomena affect each other. We consider two different values of the next-nearest neighbor hopping parameter, that are appropriate for describing cuprate superconductors. We observe that stripes are the optimal state in a wide doping range; the stripe wavelength reduces at increasing doping, until stripes melt into a uniform state for large values of doping. Superconducting pair-pair correlations, indicating the presence of superconductivity, are always suppressed in the presence of stripes. Our results suggest that the phase diagram for the single-band Hubbard model is dominated by stripes, with superconductivity being possible only in a narrow doping range between striped states and a nonsuperconducting metal.
A next-nearest-neighbor hopping t' in the t-t'-J model has a different sign between the hole- and electron-doped systems of high-Tc{\mathit{T}}_{\mathit{c}}Tc​ cuprates: t'0 for the hole-doped system and t'>0 for the electron-doped system. We show that the sign is responsible for the remarkable difference of antiferromagnetic (AF) phases between the two systems. To reveal this and clarify the role of t', we examine magnetic excitations of the t-t'-J model by employing exact diagonalization techniques for 4\ifmmode\times\else\texttimes\fi{}4 and \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 lattices. In the low-doping region (two-hole case of the \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 lattice), AF spin correlations are stabilized for the case of t'>0, i.e., electron-doping case, but not for the case of t'0. In the high-doping region (four-hole case of the 4\ifmmode\times\else\texttimes\fi{}4 lattice and more) magnetic excitations are mainly controlled by the geometry of the Fermi surface of the noninteracting system.
We investigate the effects of the next-nearest-neighbor (${t}^{\ensuremath{'}}$) and the third-nearest-neighbor (${t}^{\ensuremath{'}\ensuremath{'}}$) hopping terms on superconductivity correlation in the 2D hole-doped extended $t\ensuremath{-}J$ model based on the variational Monte Carlo, mean-field calculation and exact diagonalization method. Despite the diversity of the methods employed, the results all point to a consistent conclusion: While the ddd-wave superconductivity correlation is slightly suppressed by ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{'}\ensuremath{'}}$ in underdoped regions, it is greatly enhanced in the optimal and overdoped regions. The optimal Tc{T}_{c}Tc​ is a result of the balance of these two opposite trends.
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.
In this paper, the effect of the next-earest (t ′ ) and third-earest (t ′ ′ ) hopping terms on superconductivity (SC) of the two-dimensional (2D) extended t-J model is studied by the variational Monte-Carlo (VMC) method. For hole-doped systems, the d-wave pairing correlation is suppressed by t ′ and t ′ ′ for underdoped cases, while it can be greatly enhanced by proper values of t ′ and t ′ ′ for the overdoped ones. This behavior results from the deformation of the Fermi surfaces. PACS numbers: 74.20.-z, 71.18.+y The 2D t-J model is one of the most popular models for studying the properties of the high-temperature superconductivity (HTS) [1, 2]. Yet the problem whether this model can give such high Tc for the cuprates or not is still under debate [4–7]. It has been well accepted that the next-nearest-neighbor (t ′ ) and the third-nearest-neighbor (t ′ ′) hopping terms are necessary for models to explain several experiments like angle-resolved photoemission (ARPES) of HTS [3]. However, the effect of t ′ and t ′ ′ on pairing correlation is also controversial. Previous DMRG studies of the two-dimensional (2D) extended t-J model show that the SC is suppressed (enhanced) for negative (positive) next-nearestneighbor hopping t ′ /t [8]. But results from first-principle calculation show that t ′ /t = −0.3 maximizes SC at optimal doping [9]. The Hamiltonian of the extended t-J model is H = Ht + HJ = − ∑ ij tij(˜c † i,σ ˜cj,σ + H.C.) + J ∑