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Journal of Physics A Mathematical and General

Investigation of charge stripe formation in an extendedt–Jmodel

Tôru Sakai

Published Aug 20, 2003• 1 citation
Publisher

Abstract

We consider a possible mechanism of the charge stripes in the high- T c cuprates, based on some additional interactions in the two-dimensional t – J model; the next-nearest-neighbour and/or four-spin (ring) exchange interactions. The many-hole correlation functions obtained by numerical exact diagonalization of a finite-cluster t – J model including the correction terms indicate the realization of the mechanism and give some preliminary phase diagrams. A realistic combination of these additional terms is also studied.

DOI
10.1088/0305-4470/36/35/315

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We consider a possible mechanism of the charge stripes in the high- T c cuprates, based on some additional interactions in the two-dimensional t – J model; the next-nearest-neighbour and/or four-spin (ring) exchange interactions. The many-hole correlation functions obtained by numerical exact diagonalization of a finite-cluster t – J model including the correction terms indicate the realization of the mechanism and give some preliminary phase diagrams. A realistic combination of these additional terms is also studied.
The two-dimensional extended $t\ensuremath{-}J$ model is studied computationally in a broad region of parameter space, motivated by recent photoemission experiments for the undoped cuprate Ca2CuO2Cl2{\mathrm{Ca}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}Ca2​CuO2​Cl2​ [F. Ronning et al., Science 282, 2067 (1998)]. The one-hole ground state is shown to develop robust antiferromagnetic (AF) correlations between spins separated by the mobile hole (i.e., across the hole). This effect tends to decouple charge from spin, and the quasiparticle weight becomes negligible, particularly at momenta $(0,\ensuremath{\pi})\ensuremath{-}(\ensuremath{\pi},0).$ Studies with more holes show precursors of metallic stripe formation, with holes sharing their individual spin arrangements, and AF correlations generated across the stripe.
Abstract Several state-of-the-art numerical methods have observed static or fluctuating spin and charge stripes in doped two-dimensional Hubbard models, suggesting that these orders play a significant role in shaping the cuprate phase diagram. Many experiments, however, also indicate that the cuprates have strong electron-phonon (e-ph) coupling, and it is unclear how this interaction influences stripe correlations. We study static and fluctuating stripe orders in the doped single-band Hubbard-Holstein model using zero temperature variational Monte Carlo and finite temperature determinant quantum Monte Carlo. We find that the lattice couples more strongly with the charge component of the stripes, leading to an enhancement or suppression of stripe correlations, depending on model parameters like the next-nearest-neighbor hopping t′{t}^{{\prime} }t′ t′ or phonon energy Ω. Our results help elucidate how thee-ph interaction can tip the delicate balance between stripe and superconducting correlations in the Hubbard-Holstein model with implications for our understanding of the high-Tccuprates.
We investigate the two-dimensional t-J model at a hole doping of x=18x\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\frac{1}{8}x=81​. The low-energy states are uniform (not striped). We find numerous excited states with charge density wave structures, which may be interpreted as striped phases. Some of these are consistent with neutron scattering data on cuprates and nickelates. Without additional terms in the t-J Hamiltonian, stripes can be stabilized only as ground states through the application of artificial boundary conditions.
The two-dimensional $t\ensuremath{-}J$ model with and without ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$ hopping-terms is studied by exact diagonalization on a $5\ifmmode\times\else\texttimes\fi{}4$ cluster, which realizes a hole stripe in y direction in a spin-Peierls phase. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle peaks in the single-particle spectrum is in good agreement with bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}.$ The resulting spectral weight distribution and Fermi surface agree well with experimental angle-resolved photoemission spectra on La1.28Nd0.6Sr0.12CuO4.{\mathrm{La}}_{1.28}{\mathrm{Nd}}_{0.6}{\mathrm{Sr}}_{0.12}{\mathrm{CuO}}_{4}.La1.28​Nd0.6​Sr0.12​CuO4​.
The 2D t-J model with and without t' and t'' hopping-terms is studied by exact diagonalization on a 5 x 4 cluster, which realizes a hole stripe in y-direction in a dimerized singlet background. Next nearest hopping terms with a sign appropriate for hole-doped cuprates enhance the stripe formation. The dispersion of the quasiparticle-peaks in the single-particle spectrum is in good agreement with a simple bond operator theory for hole motion in the spin-Peierls phase, particularly so for realistic values of t' and t''. The resulting spectral weight distribution and Fermi surface agree well with experimental ARPES spectra on La_1.28 Nd_0.6 Sr_0.12 Cu O_4.