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arXiv:cond-mat/0108198 · Physical Review Letters

Stripes and Spin Incommensurabilities Are Favored by Lattice Anisotropies

Federico Becca, Luca Capriotti, Sandro Sorella

Published Sep 26, 2001• 30 citations
arXivHTMLPDF

Abstract

Structural distortions in cuprate materials give a natural origin for anisotropies in electron properties. We study a modified one-band t-J model in which we allow for different hoppings and antiferromagnetic couplings in the two spatial directions (t(x) not equal to t(y) and Jx not equal to J(y)). Incommensurate peaks in the spin structure factor show up only in the presence of a lattice anisotropy, whereas charge correlations, indicating enhanced fluctuations at incommensurate wave vectors, are present but almost unaffected with respect to the isotropic case.

DOI
10.1103/physrevlett.87.167005

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Structural distortions in cuprate materials give a natural origin for anisotropies in electron properties. We study a modified one-band t-J model in which we allow for different hoppings and antiferromagnetic couplings in the two spatial directions (t(x) not equal to t(y) and Jx not equal to J(y)). Incommensurate peaks in the spin structure factor show up only in the presence of a lattice anisotropy, whereas charge correlations, indicating enhanced fluctuations at incommensurate wave vectors, are present but almost unaffected with respect to the isotropic case.
Abstract. Magnetic and charge susceptibilities of the two-dimensional repulsive Hubbard model are investigated applying a strong coupling diagram technique in which the expansion in powers of the hopping constants is used. For small lattices and high temperatures results are in agreement with Monte Carlo simulations. With the departure from half-filling x the low-frequency magnetic susceptibility becomes incommensurate and the incommensurability parameter grows with x. The incommensurability, its dependence on frequency and on x resemble experimental results in lanthanum cuprates. Also for finite x sharp maxima appear in the static charge susceptibility. The maxima are finite which points to the absence of the long-range charge ordering (static stripes). However, for x ≈ 0.12 the maxima are located near the momenta (0, ±π/2), (±π/2, 0). In this case an interaction of carriers with tetragonal distortions can stabilize stripes with the wavelength of four lattice spacings, as observed in the low-temperature tetragonal phase of cuprates. As follows from the obtained results, the magnetic incommensurability is not a consequence of the stripes. The Hubbard model is thought to be appropriate to describe the main features of electron correlations in narrow energy bands, leading to collective effects such as magnetism and
We consider the slave-fermion Schwinger-boson decomposition of an effective model obtained through a systematic low-energy reduction of the three-band Hubbard Hamiltonian. The model includes a three-site term t ′′ similar to that obtained in the large- U limit of the Hubbard model but of opposite sign for realistic or large O-O hopping. For parameters close to the most realistic ones for the cuprates, the mean-field solution exhibits d + s superconductivity (predominantly d x 2 − y 2 ) with a dependence on doping x very similar to the experimentally observed. We also obtained incommensurate peaks at wave vectors ∼ π(1,1 ± 2 x ) in the spin structure factor, which also agree with experiment.
The one-band t–J model captures strong correlations in cuprate high-temperature superconductors. It accounts for the various intertwined spin and charge orders, and the superconductivity in the phase diagrams. To see the correlation effect on the intertwined orders, we implement the density matrix renormalization group method to simulate the t–J model in a small J case with t/J = 10, which is in a deeper Mott region than that with t/J ≃ 3 in cuprate superconducting compounds. We examine the results on a six-leg lattice with both the nearest and next-nearest-neighbor hoppings and antiferromagnetic coupling, and find the absence of superconductivity and enhanced intertwined spin and charge orders in the phase diagram. Besides the stripe phases, we find a new SDW + CDW phase in which the spin modulation is a (π, π) antiferromagnetism, while the wavelength of the charge modulation is shorter than that of the stripe phases. Our results suggest the enhanced intertwined orders and suppressed superconductivity in the deep Mott region.
Motivated by the effect of symmetry breaking in cuprates superconductors YBa[Formula: see text]Cu[Formula: see text]O[Formula: see text], we employ the renormalized mean-field theory to study the presence of uniform superconducting and charge-ordered states in two anisotropic t-J-U models, either with hopping strength anisotropy or antiferromagnetic interaction anisotropy. In the case of uniform superconducting state, compared with the isotropic t-J-U model with only [Formula: see text]-wave superconducting state, there is an additional s-wave superconducting state in the model with hopping strength anisotropy. Meanwhile, the hopping anisotropy may enhance the critical Coulomb interaction [Formula: see text] at the Mott insulator to the Gossamer superconductor transition point, and strong hopping anisotropy may weaken the superconducting state. In the case of a charge-ordered state, hopping anisotropy may suppress the amplitude of the charge density waves and pair density waves, which originate from local Coulomb interactions. These results indicate that the effects of hopping anisotropy and local Coulomb interactions are competitive. Moreover, the antiferromagnetic interaction anisotropy only weakly suppresses the superconducting gap and density wave amplitude. Our results show that the t-J-U model with hopping anisotropy is qualitatively consistent with experimental superconducting pair symmetry and charge density waves in the YBa[Formula: see text]Cu[Formula: see text]O[Formula: see text] system.
The effect of the extra second neighbor hopping t' on the incommensurate spin correlation in the t-J model in the underdoped regime is studied within the fermion-spin theory. It is shown that although the extra second neighbor hopping t' is systematically accompanied with the increasing of the weight of the incommensurate peaks in the dynamical spin structure factor, for the physical reasonable small value of t' the qualitative behavior of the incommensurate spin correlation in the t-t'-J model is the same as in the case of t-J model.
The high-temperature superconducting cuprates host unidirectional spin- and charge-density-wave orders that can intertwine with superconductivity in nontrivial ways. While the charge components of these stripes have now been observed in nearly all cuprate families, their detailed evolution with doping varies across different materials and at high and low temperatures. We address this problem using nonperturbative determinant quantum Monte Carlo calculations for the three-band Hubbard model. Using an efficient implementation, we can resolve the model's fluctuating spin and charge modulations and map their evolution as a function of the charge transfer energy and doping. We find that the incommensurability of the charge modulations is decoupled from the spin modulations and decreases with hole doping, consistent with experimental measurements at high temperatures. These findings support the proposal that the high-temperature charge correlations are distinct from the intertwined stripe order observed at low-temperature and in the single-band Hubbard model.