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arXiv:1209.0049 · Physical Review B

Determinant quantum Monte Carlo study of the enhancement of d -wave pairing by charge inhomogeneity

Rubem Mondaini, Tao Ying, Thereza Paiva, Richard T. Scalettar

Published Nov 7, 2012• 36 citations
arXivHTMLPDF

Abstract

Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO${}_{2}$ planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two-dimensional Hubbard Hamiltonian. In this paper, we use determinant quantum Monte Carlo to show that if a stripe density pattern is imposed on the model, the $d$-wave pairing vertex is significantly enhanced. We attribute this enhancement to an increase in antiferromagnetic order which is caused by the appearance of more nearly half-filled regions when the doped holes are confined to the stripes. We also observe a $\ensuremath{\pi}$-phase shift in the magnetic order.

DOI
10.1103/physrevb.86.184506

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Physical Review B•Mar 14, 2012•11 citations
Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO2{}_{2}2​ planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two-dimensional Hubbard Hamiltonian. In this paper, we use determinant quantum Monte Carlo to show that if a stripe density pattern is imposed on the model, the ddd-wave pairing vertex is significantly enhanced. We attribute this enhancement to an increase in antiferromagnetic order which is caused by the appearance of more nearly half-filled regions when the doped holes are confined to the stripes. We also observe a \ensuremathπ\ensuremath{\pi}\ensuremathπ-phase shift in the magnetic order.
Recent experimental results of angle-resolved photoemission spectroscopy suggested that an additional strong nearest neighbor attraction in the Hubbard model might be significant for the doped cuprates. The stripe-ordered patterns, which are formed by the inhomogeneous distribution of spin, charge, and pairing correlations in CuO2{\mathrm{CuO}}_{2}CuO2​ planes, are a well-known feature of the doped cuprates. By employing constrained path quantum Monte Carlo, we examine the effect of the nearest neighbor attraction on a two-dimensional repulsive Hubbard model. Within and across the stripe regions, the ground-state spin correlations and the ddd-wave pairing correlation are calculated. We found that the spin-spin correlation is the largest when the interstripe region is nearly half filled, and we also found the ddd-wave superconducting correlation of the neighboring sites is enhanced in the presence of the stripe pattern. This reveals the crucial effects of the strong nearest neighbor attraction on superconductivity in doped cuprates.
While the stripe phase has been observed not only in monolayer cuprates but also in bilayer cuprates, research on its behavior in bilayer cuprates has been limited. Using constrained path quantum Monte Carlo, we explore the effect of stripes on the bilayer square lattice. We find the system exhibits short-range antiferromagnetism, which is enhanced by stripes and is strongest when the electron density of the interstriped rows reaches half-filling. The hole doping concentration plays a crucial role in the interaction between stripes and superconductivity. The ddd-wave pairing is enhanced by stripe potential V0{V}_{0}V0​ at the hole doping ${\ensuremath{\delta}}_{h}=1/4$, whereas it is suppressed by stripe potential V0{V}_{0}V0​ at the hole doping ${\ensuremath{\delta}}_{h}=1/8$. We elucidate this phenomenon through an analysis of the magnetism of the interstriped rows. Furthermore, the effective ddd-wave pairing is stronger in the bilayer model compared to the monolayer model when stripes are introduced on the square lattice. Overall, our unbiased numerical simulations provide a further understanding of the crossed bilayer square lattice model.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near 1/81/81/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/51/51/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.
Determinant quantum Monte Carlo (DQMC) is used to determine the pairing and magnetic response for a Hubbard model built up from four-site clusters---a two-dimensional square lattice consisting of elemental $2\ifmmode\times\else\texttimes\fi{}2$ plaquettes with hopping ttt and on-site repulsion UUU coupled by an interplaquette hopping ${t}^{\ensuremath{'}}\ensuremath{\le}t$. Superconductivity in this geometry has previously been studied by a variety of analytic and numeric methods, with differing conclusions concerning whether the pairing correlations and transition temperature are raised near half filling by the inhomogeneous hopping or not. For U/t=4U/t=4U/t=4, DQMC indicates an optimal ${t}^{\ensuremath{'}}/t\ensuremath{\approx}0.4$ at which the pairing vertex is most attractive. The optimal ${t}^{\ensuremath{'}}/t$ increases with U/tU/tU/t. We then contrast our results for this plaquette model with a hamiltonian which instead involves a regular pattern of site energies whose large site energy limit is the three-band CuO2{\mathrm{CuO}}_{2}CuO2​ model; we show that there the inhomogeneity rapidly, and monotonically, suppresses pairing.
We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density and pair field, of the mean-field ground state of the t-J model. It leads to the stripe patterns we have found numerically in a generalized t-J-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust d-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valence-bond (AF-RVB) stripes shown by the well-known Yamada plot. On the other hand, due to a long-range AF order in electron-doped materials, a stripe structure with the "in-phase" magnetic domain (IPMD) is obtained in the underdoped regime instead of the AF-RVB stripe. The IPMD stripe with the largest period permitted by lattice size is stabilized near the underdoped region and it excludes the Yamada plot from electron-doped cases. Based on finite lattice size to which we can reach, the existence of IPMD stripes may imply an electronic phase separation into an electron-rich and an insulating half-filled AF long-range ordered domains in electron-doped compounds.
We carry out the variational Monte Carlo calculation to examine spatially inhomogeneous states in hole- and electron-doped cuprates. By using Gutzwiller approximation, we consider the excitations, arising from charge density, spin density, and pair field, of the mean-field ground state of the ttt-JJJ model. It leads to the stripe patterns we have found numerically in a generalized ttt-JJJ-type model including mass renormalization from the electron-phonon coupling. In the hole-doped side, a robust ddd-wave superconducting order results in the formation of the half-doped antiferromagnetic resonating-valence-bond (AF-RVB) stripes shown by the well-known Yamada plot. On the other hand, due to a long-range AF order in electron-doped materials, a stripe structure with the ``in-phase'' magnetic domain (IPMD) is obtained in the underdoped regime instead of the AF-RVB stripe. The IPMD stripe with the largest period permitted by lattice size is stabilized near the underdoped region and it excludes the Yamada plot from electron-doped cases. Based on finite lattice size to which we can reach, the existence of IPMD stripes may imply an electronic phase separation into an electron-rich and an insulating half-filled AF long-range ordered domains in electron-doped compounds.