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arXiv:cond-mat/0102527 · Physical review. B, Condensed matter

Nearest-neighbor attraction stabilizes staggered currents in the two-dimensional Hubbard model

Tudor D. Stanescu, Philip Phillips

Published Nov 26, 2001• 13 citations
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Abstract

Using a strong-coupling approach, we show that staggered current vorticity does not obtain in the repulsive two-dimensional Hubbard model for large on-site Coulomb interactions, as in the case of the copper oxide superconductors. This trend also persists even when nearest-neighbor repulsions are present. However, staggered flux ordering emerges when attractive nearest-neighbor Coulomb interactions are included. Such ordering opens a gap along the $(\ensuremath{\pi},0)\ensuremath{-}(0,\ensuremath{\pi})$ direction and persists over a reasonable range of doping.

DOI
10.1103/physrevb.64.220509

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An extended multiband Hubbard model of the two-dimensional CuO2{\mathrm{O}}_{2}O2​ planes of high-Tc{T}_{c}Tc​ superconductors is examined by exact diagonalization of the Hamiltonian for small clusters with periodic boundary conditions. Holes are shown to bind in the limit of large Cu-site and nearest-neighbor Cu-O Coulomb repulsion. A simple explanation of the source of the binding energy is given in this strong-coupling limit. The more realistic case of relatively weak nearest-neighbor repulsion is also examined, and suggestive evidence is presented that the effective attraction will also exist in the thermodynamic limit for this case.
We study a three-band extended Hubbard model on a CuO3{\mathrm{CuO}}_{3}CuO3​ system by the density-matrix renormalization group method. Our system has geometry similar to that of a section of the CuO2{\mathrm{CuO}}_{2}CuO2​ plane of the copper-oxide superconductors. We have studied the effects of nearest-neighbor repulsions on the current-current correlations of two model CuO3{\mathrm{CuO}}_{3}CuO3​ systems. We have calculated several types of staggered current correlations as a function of various model parameters such as interaction strengths and filling. We show that repulsive interactions are clearly capable of increasing the magnitude of the current-current correlations in both models studied. The long-distance behavior of the current-current correlations is qualitatively influenced by V. We show that repulsive interactions are capable of enhancing correlations involving at least one copper-oxygen rung over distances comparable to the length of the system. In some cases, V decreases the exponent corresponding to the power-law decay, leading to a considerable slowing down of the long-distance decay of the current-current correlations, compared to that of the Hubbard model.
An exact-diagonalization technique on small clusters is used to study the ground states and single-particle excitations of the Hubbard model with on-site (U) and nearest-neighbor (V) Coulombic repulsive interactions. It is shown that the long-range charge-density-wave state realized in a half-filled two-dimensional square lattice for 4V\ensuremath{\gtrsim}U persists up to quarter filling, and that the doped carriers form a small Fermi surface that encloses an area corresponding to the number of doped carriers rather than the total number of electrons involved in the system. The present result offers a well-defined counterexample in the discussion of the Fermi-surface dimensions of strongly correlated electron systems, and may provide a complementary understanding of the large Fermi surface believed to exist in the ordinary Hubbard model.
We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site (UUU) and nearest-neighbor (VVV) interactions, at weak couplings. We show that the charge-density wave phase that is known to occur at half filling when 4V>U4V>U4V>U gives way to a dxy{d}_{xy}dxy​-wave superconducting instability away from half filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive VVV and a range of on-site repulsive interaction UUU. In addition, when nesting is further suppressed and in the presence of a nearest-neighbor attraction, a triplet time-reversal breaking (px+ipy)({p}_{x}+i{p}_{y})(px​+ipy​)-wave pairing instability emerges, competing with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ pairing state that is known to dominate at fillings just slightly away from half. At even smaller fillings, where the Fermi surface no longer presents any nesting, the (px+ipy)({p}_{x}+i{p}_{y})(px​+ipy​)-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while dxy{d}_{xy}dxy​ pairing occurs in the presence of on-site attraction. Our results suggest that zero-energy Majorana fermions can be realized on a square lattice in the presence of a magnetic field. For a system of cold fermionic atoms on a two-dimensional square optical lattice, both an on-site repulsion and a nearest-neighbor attraction would be required, in addition to rotation of the system to create vortices. We discuss possible ways of experimentally engineering the required interaction terms in a cold atom system.
Dynamic cluster quantum Monte Carlo calculations for a doped two-dimensional extended Hubbard model are used to study the stability and dynamics of ddd-wave pairing when a nearest-neighbor Coulomb repulsion VVV is present in addition to the on-site Coulomb repulsion UUU. We find that ddd-wave pairing and the superconducting transition temperature Tc{T}_{c}Tc​ are only weakly suppressed as long as VVV does not exceed U/2U/2U/2. This stability is traced to the strongly retarded nature of pairing that allows the ddd-wave pairs to minimize the repulsive effect of VVV. When VVV approaches U/2U/2U/2, large momentum charge fluctuations are found to become important and to give rise to a more rapid suppression of ddd-wave pairing and Tc{T}_{c}Tc​ than for smaller VVV.