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arXiv:1303.7468 · Physical Review B

Unconventional superconducting phases for the two-dimensional extended Hubbard model on a square lattice

Wen-Min Huang, Chen-Yen Lai, Chuntai Shi, Shan-Wen Tsai

Published Aug 12, 2013• 23 citations
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Abstract

We study the phase diagram of the extended Hubbard model on a two-dimensional square lattice, including on-site ($U$) and nearest-neighbor ($V$) interactions, at weak couplings. We show that the charge-density wave phase that is known to occur at half filling when $4V>U$ gives way to a ${d}_{xy}$-wave superconducting instability away from half filling, when the Fermi surface is not perfectly nested, and for sufficiently large repulsive $V$ and a range of on-site repulsive interaction $U$. In addition, when nesting is further suppressed and in the presence of a nearest-neighbor attraction, a triplet time-reversal breaking $({p}_{x}+i{p}_{y})$-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 $({p}_{x}+i{p}_{y})$-wave superconducting phase dominates in the whole regime of on-site repulsions and nearest-neighbor attractions, while ${d}_{xy}$ 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.

DOI
10.1103/physrevb.88.054504

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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 dx2\ensuremath−y2{d}_{{x}^{2}\ensuremath{-}{y}^{2}}dx2\ensuremath−y2​ 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.
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The two-dimensional (2D) Hubbard model is widely believed to contain the key ingredients of high-temperature superconductivity in cuprate materials. Here, we report a constrained path quantum Monte Carlo (CPQMC) study of the square-lattice extended Hubbard model with on-site Coulomb repulsion U and nearest-neighbor (NN) electron attraction V. Upon doping δδδ= 0.125, we find that the NN electron attraction V can notably drive an exotic spin-triplet (p-wave) superconducting (SC) phase, and enhance the p-wave SC correlations with the increase of V. But in the intermediate coupling regime, the dx2−y2d_{x^2-y^2}dx2−y2​-wave (d-wave) does not significantly increase with the increase of V, indicating that the d-wave is not affected by V in strongly correlated system. Besides the pairing phase, a spin density wave (SDW) only exists near the half-filling in the particle-hole channel, and doping disrupts the formation of SDW order. Especially, the NN electron attraction V has no significant effect on SDW, reflecting the consistent relationship between d-wave SC and spin correlation. Moreover, as doping increases, the dominant region of p-wave also expands, further suppressing the presence of d-wave, which may help explain the disappearance of d-wave SC in overdoped cuprate superconductors. We also find the d-wave exhibits a singular nonzero (near point (2π/3,π2π/3, π2π/3,π)) condensation structure in momentum space, resulting in a different staggered behavior in the x and y direction with distance in real space. On the contrary, the p-wave condensed at zero momentum, and the p-wave correlation exhibits exponential decay in real space. Our work suggests the p-wave SC region can be induced and further broadened by the NN electron attraction V, offering a feasible mechanism to realize p-wave superconductivity in realistic cuprate materials.
Motivated by recent experimental realization of the tunability of many-body interactions in ultracold fermionic gases trapped in optical lattices, we investigate analytically effects of nearest-neighboring diagonal three-body (T) and four-body (F) couplings on the one-dimensional conventional extended Hubbard model with on-site (U) and inter-site (V) interactions. Applying the bosonization and renormalization-group techniques, we present quantum phase diagrams at half filling and in the weak-coupling regime. The result shows that, whether the three-body or four-body effective attraction may give rise to superconducting phases in the region for repulsive U and V. Besides, the four-body coupling can lead to a bond-spin-density-wave phase for F > 0 and a bond-charge-density-wave phase for F < 0.
We investigate the phase diagram of the extended Hubbard model on a half-filled honeycomb lattice through determinant quantum Monte Carlo simulations. At zero temperature, the repulsive Hubbard model undergoes a transition to an antiferromagnetic state only for sufficiently strong on-site coupling UUU. However, the inclusion of a repulsive extended interaction VVV between fermions in nearest-neighbor orbitals induces a charge-ordered phase. For attractive interactions, we also identify superconducting and phase-separated phases. We have determined a complete phase diagram with the aid of structure factors associated with various orderings, combined with measurements of double occupancy and the average sign of fermionic determinants. We have established that the semimetallic phase forms a zone from which ordered phases are excluded, preventing the stabilization of a superconducting phase with ddd-wave symmetry, i.e., only sss-wave pairing is allowed.
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We study density wave instabilities in a doubly degenerate Fermi-Fermi mixture with $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry on a square lattice. For sufficiently large on-site inter-species repulsion, when the two species of fermions are both at half-filling, two conventional (sss wave) number density waves are formed with a $\ensuremath{\pi}$-phase difference between them to minimize the interspecies repulsion. Upon moving one species away from half-filling, an unconventional density wave with dxy{d}_{xy}dxy​-wave symmetry emerges. When both species are away from the vicinity of half-filling, superconducting instabilities dominate. We present results of a functional renormalization-group calculation that maps out the phase diagram at weak couplings. Also, we provide a simple explanation for the emergence of the dxy{d}_{xy}dxy​-density wave phase based on a four-patch model. We find a robust and general mechanism for dxy{d}_{xy}dxy​-density-wave formation that is related to the shape and size of the Fermi surfaces. The density imbalance between the two species of fermions in the vicinity of half-filling leads to a phase-space discrepancy for different interspecies umklapp couplings. Using a phase-space argument for leading corrections in the one-loop renormalization-group approach to fermions, we show that the phase-space discrepancy in our system causes opposite flows for the two leading intraspecies umklapp couplings and that this triggers the dxy{d}_{xy}dxy​-density-wave instability.