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arXiv:cond-mat/0307553 · Physical Review B

Quantum Monte Carlo study of the pairing symmetry competition in the Hubbard model

Kazuhiko Kuroki, Yukio Tanaka, T. Kimura, Ryotaro Arita

Published Jun 18, 2004• 31 citations
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Abstract

To shed light into the pairing mechanism of possible spin triplet superconductors ${(\text{TMTSF})}_{2}X$ and ${\text{Sr}}_{2}{\text{RuO}}_{4}$, we study the competition among various spin singlet and triplet pairing channels in the Hubbard model by calculating the pairing interaction vertex using the ground state quantum Monte Carlo technique. We model ${(\text{TMTSF})}_{2}X$ by a quarter-filled quasi-one-dimensional (quasi-1D) Hubbard model, and the $\ensuremath{\gamma}$ band of ${\text{Sr}}_{2}{\text{RuO}}_{4}$ by a two-dimensional (2D) Hubbard model with a band filling of $\ensuremath{\sim}4∕3$. For the quasi-1D system, we find that triplet $f$-wave pairing not only dominates over the triplet $p$ wave in agreement with the spin fluctuation theory, but also looks unexpectedly competitive against $d$ waves. For the 2D system, although the results suggest the presence of an attractive interaction in the triplet pairing channels, the $d$-wave pairing interaction is found to be larger than those of the triplet channels.

DOI
10.1103/physrevb.69.214511

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The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while B1g{B}_{1g}B1g​ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) and B2g{B}_{2g}B2g​ (dxy{d}_{xy}dxy​) pairing dominates in the absence of repulsive longer-range Coulomb interactions VNN{V}_{\mathrm{NN}}VNN​, the latter induces pairing in other symmetry channels, including, e.g., A2g{A}_{2g}A2g​ (ggg-wave), nodal A1g{A}_{1g}A1g​ (extended sss-wave), or nodal Eu{E}_{u}Eu​ (ppp-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction, VNN<0{V}_{\mathrm{NN}}<0VNN​<0, on the superconducting gap structure. Depending on the electronic filling, such an attraction boosts Eu{E}_{u}Eu​ (ppp-wave) spin-triplet or B1g{B}_{1g}B1g​ (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) spin-singlet ordering.
Phase boundary between spin singlet and triplet superconductivity in the extended Hubbard model with exchange interaction on a square lattice is calculated within meanfield approximation. Basically, antiferromagnetic exchange interaction J is advantageous for the singlet pairing, while ferromagnetic J prefers the triplet pairing. When off-site interaction V is repulsive, the singlet phase and the triplet phase are separated by normal state in the phase diagram against V and J . If V is effectively attractive, however, the singlet and triplet states can compete against each other. We calculate the phase boundary between singlet and triplet phase for various band filling. It is shown that the triplet phase penetrates rather deeply into antiferromagnetic exchange regime for lower band filling, whereas the penetration of the singlet phase is confined in a narrow range of ferromagnetic exchange regime.
Ferromagnetiam and superconductivity in a two-dimensional triangular-lattice Hubbard model are studied using the density-matrix renormalization group method. We propose a mechanism of the {\it f}-wave spin-triplet pairing derived from the three-site cyclic-exchange ferromagnetic interactions. We point out that a triangular network of hopping integrals, which is required for the three-site cyclic hopping processes, is contained in the (possibly) spin-triplet superconducting systems, such as Bechgaard salts (TMTSF)2_22​X, cobalt oxide Na0.35_{0.35}0.35​CoO2_22​$\cdot1.3H1.3H1.3H_2O,andlayeredperovskiteSrO, and layered perovskite SrO,andlayeredperovskiteSr_2RuORuORuO_4$.
We study the spin-fluctuation-mediated superconducting pairing gap in a weak-coupling approach to the Hubbard model for a two-dimensional square lattice in the paramagnetic state. Performing a comprehensive theoretical study of the phase diagram as a function of filling, we find that the superconducting gap exhibits transitions from ppp-wave at very low electron fillings to ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave symmetry close to half filling in agreement with previous reports. At intermediate filling levels, different gap symmetries appear as a consequence of the changes in the Fermi surface topology and the associated structure of the spin susceptibility. In particular, the vicinity of a Van Hove singularity in the electronic structure close to the Fermi level has important consequences for the gap structure in favoring the otherwise subdominant triplet solution over the singlet ddd-wave solution. By solving the full gap equation, we find that the energetically favorable triplet solutions are chiral and break time-reversal symmetry. Finally, we also calculate the detailed angular gap structure of the quasiparticle spectrum, and show how spin-fluctuation-mediated pairing leads to significant deviations from the first harmonics both in the singlet ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ gap as well as the chiral triplet gap solution.
We study the effect of the nearest neighbor anisotropic exchange interaction on superconductivity in extended Hubbard model in a square lattice. This Hamiltonian is one of a base model to describe various effects on triplet superconductors, e.g. Sr 2 RuO 4 , because the ferromagnetic exchange is advantagous for triplet pairing. Within a one-band meanfield approximation, we calculate the critical temperatures of spin singlet and triplet superconductivity. We obtain a phase diagram in the longitudinal vs transverse exchange couplings and we show how the stable pairing state is controlled by the anisotropy of the exchange interaction.