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arXiv:0810.3387

Spin-triplet f-wave pairing due to three-site cyclic-exchange ferromagnetic interactions

Satoshi Nishimoto, Y. Ohta

Published Oct 19, 2008• 0 citations
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Abstract

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)$_2$X, cobalt oxide Na$_{0.35}$CoO$_2$$\cdot$1.3H$_2$O, and layered perovskite Sr$_2$RuO$_4$.

DOI
10.48550/arxiv.0810.3387

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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​CoO_2$$\cdot1.3H2_22​O, and layered perovskite Sr2_22​RuO4_44​.
We investigate the interplay between ferromagnetism and unconventional superconductivity in a two-dimensional anisotropic triangular-lattice Hubbard model using the density-matrix renormalization group (DMRG) method. A novel mechanism for spin-triplet f -wave superconductivity is identified, driven by three-site cyclic-exchange interactions. This mechanism highlights the crucial role of lattice anisotropy and triangular hopping networks in stabilizing ferromagnetic correlations necessary for spin-triplet pairing. The slow decay of pair-correlation functions and their sign change under a π / 3 rotation confirm the dominant f -wave symmetry of the superconducting state. These findings offer a unified theoretical framework for understanding unconventional superconductivity in strongly correlated electron systems, with potential relevance to materials such as Bechgaard salts ( TMTSF ) 2 X , cobalt oxide Na 0 . 35 CoO 2 ⋅ 1 . 3 H 2 O , and layered perovskite Sr 2 RuO 4 . • Identifies a mechanism for spin-triplet superconductivity via three-site cyclic exchange. • Demonstrates f -wave pairing symmetry in a triangular-lattice Hubbard model. • Shows lattice anisotropy promotes ferromagnetism that stabilizes triplet pairing.
Spin-triplet superconductivity is actively pursued in condensed matter physics due to the potential applications in topological quantum computations. The related pairing mechanism involving the interaction remains an important research topic. Here we propose a universal approach to obtain p-wave triplet superconductivity in the Hubbard models by simply changing the sign of the hopping amplitudes of the spin-down electrons, and apply it to three prototype two-dimensional lattices (honeycomb, square, and triangular). The parent Hamiltonian at half filling has long-range magnetic order, which is ferromagnetic in all three directions for the frustrated triangular lattices, and ferromagnetic (antiferromagnetic) in the xy plane (z direction) for the bipartite honeycomb and square lattices. The magnetic transitions occur at some critical interactions on honeycomb and triangular lattices, which are estimated by finite-size scalings. When the systems are doped, we find the triplet p-wave pairing is a dominating superconducting instability. We demonstrate its emergence is closely related to the strong ferromagnetic spin fluctuations induced by the doping. Our results provide an understanding of the microscopical triplet-pairing mechanism, and will be helpful in the search for spin-triplet superconducting materials.
Recent experimental progress has established the twisted bilayer transition metal dichalcogenide (TMD) as a highly tunable platform for studying many-body physics. Particularly, the homobilayer TMDs under displacement field are believed to be described by a generalized triangular-lattice Hubbard model with a spin-dependent hopping phase $\ensuremath{\theta}$. To explore the effects of $\ensuremath{\theta}$ on the system, we perform density matrix renormalization group calculations for the relevant triangular lattice t-J model. By changing $\ensuremath{\theta}$ at small hole doping, we obtain a region of quasi-long-range superconducting order coexisting with charge and spin density wave within $0<\ensuremath{\theta}<\ensuremath{\pi}/3$. The superconductivity is composed of a dominant spin singlet ddd-wave and a subdominant triplet ppp-wave pairing. Intriguingly, the ${S}_{z}=\ifmmode\pm\else\textpm\fi{}1$ triplet pairing components feature pair-density waves. In addition, we find a region of triplet superconductivity coexisting with charge-density wave and ferromagnetism within $\ensuremath{\pi}/3<\ensuremath{\theta}<2\ensuremath{\pi}/3$, which is related to the former phase at smaller $\ensuremath{\theta}$ by a combined operation of spin-flip and gauge transformation. Our findings provide insights and directions for experimental search for exotic superconductivity in twisted TMD systems.
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To shed light into the pairing mechanism of possible spin triplet superconductors (TMTSF)2X{(\text{TMTSF})}_{2}X(TMTSF)2​X and Sr2RuO4{\text{Sr}}_{2}{\text{RuO}}_{4}Sr2​RuO4​, 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 (TMTSF)2X{(\text{TMTSF})}_{2}X(TMTSF)2​X by a quarter-filled quasi-one-dimensional (quasi-1D) Hubbard model, and the $\ensuremath{\gamma}$ band of Sr2RuO4{\text{Sr}}_{2}{\text{RuO}}_{4}Sr2​RuO4​ 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 fff-wave pairing not only dominates over the triplet ppp wave in agreement with the spin fluctuation theory, but also looks unexpectedly competitive against ddd waves. For the 2D system, although the results suggest the presence of an attractive interaction in the triplet pairing channels, the ddd-wave pairing interaction is found to be larger than those of the triplet channels.
With the discovery of strong-coupling physics and superconductivity in moir\'e superlattices, it is essential to have an understanding of strong-coupling driven superconductivity in systems with trigonal symmetry. The simplest lattice model with trigonal symmetry is the triangular lattice Hubbard model. Although the triangular lattice spin model is a heavily studied model in the context of frustration, studies of the hole-doped triangular lattice Hubbard model are rare. Here, we use density matrix renormalization group to investigate the dominant superconducting channels in the hole-doped triangular lattice Hubbard model over a range of repulsive interaction strengths. We find a clear transition from ppp-wave superconductivity at a moderate on-site repulsion strength (U/t=2U/t=2U/t=2) at filling above 1/4 ($n\ensuremath{\sim}0.65$) to ddd-wave superconductivity at a strong on-site repulsion strength (U/t=10U/t=10U/t=10) at filling below 1/4 ($n\ensuremath{\sim}0.4$). The unusual tunability that moir\'e superlattices offer in controlling U/tU/tU/t would open up the opportunity to realize this transition between ddd-wave and ppp-wave superconductivity.