Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2303.04004

Universal approach to p-wave triplet superconductivity in the Hubbard models

Wanpeng Han, Xingchuan Zhu, Shiping Feng, Huaiming Guo

Published Mar 7, 2023• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2303.04004

Related papers

Spin-triplet f-wave pairing via cyclic exchange in the anisotropic triangular Hubbard model: A route to unconventional superconductivity

Satoshi Nishimoto, Y. Ohta

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.

Physica C Superconductivity•May 29, 2025•0 citations

Strongly correlated electrons on the honeycombb lattice: magnetism and superconductivity

F. G. Ribeiro

In view of quite recent experimental activities on magnetic and superconducting properties of honeycomb and hexagonal lattice based materials, in this thesis we have used field-theoretic and many-body methods to investigate magnetic and superconducting properties of the large-U Hubbard model on the honeycomb lattice at half-filling and in the hole-doped regime. Within the framework of a functional-integral approach, we obtain the Lagrangian density associated with the charge (Grassmann fields) and spin [SU(2) gauge fields] degrees of freedom. The Hamiltonian related to the charge degrees of freedom is exactly diagonalized. In the strong-coupling regime, we derive a perturbative low-energy theory suitable to describe the (quantum) magnetic and superconducting phases at half-filling and in the hole-doped regime. At half-filling, we deal with the underlying spin degrees of freedom of the quantum antiferromagnetic (AF) Heisenberg model by employing a second-order spin-wave analysis, in which case we have calculated the ground-state energy and the staggered magnetization; the results are in very good agreement with previous studies. Further, in the continuum, we derive a nonlinear σ-model with a topological Hopf term that describes the AF-VBS (valence bond solid) competition. In the challenging hole-doped regime, our approach allows the derivation of a t-J Hamiltonian, and the analysis of the role played by charge and spin quantum fluctuations on the ground-state energy and, particularly, on the breakdown of the AF order at a critical hole doping; the results are benchmarked against recent Grassmann tensor product state simulations. In addition, we have performed an extensive study of the electronic structure of the doped system for each competing phase: AF, ferromagnetic (FM), and (spin-singlet pairing) s-, dx₂₋ʏ₂ – and idxʏ -wave superconducting (SC) state induced by purely electronic effects. In this context, an energetic analysis of the ground state of these phases reveal that the AF order prevails for low hole doping, while a dominantly chiral dx₂₋ʏ₂ + idxʏ superconducting state was found in the vicinity of the Van Hove singularity (high hole doping). We also stress that a thermodynamic analysis of the superconducting phase shows that the critical temperature is directly related to the exchange constant J = 4t²/U, in which t denotes the hopping amplitude and U the on-site Coulomb repulsion of the Hubbard model (purely electronic origin). Remarkably, the competition between the AF and dx₂₋ʏ₂ + idxʏ SC phases takes place by the occurrence of a first-order transition accompanied by a spatial phase separation of the referred phases.

•Aug 28, 2015•0 citations

Quantum simulations on square and triangular Hubbard models

Kuang-Shing Chen

In this thesis we try to understand the unconventional superconducting mechanism on cuprates and organic superconductors (or sodium cobaltates) which can be modeled by a two-dimensional square- and triangular-lattice Hubbard model respectively. The formation of the superconducting dome requires explanations of feasible scenarios. Generally speaking, pairing strength is provided by magnetic fl_x001D_uctuations in the strongly correlated region and the structure of the Fermi surface in this region will favor superconducting pairings with a certain type of symmetry. For the cuprate physics, a superconducting dome composed of d-wave pairings has been identified experimentally. We study the Hubbard model on square lattices and _x001C_find that the pairing strength is originated from anti-ferromagnetic instabilities, and the nearly nested Fermi surface with the square symmetry further supports the d-wave pairing. Moreover, our results show there is a quantum critical point (QCP) beneath the superconducting dome. The QCP is a zero-temperature instability which separates the Fermi liquid and pseudogap regions and exhibits the quantum _x001D_fluctuations which may lead to a high superconducting transition temperature. Above the QCP, a V-shape marginal Fermi liquid region associated with the quantum critical phenomena is also identi_x001C_fied. Using next-nearest-neighbor hopping, chemical potential, and temperature as control parameters, there is a line of Lifshitz transition associated with the change of topology of the Fermi surface. Along the Lifshitz line with t'<=0, the marginal Fermi liquid region prevails, the peak of density of states crosses the Fermi level, and the bare d-wave pairing susceptibility shows a universal scaling with the exponent consistent with theoretical proposals. For the triangular-lattice Hubbard model in the strongly correlated region, we _x001C_find a d+id superconducting pairing on the hole-doped side of the phase diagram. Here the pairing strength comes from the instabilities of the anti-ferromagnetic order (120-degree-spin structure), and the nested hexagon-deformed Fermi surface with the triangular symmetry further boosts the d+id symmetry. Due to the strong competition between electronic interactions and geometric frustrations, the superconductivity and other novel features of the system equal to or above half fi_x001C_lling requires future studies. The numerical tool we apply to study these systems is the dynamical cluster approximation with continuous-time quantum Monte Carlo as the solver. Our approach includes nonlocal correlations embedded in a mean _x001C_field host and is a most up-to-date and reliable approach in dealing with the above mentioned strongly correlated systems valid in the thermodynamic limit. Our _x001C_findings shine light on future investigations of the nature

Civil War Book Review•Jun 17, 2013•0 citations

Singlet, triplet, and pair density wave superconductivity in the doped triangular-lattice moiré system

Feng Chen, D. N. Sheng

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 $d$-wave and a subdominant triplet $p$-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.

arXiv:2302.06765•Physical review. B./Physical review. B•Nov 13, 2023•21 citations

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

Satoshi Nishimoto, Y. Ohta

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$.

arXiv:0810.3387•Oct 19, 2008•0 citations

Spin-triplet superconductivity in repulsive Hubbard models with disconnected Fermi surfaces: A case study on triangular and honeycomb lattices

Kazuhiko Kuroki, Ryotaro Arita

We propose that spin-fluctuation-mediated spin-triplet superconductivity may be realized in repulsive Hubbard models with disconnected Fermi surfaces. The idea is confirmed for Hubbard models on triangular (dilute band filling) and honeycomb (near half-filling) lattices using fluctuation exchange approximation, where triplet pairing order parameter with $f\ensuremath{-}\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}$ symmetry is obtained. Possible relevance to real materials is suggested.

arXiv:cond-mat/0004381•Physical review. B, Condensed matter•Apr 6, 2001•44 citations
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.
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.
In view of quite recent experimental activities on magnetic and superconducting properties of honeycomb and hexagonal lattice based materials, in this thesis we have used field-theoretic and many-body methods to investigate magnetic and superconducting properties of the large-U Hubbard model on the honeycomb lattice at half-filling and in the hole-doped regime. Within the framework of a functional-integral approach, we obtain the Lagrangian density associated with the charge (Grassmann fields) and spin [SU(2) gauge fields] degrees of freedom. The Hamiltonian related to the charge degrees of freedom is exactly diagonalized. In the strong-coupling regime, we derive a perturbative low-energy theory suitable to describe the (quantum) magnetic and superconducting phases at half-filling and in the hole-doped regime. At half-filling, we deal with the underlying spin degrees of freedom of the quantum antiferromagnetic (AF) Heisenberg model by employing a second-order spin-wave analysis, in which case we have calculated the ground-state energy and the staggered magnetization; the results are in very good agreement with previous studies. Further, in the continuum, we derive a nonlinear σ-model with a topological Hopf term that describes the AF-VBS (valence bond solid) competition. In the challenging hole-doped regime, our approach allows the derivation of a t-J Hamiltonian, and the analysis of the role played by charge and spin quantum fluctuations on the ground-state energy and, particularly, on the breakdown of the AF order at a critical hole doping; the results are benchmarked against recent Grassmann tensor product state simulations. In addition, we have performed an extensive study of the electronic structure of the doped system for each competing phase: AF, ferromagnetic (FM), and (spin-singlet pairing) s-, dx₂₋ʏ₂ – and idxʏ -wave superconducting (SC) state induced by purely electronic effects. In this context, an energetic analysis of the ground state of these phases reveal that the AF order prevails for low hole doping, while a dominantly chiral dx₂₋ʏ₂ + idxʏ superconducting state was found in the vicinity of the Van Hove singularity (high hole doping). We also stress that a thermodynamic analysis of the superconducting phase shows that the critical temperature is directly related to the exchange constant J = 4t²/U, in which t denotes the hopping amplitude and U the on-site Coulomb repulsion of the Hubbard model (purely electronic origin). Remarkably, the competition between the AF and dx₂₋ʏ₂ + idxʏ SC phases takes place by the occurrence of a first-order transition accompanied by a spatial phase separation of the referred phases.
In this thesis we try to understand the unconventional superconducting mechanism on cuprates and organic superconductors (or sodium cobaltates) which can be modeled by a two-dimensional square- and triangular-lattice Hubbard model respectively. The formation of the superconducting dome requires explanations of feasible scenarios. Generally speaking, pairing strength is provided by magnetic fl_x001D_uctuations in the strongly correlated region and the structure of the Fermi surface in this region will favor superconducting pairings with a certain type of symmetry. For the cuprate physics, a superconducting dome composed of d-wave pairings has been identified experimentally. We study the Hubbard model on square lattices and _x001C_find that the pairing strength is originated from anti-ferromagnetic instabilities, and the nearly nested Fermi surface with the square symmetry further supports the d-wave pairing. Moreover, our results show there is a quantum critical point (QCP) beneath the superconducting dome. The QCP is a zero-temperature instability which separates the Fermi liquid and pseudogap regions and exhibits the quantum _x001D_fluctuations which may lead to a high superconducting transition temperature. Above the QCP, a V-shape marginal Fermi liquid region associated with the quantum critical phenomena is also identi_x001C_fied. Using next-nearest-neighbor hopping, chemical potential, and temperature as control parameters, there is a line of Lifshitz transition associated with the change of topology of the Fermi surface. Along the Lifshitz line with t'<=0, the marginal Fermi liquid region prevails, the peak of density of states crosses the Fermi level, and the bare d-wave pairing susceptibility shows a universal scaling with the exponent consistent with theoretical proposals. For the triangular-lattice Hubbard model in the strongly correlated region, we _x001C_find a d+id superconducting pairing on the hole-doped side of the phase diagram. Here the pairing strength comes from the instabilities of the anti-ferromagnetic order (120-degree-spin structure), and the nested hexagon-deformed Fermi surface with the triangular symmetry further boosts the d+id symmetry. Due to the strong competition between electronic interactions and geometric frustrations, the superconductivity and other novel features of the system equal to or above half fi_x001C_lling requires future studies. The numerical tool we apply to study these systems is the dynamical cluster approximation with continuous-time quantum Monte Carlo as the solver. Our approach includes nonlocal correlations embedded in a mean _x001C_field host and is a most up-to-date and reliable approach in dealing with the above mentioned strongly correlated systems valid in the thermodynamic limit. Our _x001C_findings shine light on future investigations of the nature
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.
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 propose that spin-fluctuation-mediated spin-triplet superconductivity may be realized in repulsive Hubbard models with disconnected Fermi surfaces. The idea is confirmed for Hubbard models on triangular (dilute band filling) and honeycomb (near half-filling) lattices using fluctuation exchange approximation, where triplet pairing order parameter with $f\ensuremath{-}\mathrm{w}\mathrm{a}\mathrm{v}\mathrm{e}$ symmetry is obtained. Possible relevance to real materials is suggested.