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arXiv:2405.08438 · Physical review. B./Physical review. B

Magnetic fluctuations and dominant superconducting pairing symmetry near the tunable Van Hove singularity

Xiaohan Kong, Boyang Wen, Kaiyi Guo, Ying Liang, Tianxing Ma

Published May 14, 2024• 1 citation
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Abstract

We have investigated the magnetism and pairing correlations of the triangular lattice based on the Hubbard model using the determinant quantum Monte Carlo method and the constrained path Monte Carlo. The results show that the presence of the next-nearest-neighbor hopping integral ${t}^{\ensuremath{'}}$ introduces an additional energy scale to the system, and through ${t}^{\ensuremath{'}}$, one can regulate the shape of the density of states and thus the position of the van Hove singularity point. Increasing inverse temperature $\ensuremath{\beta}$ and on-site interaction $U$ favor the formation of ferromagnetic correlation in a rather large filling region, and the calculations for different lattice sizes show that the range of the ferromagnetic correlations is smaller than the smallest lattice simulated at the investigated temperatures. We study the different pairing correlations of the triangular lattice near several typical fillings and show that the $f$-wave pairing dominates the system in the filling region near the van Hove singularity point with a high density of states, where the ferromagnetic correlation is also enhanced. When the filling is close to half-filling, the pairing susceptibility with $f$ wave is suppressed and the pairing susceptibility of ${f}_{n}$ wave is enhanced, however, both the effective pairing interaction with $f$ wave and ${f}_{n}$ wave are negative, which indicates that neither $f$-wave nor ${f}_{n}$-wave superconductivity may exist. Finally, we find that the pairing channel of different symmetry in the system maybe closely related to the magnetic properties. Ferromagnetic fluctuation favors the formation of $f$-wave pairing, while antiferromagnetic fluctuation tends to promote ${f}_{n}$-wave pairing.

DOI
10.1103/physrevb.109.205133

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We have investigated the magnetism and pairing correlations of the triangular lattice based on the Hubbard model using the determinant quantum Monte Carlo method and the constrained path Monte Carlo. The results show that the presence of the next-nearest-neighbor hopping integral t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′ introduces an additional energy scale to the system, and through t\ensuremath′{t}^{\ensuremath{'}}t\ensuremath′, one can regulate the shape of the density of states and thus the position of the van Hove singularity point. Increasing inverse temperature \ensuremathβ\ensuremath{\beta}\ensuremathβ and on-site interaction UUU favor the formation of ferromagnetic correlation in a rather large filling region, and the calculations for different lattice sizes show that the range of the ferromagnetic correlations is smaller than the smallest lattice simulated at the investigated temperatures. We study the different pairing correlations of the triangular lattice near several typical fillings and show that the fff-wave pairing dominates the system in the filling region near the van Hove singularity point with a high density of states, where the ferromagnetic correlation is also enhanced. When the filling is close to half-filling, the pairing susceptibility with fff wave is suppressed and the pairing susceptibility of fn{f}_{n}fn​ wave is enhanced, however, both the effective pairing interaction with fff wave and fn{f}_{n}fn​ wave are negative, which indicates that neither fff-wave nor fn{f}_{n}fn​-wave superconductivity may exist. Finally, we find that the pairing channel of different symmetry in the system maybe closely related to the magnetic properties. Ferromagnetic fluctuation favors the formation of fff-wave pairing, while antiferromagnetic fluctuation tends to promote fn{f}_{n}fn​-wave pairing.
Abstract We investigate magnetic correlation in the triangular lattice Hubbard model using determinant quantum Monte Carlo simulations. Focusing on the role of next-nearest-neighbor hopping t ′ and electron filling 〈 n 〉, we demonstrate that regions of high density of states, particularly near van Hove singularity (VHS) points, significantly enhance short-range ferromagnetic correlations as measured by the uniform spin susceptibility χ (Γ). Specifically, χ (Γ), quantifying ferromagnetic fluctuations, is amplified at fillings corresponding to the VHS for a given t ′ . Increasing the on-site Coulomb repulsion U further strengthens these ferromagnetic correlations, with a more pronounced effect at lower temperatures, and the observed ferromagnetic correlations are found to be short-ranged. Conversely, near half-filling 〈 n 〉 = 1.0, larger t ′ values promote antiferromagnetic (AFM) fluctuations, evidenced by an increase in χ ( K ). Our results reveal that t ′ and filling act as effective tuning parameters for manipulating the competition between ferromagnetic and AFM fluctuations in the triangular lattice.
We perform a numerical study using both determinantal and constrain path Monte Carlo methods to investigate the magnetic and pairing properties of the single-band Hubbard model on the triangular lattice. We find that the system in the filling region ⟨n⟩=1.5−−1.85⟨n⟩=1.5--1.85⟨n⟩=1.5−−1.85 shows a short-ranged ferromagnetic correlation, and the on-site Coulomb interaction tends to strengthen ferromagnetic fluctuation slightly. It is shown that the large density of states near the Van Hove singularity point plays an important role in the enhancement of ferromagnetic fluctuation. In the ferromagnetic region, we observe that the fff-wave pairing correlation tends to increase faster than other pairing correlations. However, it is subtle to stabilize the fff-wave pairing since the effective pairing interaction was found to be very small.
A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$=-0.35t as a model for high-temperature superconductors. Magnetic properties are analyzed using the two-particle self-consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite ${\mathit{t}}^{\ensuremath{'}}$ and at ${\mathit{t}}^{\ensuremath{'}}$=0 but for two totally different physical reasons. When ${\mathit{t}}^{\ensuremath{'}}$=0, it is induced by antiferromagnetic correlations while at ${\mathit{t}}^{\ensuremath{'}}$=-0.35t it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with T-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the d-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.
We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2{t}_{2}t2​) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t2{t}_{2}t2​\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.
We use a novel temperature-flow renormalization group technique to analyze magnetic and superconducting instabilities in the two-dimensional ${t\ensuremath{-}t}^{\ensuremath{'}}$ Hubbard model for particle densities close to the Van Hove filling as a function of the next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$. In the one-loop flow at the Van Hove filling, the characteristic temperature for the flow to strong coupling is suppressed drastically around ${t}_{c}^{\ensuremath{'}}\ensuremath{\approx}\ensuremath{-}0.33t$, suggesting a quantum critical point between ddd-wave pairing at moderate ${t}^{\ensuremath{'}}>{t}_{c}^{\ensuremath{'}}$ and ferromagnetism for ${t}^{\ensuremath{'}}<{t}_{c}^{\ensuremath{'}}$. Upon increasing the particle density in the latter regime, the leading instability occurs in the triplet pairing channel.
A quantum critical point is found in the phase diagram of the two-dimensional Hubbard model [Vidhyadhiraja et al., Phys. Rev. Lett. 102, 206407 (2009)]. It is due to the vanishing of the critical temperature associated with a phase-separation transition, and it separates the non-Fermi-liquid region from the Fermi liquid. Near the quantum critical point, the pairing is enhanced since the real part of the bare ddd-wave pairing susceptibility exhibits an algebraic divergence with decreasing temperature, replacing the logarithmic divergence found in a Fermi liquid [Yang et al., Phys. Rev. Lett. 106, 047004 (2011)]. In this paper, we explore the single-particle and transport properties near the quantum critical point using high-quality estimates of the self-energy obtained by direct analytic continuation of the self-energy from the continuous-time quantum Monte Carlo method. We focus mainly on a van Hove singularity coming from the relatively flat dispersion that crosses the Fermi level near the quantum critical filling. The flat part of the dispersion orthogonal to the antinodal direction remains pinned near the Fermi level for a range of doping that increases when we include a negative next-near-neighbor hopping ${t}^{\ensuremath{'}}$ in the model. For comparison, we calculate the bare ddd-wave pairing susceptibility for noninteracting models with the usual two-dimensional tight-binding dispersion and a hypothetical quartic dispersion. We find that neither model yields a van Hove singularity that completely describes the critical algebraic behavior of the bare ddd-wave pairing susceptibility found in the numerical data. The resistivity, thermal conductivity, thermopower, and the Wiedemann-Franz law are examined in the Fermi liquid, marginal Fermi liquid, and pseudogap doping regions. A negative next-near-neighbor hopping ${t}^{\ensuremath{'}}$ increases the doping region with marginal Fermi liquid character. Both TTT and negative ${t}^{\ensuremath{'}}$ are relevant variables for the quantum critical point, and both the transport and the displacement of the van Hove singularity with filling suggest that they are qualitatively similar in their effect.